# Programs for A150000-A199999

List of integer sequences with links to LODA programs.

- A150500 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 1), (0, 1, 0), (1, 1, -1), (1, 1, 1)}
- A151019 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (-1, 0, 0), (1, 1, 0), (1, 1, 1)}
- A151090 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 0), (0, 0, 1), (0, 1, 0), (1, 1, 1)}.
- A151093 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, -1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}
- A151162 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (1, 0, 0), (1, 0, 1), (1, 1, 0)}
- A151241 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (-1, 0, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}
- A151251 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (0, 0, 1), (0, 1, 0), (1, 1, 0), (1, 1, 1)}
- A151253 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (0, 0, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}.
- A151254 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1)}.
- A151281 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (1, 0), (1, 1)}.
- A151282 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), (1, 1)}.
- A151292 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (0, 1), (1, 1)}
- A151312 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (1, -1), (1, 0), (1, 1)}.
- A151318 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, 1), (1, 0), (1, 1)}
- A151323 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), (0, 1), (1, 0), (1, 1)}.
- A151332 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 4 n steps taken from {(-1, -1), (-1, 1), (1, 0)}
- A151341 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, 0)}.
- A151345 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 1)}.
- A151362 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2*n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 0), (1, 1)}.
- A151374 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0, 0), ending on the vertical axis and consisting of 2n steps taken from {(-1, -1), (-1, 0), (1, 1)}.
- A151379 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 0), (1, -1), (1, 1)}.
- A151383 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, 1)}
- A151403 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 0), (-1, 1), (1, 0), (1, 1)}.
- A151410 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 0), (1, -1), (1, 0), (1, 1)}.
- A151471 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 0), (1, 1)}.
- A151478 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 1)}.
- A151483 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0)}.
- A151502 (program): a(n) = A006720(n)^4 (fourth powers of Somos-4 sequence).
- A151542 (program): Generalized pentagonal numbers: a(n) = 12*n + 3*n*(n-1)/2.
- A151548 (program): When A160552 is regarded as a triangle with rows of lengths 1, 1, 2, 4, 8, 16, …, this is what the rows converge to.
- A151549 (program): a(n) = (A151548(n)-1)/2.
- A151550 (program): Expansion of g.f. Product_{n >= 1} (1 + x^(2^n-1) + 2*x^(2^n)).
- A151551 (program): G.f.: (1 + 3x) * Product_{n>=1} (1 + x^(2^n-1) + 2*x^(2^n)).
- A151552 (program): G.f.: Product_{k>=1} (1 + x^(2^k-1) + x^(2^k)).
- A151553 (program): G.f.: (1 + x) * Product_{n>=1} (1 + x^(2^n-1) + x^(2^n)).
- A151554 (program): G.f.: (1 + 2x) * Product_{n>=1} (1 + x^(2^n-1) + x^(2^n)).
- A151555 (program): G.f.: (1 + 2x) * Product_{n>=1} (1 + x^(2^n-1) + 2*x^(2^n)).
- A151566 (program): Leftist toothpicks (see Comments for definition).
- A151568 (program): a(0)=1, a(1)=1; a(2^i+j)=2*a(j)+a(j+1) for 0 <= j < 2^i.
- A151569 (program): a(0)=1, a(1)=2; a(2^i+j)=2*a(j)+a(j+1) for 0 <= j < 2^i.
- A151575 (program): G.f.: (1+x)/(1+x-2*x^2).
- A151576 (program): Number of permutations of 1..n arranged in a circle with exactly 3 adjacent element pairs in decreasing order.
- A151577 (program): Number of permutations of 1..n arranged in a circle with exactly 4 adjacent element pairs in decreasing order.
- A151583 (program): Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
- A151590 (program): Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
- A151597 (program): Number of permutations of 4 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
- A151603 (program): Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
- A151607 (program): Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
- A151610 (program): Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
- A151665 (program): G.f.: Product_{k>=0} (1 + 3*x^(4^k)).
- A151666 (program): Number of partitions of n into distinct powers of 4.
- A151667 (program): Number of partitions of n into distinct powers of 5.
- A151668 (program): G.f.: Product_{k>=0} (1 + 2*x^(3^k)).
- A151669 (program): G.f.: Product_{k>=0} (1 + 2*x^(4^k)).
- A151670 (program): G.f.: Product_{k>=0} (1 + 2*x^(5^k)).
- A151671 (program): G.f.: Product_{k >= 0} (1 + 3*x^(5^k)).
- A151672 (program): G.f.: Product_{k>=0} (1 + 4*x^(3^k)).
- A151673 (program): G.f.: Product_{k>=0} (1 + 4*x^(4^k)).
- A151674 (program): G.f.: Product_{k >= 0} (1 + 4*x^(5^k)).
- A151675 (program): Row sums of A154685.
- A151677 (program): a(n) = sum_{k >= 0} binomial(3*wt(n+k),k), where wt() = A000120().
- A151678 (program): a(n) = sum_{k >= 0} binomial(wt(n+k),2*k), where wt() = A000120().
- A151679 (program): a(n) = sum_{k >= 0} binomial(2*wt(n+k),k), where wt() = A000120().
- A151680 (program): a(n) = sum_{k >= 0} binomial(wt(n+k),k+1), where wt() = A000120().
- A151681 (program): a(n) = sum_{k >= 0, k even} binomial(wt(n+k),k+1), where wt() = A000120().
- A151682 (program): a(n) = sum_{k >= 0, k odd} binomial(wt(n+k),k+1), where wt() = A000120().
- A151685 (program): a(n) = Sum_{k >= 0} bin2(wt(n+k),k+1), where bin2(i,j) = A013609(i,j), wt(i) = A000120(i).
- A151687 (program): G.f.: x + x^2 * Product_{n>=0} (1 + x^(2^n-1) + x^(2^n)).
- A151688 (program): G.f.: Product_{n>=0} (1 + x^(2^n-1) + 2*x^(2^n)).
- A151689 (program): a(n) = sum_{k >= 1} 2^wt(k) * binomial(wt(n+k),k).
- A151690 (program): A151689/2.
- A151692 (program): G.f.: Product_{k>=2} (1 + x^(2^k-1) + x^(2^k)).
- A151702 (program): a(0)=1, a(1)=0; a(2^i + j) = a(j) + a(j+1) for 0 <= j < 2^i.
- A151704 (program): a(0)=1, a(1)=0; a(2^i+j) = 2*a(j) + a(j+1) for 0 <= j < 2^i.
- A151712 (program): a(n) = A048883(n) + 1.
- A151714 (program): When A151552 is written as a triangle the rows converge to this.
- A151740 (program): Composites that are the sum of two consecutive composite numbers.
- A151741 (program): Composite which are the sum of three consecutive composite numbers.
- A151746 (program): G.f.: (1-2*x-5*x^2+4*x^3)/((1-4*x)*(1-x)^2).
- A151749 (program): a(0) = 1, a(1) = 3; a(n+2) = (a(n+1) + a(n))/2 if 2 divides (a(n+1) + a(n)), a(n+2) = a(n+1) + a(n) otherwise.
- A151754 (program): Number of n-digit numbers that are divisible by 5^n.
- A151757 (program): Positive integers n, excluding 1 and 2^i+1 for all i, having wt <= 3.
- A151758 (program): G.f.: Theta^2-Theta, where Theta = Sum_{k>=0} x^(2^k).
- A151763 (program): If n is a prime == 1 mod 4 then a(n) = 1, if n is a prime == 3 mod 4 then a(n) = -1, otherwise a(n) = 0.
- A151774 (program): Characteristic function of numbers with binary weight 2 (A018900).
- A151779 (program): a(1)=1; for n > 1, a(n)=6*5^{wt(n-1)-1}.
- A151780 (program): a(n) = 5^(wt(n) - 1) where wt(n) = A000120(n).
- A151781 (program): Partial sums of A151779.
- A151782 (program): a(1)=1; for n > 1, a(n)=8*7^{wt(n-1)-1}.
- A151783 (program): a(n) = 4^(wt(n) - 1) where wt(n) = A000120(n).
- A151784 (program): a(n) = 6^(wt(n) - 1) where wt(n) = A000120(n).
- A151785 (program): a(n) = 7^(wt(n) - 1) where wt(n) is the binary weight of n (A000120).
- A151786 (program): a(n) = 8^(wt(n)-1) where wt(n) is the binary weight of n (A000120).
- A151787 (program): a(1)=1; for n > 1, a(n)=3*2^{wt(n-1)-1}.
- A151788 (program): Partial sums of A151787.
- A151789 (program): a(1)=1; for n > 1, a(n)=5*4^{wt(n-1)-1}.
- A151790 (program): Partial sums of A151789.
- A151791 (program): a(1)=1; for n > 1, a(n) = 7*6^(wt(n-1)-1).
- A151792 (program): Partial sums of A151791.
- A151793 (program): Partial sums of A151782.
- A151794 (program): a(1)=2, a(2)=4, a(3)=6; a(n+3) = a(n+2)+ 2*a(n), n>=1.
- A151798 (program): a(0)=1, a(1)=2, a(n)=4 for n>=2.
- A151799 (program): Version 2 of the “previous prime” function: largest prime < n.
- A151800 (program): Least prime > n (version 2 of the “next prime” function).
- A151816 (program): a(n) = n! - A001147(n)^2.
- A151817 (program): a(n) = 2*(2*n)!/n!.
- A151819 (program): First component x of pairs (x,y) where x!+y! is a square, sorted on x.
- A151821 (program): Powers of 2, omitting 2 itself.
- A151842 (program): a(3n)=n, a(3n+1)=2n+1, a(3n+2)=n+1.
- A151859 (program): a(0)=0; a(1)=0; a(2)=0; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=2*a(j) + a(j + 1) except we add 1 if j=2^i-1.
- A151860 (program): If A151859 is regarded as a triangle then the rows converge to this sequence.
- A151861 (program): a(0)=0; a(1)=1; a(2)=1; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=2*a(j) + a(j + 1) except we add 1 if j=2^i-1.
- A151862 (program): If A151861 is regarded as a triangle then the rows converge to this sequence.
- A151863 (program): a(0)=1; a(1)=0; a(2)=2; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=2*a(j) + a(j + 1) except we add 1 if j=2^i-1.
- A151864 (program): If A151863 is regarded as a triangle then the rows converge to this sequence.
- A151881 (program): Sum (number of cycles)^2 over all n! permutations of [1..n].
- A151885 (program): Similar to the original toothpick sequence A139250, except that the rule is now: a toothpick changes state if its midpoint is adjacent to exactly one ON toothpick.
- A151888 (program): Net increase in number of ON toothpicks at generation n in A151885.
- A151889 (program): a(1)=2, a(2)=3; a(2k-1)=2a(2k-2)+a(2k-3), a(2k)=3a(2k-2)+2a(2k-3), k >= 2.
- A151890 (program): Triangle read by rows: T(l,c) = 2*l*c + l + c (0 <= c <= l).
- A151898 (program): First differences of Frobenius numbers for 7 successive numbers A138987.
- A151899 (program): Period 6: repeat [0, 0, 1, 1, 1, 2].
- A151902 (program): a(n) = wt(k) + f(j) if n = 6k+j, 0 <= j < 6, where wt() = A000120(), f() = A151899().
- A151904 (program): a(n) = (3^(wt(k)+f(j))-1)/2 if n = 6k+j, 0 <= j < 6, where wt = A000120, f = A151899.
- A151905 (program): a(0) = a(2) = 0, a(1) = 1; for n >= 3, n = 3*2^k+j, 0 <= j < 3*2^k, a(n) = A151904(j).
- A151906 (program): a(0) = 0, a(1) = 1; for n>1, a(n) = 8*A151905(n) + 4.
- A151907 (program): Partial sums of A151906.
- A151910 (program): First differences of A001682.
- A151912 (program): Expansion of (1-8x-8x^3)/(1-2x+4x^2)^2.
- A151914 (program): a(0)=0, a(1)=4; for n>=2, a(n) = (8/3)*(Sum_{i=1..n-1} 3^wt(i)) + 4, where wt() = A000120().
- A151915 (program): Wythoff AAAA numbers.
- A151916 (program): Numbers n such that A108197(n) = 0.
- A151917 (program): a(0)=0, a(1)=1; for n>=2, a(n) = (2/3)*(Sum_{i=1..n-1} 3^wt(i)) + 1, where wt() = A000120().
- A151919 (program): a(n) = (-2)^n*A_{n,3}(1/2) where A_{n,k}(x) are the generalized Eulerian polynomials.
- A151920 (program): a(n) = (Sum_{i=1..n+1} 3^wt(i))/3, where wt() = A000120().
- A151921 (program): Net gain in number of ON cells at stage n of the cellular automaton described in A079317.
- A151922 (program): Number of first-quadrant cells (including the two boundaries) that are “ON” after n-th stage of the Holladay-Ulam cellular automaton.
- A151923 (program): A079316(2n+1).
- A151927 (program): Decimal expansion of 4*Pi^4/3.
- A151928 (program): Decimal expansion of 8*Pi^6/27.
- A151929 (program): First differences of A070952.
- A151930 (program): First differences of A001316.
- A151931 (program): First differences of A071049.
- A151948 (program): a(n) = tau(sigma(phi(n))).
- A151949 (program): a(n) = image of n under the Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).
- A151953 (program): Primes of the form 6*n^2+17.
- A151954 (program): Expansion of Product_{k>0} (1-k^2*x^k)^(-1/k).
- A151961 (program): Semiperimeter of the n-th Heronian triangle.
- A151969 (program): a(n) = smallest integer >= n which has only prime factors 2 and 5.
- A151970 (program): a(n) = smallest integer >= n which has only prime factors 3 and 5.
- A151971 (program): Numbers n such that n^2 - n is divisible by 21.
- A151972 (program): Numbers that are congruent to {0, 1, 6, 10} mod 15.
- A151973 (program): Numbers n such that n^2 - n is divisible by 24.
- A151974 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)/8.
- A151975 (program): The number of ways one can flip seven consecutive tails (or heads) when flipping a coin n times.
- A151976 (program): Minimal recursive sequence beginning with 5 similar to N with respect to property of integer to be or not to be in A079523.
- A151977 (program): Numbers that are congruent to {0, 1} mod 16.
- A151978 (program): Numbers that are congruent to {0, 1} mod 17.
- A151979 (program): Numbers congruent to {0, 1} (mod 19).
- A151980 (program): Numbers n such that n^2 - n is divisible by 20.
- A151981 (program): Numbers n such that n^2 - n is divisible by 48.
- A151982 (program): Arrangement of Fibonacci-numbers in a centered triangular fashion, such that every number is the difference and/or sum of adjacent numbers.
- A151983 (program): Numbers congruent to {0, 1} mod 32.
- A151984 (program): Numbers that are congruent to {0, 1} mod 64.
- A151988 (program): G.f.: (x*(x^4+1)*(x^2-x+1)*(x^2+x+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2).
- A151989 (program): a(n) = A001512(n)/24 = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)/24.
- A151990 (program): If p and q are (odd) twin primes and q > p then p*q^2 + (p + q) + 1 is divisible by 6; a(n) = (p*q^2 + (p + q) + 1)/6.
- A151997 (program): a(n) = (n 1’s followed by a 3)^2.
- A151998 (program): Directed genus of the binary de Bruijn graph D_n.
- A152009 (program): (L)-sieve transform of {1,4,7,10,…,3n-2,…} (A016777)
- A152010 (program): Sum of digits of A127335(n).
- A152011 (program): a(0) = 1 and a(n) = (3^n - (-1)^n)/2 for n >= 1.
- A152015 (program): a(n) = n^3 - n^2 - n.
- A152016 (program): a(n) = n^4 - n^3 - n^2 - n.
- A152017 (program): a(n) = n^5-n^4-n^3-n^2-n.
- A152018 (program): Denominator of 1/n^2-1/(3n)^2 or of 8/(9n^2).
- A152020 (program): Denominator of 8/(9n^2) divided by 9.
- A152029 (program): a(n) = 2^n*(2*n)!/((n+1)!).
- A152030 (program): a(n)=n^6-n^5-n^4-n^3-n^2-n.
- A152031 (program): a(n) = n^5 + n^4 + n^3 + n^2 + n.
- A152032 (program): a(n) = 3/8+(3/8)*(-1)^n+((n+1)/4)*(-1)^(n+1)+((n+2)*(n+1)/4)*(-1)^(n+2).
- A152035 (program): G.f.: (1-2*x^2)/(1-2*x-2*x^2).
- A152036 (program): Triangular product sequence based 2^n times the Fibonacci version and 4 replaced with m: t(m,n)=2^n*Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].
- A152041 (program): A008893/2.
- A152046 (program): a(n) = Product_{k=1..floor((n-1)/2)} (1 + 8*cos(k*Pi/n)^2) for n >= 0.
- A152053 (program): a(n) = A144433(3n+1) + A144433(3n+2) + A144433(3n+3).
- A152055 (program): a(n) = ((8+sqrt3)^n + (8-sqrt3)^n/2.
- A152056 (program): a(n) = ((9+sqrt(3))^n + (9-sqrt(3))^n)/2.
- A152059 (program): a(n) is the number of ways 2n-1 seats can be occupied by at most n people for n>=1, with a(0)=1.
- A152061 (program): Counts of unique periodic binary strings of length n.
- A152064 (program): a(n) = 2*n^3 - 3*n^2 + 5.
- A152065 (program): A triangular sequence of polynomial coefficients: p(x,n)=If[n == 0, x^n - x^Floor[(n - 1)/2]*Sum[x^m, {m, 0, n - Floor[(n - 1)/2] - 1}] + 1/x, x^n - x^Floor[(n - 1)/2]*Sum[x^m, {m, 0, n - Floor[(n - 1)/2] - 1}] + 1].
- A152078 (program): Numbers a(n) for which A000695(a(n)) = A077718(n).
- A152083 (program): Number of occurrences of “I” in all Roman numerals of numbers from 1 to n
- A152086 (program): a(n) = Sum_{k=1..n-1} k*A110971(n,k).
- A152087 (program): Primes p such that q - p is not squarefree, where q is the next prime immediately following p.
- A152090 (program): a(n) = 2^n*Product_{k=1..floor((n-1)/2)} (1 + 2*cos(k*Pi/n)^2 + 4*cos(k*Pi/n)^4).
- A152094 (program): Quartic product sequence: a(n) = Product_{k=1..floor((n-1)/2)} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4 ), with m = 2*4, q=2*4^3.
- A152098 (program): Quartic product sequence: m = 4; p = 4^3; a(n) = Product_{k=1..(n-1)/2} ( 1 + m*cos(k*Pi/n)^2 + p*cos(k*Pi/n)^4 ).
- A152099 (program): Semiprimes based on powers of two and primes: a(n)=(2^Prime[n] - 1)*(2^Prime[n] + 1)=2^(2*Prime[n])-1.
- A152100 (program): G.f.: 1 - 2*x*(-7 - 10*x + x^2)/(x - 1)^4.
- A152101 (program): a(n)=16^n - 3*2^(2*n - 1) - 1.
- A152103 (program): a(n) = 2^n*Product_{k=1..floor((n-1)/2)} (1 + 2*cos(k*Pi/n)^2 + 4*cos(k*Pi/n)^4).
- A152104 (program): Quartic product sequence: a(n) = 2^n*Product_{k=1..(n-1)/2} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4), with m=6, q=4.
- A152105 (program): a(n) = ((8 + sqrt4)^n + (8 - sqrt4)^n)/2.
- A152106 (program): a(n) = (11^n + 7^n)/2.
- A152107 (program): a(n) = ((6+sqrt(5))^n+(6-sqrt(5))^n)/2.
- A152108 (program): a(n) = ((7+sqrt(5))^n + (7-sqrt(5))^n)/2.
- A152109 (program): a(n) = ((8+sqrt(5))^n + (8-sqrt(5))^n)/2.
- A152110 (program): G.f.: -2*(-2 - 11*x - 4*x^2 + x^3)/(x - 1)^4.
- A152113 (program): A001333 with terms repeated.
- A152114 (program): Numbers a(n) are obtained by the application of an algorithm which is similar to sieve of Eratosthenes for A000045: retaining A000045(3)=2, we delete all multiples of 2, which are more than 2; retaining A000045(4)=3, we delete all multiples of 3, which are more than 3, etc.
- A152117 (program): a(n) = n*(n-th prime) + (n+1)*((n+1)-th prime).
- A152118 (program): a(n) = product( 4 +4*cos(k*Pi/n)^2, k=1..(n-1)/2 ).
- A152119 (program): a(n) = Product_{k=1..(n-1)/2} (5 + 4*cos(k*Pi/n)^2).
- A152120 (program): a(n) = 2^n * Product_{k=1..(n-1)/2} (2 + 3*cos(k*Pi/n)^2).
- A152125 (program): Consider a square grid with side n consisting of n^2 cells (or points); a(n) is the minimal number of points that can be painted black so that, out of any four points forming a square with sides parallel to the sides of the grid, at least one of the four is black.
- A152126 (program): If f(x) = x^3+x^5+x^11+x^17+x^29+x^41+…, where the exponents are the smaller twin of twin prime pairs, consider {f(x)}^2 and write the exponents of that expansion down : x^6+2x^8+x^10+2x^12+…. The proposed sequence is that sequence of exponents
- A152132 (program): Maximal length of rook tour on an n X n+1 board.
- A152133 (program): Maximal length of rook tour on an n X n+2 board.
- A152134 (program): Maximal length of rook tour on an n X n+3 board.
- A152135 (program): Maximal length of rook tour on an n X n+4 board.
- A152148 (program): Riordan array [exp(-x/2)(1-2x)^(-1/4),x].
- A152151 (program): Riordan array [(1-x)exp(x/(1-x)),x]
- A152152 (program): A sequence related to sine products and the Fibonacci numbers A000045: a(n) = Product_{k=1..n} (1 + 4*sin(2*Pi*k/n)^2).
- A152158 (program): A sequence set up on the first 1000 base ten Pi digits: a(n)=a(n-1)+a(n-2)*Floor[Mod[N[Pi*10^(n - 2), 1000], 10]].
- A152161 (program): a(n) = 100*n^2 + 100*n + 21.
- A152163 (program): a(n) = a(n-1)+a(n-2), n>1 ; a(0)=1, a(1)=-1.
- A152166 (program): a(2*n) = 2^n; a(2*n+1) = -(2^(n+1)).
- A152167 (program): a(n)=-a(n-1)+3*a(n-2), n>1 ; a(0)=1, a(1)=-3 .
- A152170 (program): a(n) is the total size of all the image sets of all functions from [n] to [n]. I.e., a(n) is the sum of the cardinalities of every image set of every function whose domain and co-domain is {1,2,…,n}.
- A152171 (program): G.f. := (1-sqrt(1-4*x+4*x^2-4*x^3))/(2(1-x+x^2)x)
- A152174 (program): a(n) = -2*a(n-1)+4*a(n-2), n>1 ; a(0) = 1, a(1) = -4.
- A152179 (program): (n^2-2=A008865) mod 9. Period 9:repeat 8,2,7,5,5,7,2,8,7.
- A152185 (program): a(n) = -3*a(n-1) + 5*a(n-2), n > 1; a(0)=1, a(1)=-5.
- A152187 (program): a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=5.
- A152189 (program): Product_{k=1..floor((n-1)/2)} (1 + 4*cos(k*Pi/n)^2)*(1 + 4*sin(k*Pi/n)^2).
- A152192 (program): a(n) = Product_{k=1..floor((n-1)/2)} (1 + 4*cos(2*Pi*k/n)^2).
- A152195 (program): Triangle read by rows, A000012 * A152194
- A152198 (program): Triangle read by rows, A007318 rows repeated.
- A152199 (program): Trajectory of 7 under the map m -> A082010(m).
- A152201 (program): Triangle read by rows, A000012 * A152198
- A152203 (program): Triangle T(n,k) = (2n+1-2k)*fibonacci(k), read by rows.
- A152204 (program): Triangle read by rows: T(n,k) = 2*n-4*k+5 (n >= 0, 1 <= k <= 1+floor(n/2)).
- A152205 (program): Triangle read by rows, A000012 * A152204.
- A152206 (program): a(n) = sum of base-2 digits of A037308(n) = sum of base-10 digits of A037308(n).
- A152211 (program): a(n) = n * sigma_0(n) + sigma_1(n).
- A152223 (program): a(n) = -4*a(n-1) + 6*a(n-2) for n > 1 with a(0) = 1 and a(1) = -6.
- A152224 (program): a(n)=4*a(n-1)+6*a(n-2), n>1 ; a(0)=1, a(1)=6 .
- A152225 (program): Number of Dyck paths of semilength n with no peaks at height 0 (mod 3) and no valleys at height 2 (mod 3).
- A152226 (program): Binomial transform of A027826.
- A152231 (program): Similar to A072921 but starting with 2.
- A152232 (program): Similar to A072921 but starting with 3.
- A152233 (program): Similar to A072921 but starting with 4.
- A152234 (program): Similar to A072921 but starting with 5.
- A152235 (program): Largest squarefree number dividing the number of divisors n.
- A152236 (program): A modulo two parity function as a triangle sequence: t(n,m)=Binomial[n,m]+p(n,m); Always even parity function: p(n,m)=If[Mod[Binomial[n, m], 2] == 0, Binomial[n, m], If[Mod[Binomial[ n, m], 2] == 1 && Binomial[n, m] > 1, 1 + Binomial[n, m], 0]].
- A152237 (program): A modulo two parity function as a triangle sequence:k=1; t(n,m)=Binomial[n,m]+p(n,m); Always even parity function: p(n,m)=If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k* Binomial[n, m], 0]].
- A152238 (program): A modulo two parity function as a triangle sequence:k=2; t(n,m)=Binomial[n,m]+p(n,m); Always even parity function: p(n,m)=If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k* Binomial[n, m], 0]].
- A152239 (program): a(n) = -5*a(n-1) + 7*a(n-2) for n > 1 with a(0) = 1 and a(1) = -7.
- A152240 (program): a(n)=5*a(n-1)+7*a(n-2), n>1 ; a(0)=1, a(1)=7 .
- A152241 (program): Products of cubes of 2 successive primes.
- A152251 (program): Eigentriangle, row sums = A001519, odd-indexed Fibonacci numbers.
- A152252 (program): Triangle read by rows, M*Q, where M = an infinite lower triangular matrix with powers of 3 prefaced by a 1 in every row: (1, 1, 3, 9, 27, …) and Q = a matrix with A006012 prefaced by a 1 as the main diagonal and the rest zeros.
- A152254 (program): Twice A084773.
- A152256 (program): a(n) = (3^n - 1)*(3^n + 1)*(3^n + 1)/32.
- A152257 (program): a(n) = (3^n - 1)^2*(3^n + 1)/16.
- A152258 (program): a(n) = ((3^n - 1)*(3^n + 1))^2/2^(7 - (n mod 2)).
- A152261 (program): a(n) = ((9 + sqrt(5))^n + (9 - sqrt(5))^n)/2.
- A152262 (program): a(n) = 14*a(n-1) - 43*a(n-2), n > 1; a(0)=1, a(1)=7.
- A152263 (program): a(n) = ((8 + sqrt(6))^n + (8 - sqrt(6))^n)/2.
- A152264 (program): a(n) = ((9+sqrt(6))^n + (9-sqrt(6))^n)/2.
- A152265 (program): a(n) = ((8+sqrt(7))^n + (8-sqrt(7))^n)/2.
- A152266 (program): a(n) = ((9 + sqrt(7))^n + (9 - sqrt(7))^n)/2.
- A152267 (program): a(n) = ((9 + sqrt(8))^n + (9 - sqrt(8))^n)/2.
- A152268 (program): A hidden Markov recursion involving the matrices: M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}}; as Mh=M0.M.(M0+I); v[(n)=Mh.v(n-1): first element of v.
- A152269 (program): A switched hidden Markov recursion involving the matrices: M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}}; as Mh=M0.M.(M0+I*mod[n.2]); v[(n)=Mh.v(n-1): first element of v.
- A152271 (program): a(n)=1 for even n and (n+1)/2 for odd n.
- A152291 (program): a(n) = (n+1)^floor((n-1)/2).
- A152297 (program): Alternate binomial partial sums of binomial(2n,n)*binomial(3n,n) (A006480).
- A152298 (program): a(n) = (3^n-1)/2 if n odd, (3^n-1)/8 if n even.
- A152299 (program): A threes sequence that gets more even factors out: a(n)=(3^n - 1)*(3^n + 1)/2^(4 - Mod[n, 2]).
- A152302 (program): Marsaglia-Zaman type recursive sequence: f(x)=f(x - 1) + f(x - 2) + Floor[f(x - 1)/10]; a(n)=Mod[f(n),10].
- A152303 (program): Marsaglia-Zaman type recursive sequence as a vector Markov: M = {{0, 1}, {1, 1}}; M1 = {{0, 0}, {1/10, 0}}; v(n)=M.v(n-1)+Floor[M1.v(n-1),10] a(n)=Mod[v(n)[[1]],10].
- A152305 (program): Marsaglia-Zaman type recursive sequence: f(x)=f(x - 2) + f(x - 3) + Floor[f(x - 1)/10]; a(n)=Mod[f(n),10].
- A152390 (program): Arises in enumerating non-degenerate colorings in Brook’s Theorem.
- A152416 (program): Decimal expansion of 2 - Pi^2/6.
- A152417 (program): a(n) = (5^n - 1)/(2^(3 - (n mod 2))).
- A152418 (program): A sevens sequence: a(n)=(7^n - 1)/(2^(4 - 3*Mod[n, 2])).
- A152420 (program): Irregular triangle read by rows: T(n,k) = n*(n-2) - (k-n)*(k-n-2), with 0 <= k <= 2*n.
- A152421 (program): a(n) = binomial(A000290(n), A006218(n)).
- A152422 (program): Decimal expansion of (sqrt(3)-1)/2.
- A152423 (program): A variation of the Josephus problem, removing every other person, starting with person 1; a(n) is the last person remaining.
- A152424 (program): a[n_]:=IntegerPart[Prime[n^n]^(1/n)];
- A152429 (program): a(n) = (11^n + 5^n)/2.
- A152435 (program): a(n)=(11^n - 1)/(5*2^(3 - 2*Mod[n, 2])).
- A152436 (program): a(n)=(13^n - 1)/(3*2^(3 - Mod[n, 2])).
- A152437 (program): (17^n - 1)/(2^(5 - (n % 2))).
- A152438 (program): a(n)=(19^n - 1)/(9*2^(3 - 2*Mod[n, 2])).
- A152440 (program): Riordan matrix (1/(1-x-x^2),x/(1-x-x^2)^2).
- A152442 (program): n is included if the largest divisor of n that is coprime to d(n) is a composite, where d(n) is the number of divisors of n.
- A152448 (program): a(0)=a(1)=1, a(2)=6, a(3)=11; a(n+4) = 10*a(n+2) - a(n).
- A152450 (program): a(0)=a(1)=1, a(2)=4, a(3)=7, a(n+4) = 10*a(n+2) - a(n).
- A152455 (program): a(n) = minimal integer m such that there exists an m X m integer matrix of order n.
- A152456 (program): a(n)=1*(n+2)!-2*(n+1)!-3*n!.
- A152457 (program): Partial sums of A027444.
- A152465 (program): Degrees of irreducible representations of SL(2,9).
- A152467 (program): a(n) = floor(n/6).
- A152470 (program): Largest of three consecutive primes whose sum is a prime.
- A152476 (program): Inverse binomial transform of A005329.
- A152481 (program): Degrees of irreducible representations of SL(2,11).
- A152482 (program): Even numbers which are not the sum of 2 even semiprimes.
- A152485 (program): Degrees of irreducible representations of SL(2,13).
- A152494 (program): 1/3 of the number of permutations of 2 indistinguishable copies of 1..n with exactly 2 local maxima.
- A152499 (program): 1/12 of the number of permutations of 3 indistinguishable copies of 1..n with exactly 2 local maxima.
- A152521 (program): Juxtaposition of prime(2n-1) and prime(2n) is a prime.
- A152524 (program): a(n) is the number of L-bit words in which, if up to k bits are perturbed, the resulting change in unsigned L-bit value is n, for L=8 and k=7.
- A152527 (program): a(n) = (p(n)*p(n+1)-p(n+2))/2, where p(n) is the n-th odd prime.
- A152528 (program): a(n) = p(n)*p(n+2) - 3*p(n+1), where p(n) is the n-th prime.
- A152529 (program): a(n) = (p(n)*p(n+2) - 3*p(n+1))/2, where p(n) is the n-th odd prime.
- A152530 (program): a(n) = p(n)*p(n+2)-p(n+1), where p(n) is the n-th prime.
- A152531 (program): a(n) = (p(n)*p(n+2) - p(n+1))/2, where p(n) is the n-th odd prime.
- A152532 (program): a(n) = prime(n) * prime(n+2) - 2 * prime(n+1).
- A152535 (program): a(n) = n*prime(n) - Sum_{i=1..n} prime(i).
- A152537 (program): Convolution sequence: convolved with A000041 = powers of 2, (A000079).
- A152539 (program): Partial sum of A146538.
- A152540 (program): Primes p of the form A152539(n) + 1.
- A152548 (program): Sum of squared terms in rows of triangle A152547: a(n) = Sum_{k=0..C(n,[n/2])-1} A152547(n,k)^2.
- A152551 (program): a(n) = (2*n+1)^floor((n-1)/2).
- A152556 (program): a(n) = 2*(2*n+2)^floor((n-1)/2).
- A152568 (program): Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 2^(n - 1), T(n,k) = -2^(n - k - 1), 1 <= k <= n - 1.
- A152570 (program): Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 3^(n - 1), T(n,k) = -3^(n - k - 1), 1 <= k <= n - 1.
- A152571 (program): Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 4^(n - 1), T(n,k) = -4^(n - k - 1), 1 <= k <= n - 1.
- A152572 (program): Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 5^(n - 1), T(n,k) = -5^(n - k - 1), 1 <= k <= n - 1
- A152574 (program): Numbers n such that entering (N*0.3/N*0.1) on a Rumor LG Sprint cell phone produced the value 2 instead of 3, where N = n * (2**k) for k = 0, 1, 2, ….
- A152577 (program): a(n) = 10^(2*n - 1) + 1.
- A152579 (program): a(n) = (10*n+3)*(10*n+17).
- A152584 (program): Decimal expansion of (Pi^3)/24.
- A152594 (program): a(n) = -5*a(n-1)-2*a(n-2), n>1 ; a(0)=1, a(1)=-1 .
- A152596 (program): a(n) = 7*a(n-1) - 6*a(n-2), n>1; a(0)=1, a(1)=3.
- A152599 (program): a(n)=10*a(n-1)-12*a(n-2), n>1 ; a(0)=1, a(1)=4 .
- A152600 (program): a(n)=0^n+sum{k=0..n-1, C(n+k-1,2k)*A000108(k)*3^k*2^(n-k)}
- A152601 (program): a(n) = Sum_{k=0..n} C(n+k,2k)*A000108(k)*3^k*2^(n-k).
- A152618 (program): a(n) = (n-1)^2*(n+1).
- A152619 (program): n*(n+2)^2
- A152620 (program): a(n)=-8*a(n-1)-6*a(n-2), n>1 ; a(0)=1, a(1)=-2 .
- A152621 (program): a(n)=8*a(n-1)-6*a(n-2), n>1 ; a(0)=1, a(1)=2.
- A152622 (program): Tetrahedral numbers n*(n+1)*(n+2)/6 with n, n+1 and n+2 nonprime.
- A152623 (program): Decimal expansion of 3/2.
- A152624 (program): Decimal expansion of 7/2.
- A152627 (program): Decimal expansion of 3/4.
- A152648 (program): Decimal expansion of 2*zeta(3).
- A152649 (program): Decimal expansion of Pi^4/72.
- A152653 (program): a(n) = (n-1)! * Product_{k=1..n-2} (n-k)!.
- A152659 (program): Triangle read by rows: T(n,k) is the number of lattice paths from (0,0) to (n,n) with steps E=(1,0) and N=(0,1) and having k turns (NE or EN) (1<=k<=2n-1).
- A152661 (program): Number of permutations of [n] for which the first two entries have the same parity (n>=2).
- A152663 (program): Number of leading odd entries in all permutations of {1,2,…,n} (see example).
- A152665 (program): Number of leading even entries in all permutations of {1,2,…,n}.
- A152668 (program): Number of runs of even entries in all permutations of {1,2,…,n} (the permutation 274831659 has 3 runs of even entries: 2, 48 and 6).
- A152669 (program): Last digit of Catalan number A000108(n).
- A152670 (program): Even Catalan numbers.
- A152671 (program): Even Catalan numbers divided by 2.
- A152672 (program): a(n) is the number of distinct tuples of up to k bit locations in L-bit words, in which, if bits are perturbed, the resulting change in unsigned L-bit value is n, for L=8 and k=7.
- A152674 (program): Number of divisors of the numbers that are not squares.
- A152677 (program): Subsequence of odd terms in A000203 (sum-of-divisors function sigma), in the order in which they occur and with repetitions.
- A152678 (program): Even members of A000203.
- A152679 (program): Even members of A000203, divided by 2.
- A152680 (program): a(n) = 4*A005098(n) = A002144(n) - 1.
- A152681 (program): [x^(n+1)]Reversion[x*(1-x)/(1-3*x)].
- A152684 (program): a(n) is the number of top-down sequences (F_1, F_2, …, F_n) whereas each F_i is a labeled forest on n nodes, containing i directed rooted trees. F_(i+1) is proper subset of F_i.
- A152686 (program): Partial products of the partial products of the nonzero Fibonacci numbers.
- A152687 (program): Partial products operator applied thrice to nonzero Fibonacci numbers.
- A152689 (program): Apply partial sum operator thrice to factorials.
- A152690 (program): Partial sums of superfactorials (A000178).
- A152691 (program): Multiples of 64.
- A152692 (program): a(n) = n*3^n - n*2^n - n*1^n.
- A152714 (program): Triangle read by rows: T(n,k) = 3^min(k, n-k).
- A152716 (program): Triangle T(n,k) read by rows: T(n,k) = 4^min(k, n-k) = 4^A004197(n,k).
- A152717 (program): Triangle T(n,k) read by rows: T(n,k) = 5^min(k, n-k) = 5^A004197(n,k).
- A152718 (program): a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - a(n-4) + a(n-5), n > 5.
- A152719 (program): Triangle read by rows: T(n,k) = A000129( 1 + min(k,n-k) ), n>=0, 0<=k<=n.
- A152723 (program): In binary, count of least frequent bit of n.
- A152724 (program): In binary, count of most frequent bit of n.
- A152725 (program): a(n) = n*(n+1)*(n^4 + 2*n^3 - 2*n^2 - 3*n + 3)/2.
- A152726 (program): a(n) = n^7 - (n-1)^7 + (n-2)^7 - … + ((-1)^n)*0^7.
- A152727 (program): Smallest positive non-divisor of the n-th Fibonacci number (A000045).
- A152728 (program): a(n) + a(n+1) + a(n+2) = n^3.
- A152729 (program): a(n) = (n-2)^4 - a(n-1) - a(n-2), with a(1) = a(2) = 0.
- A152730 (program): a(n) + a(n+1) + a(n+2) = n^5, with a(1) = a(2) = 0.
- A152731 (program): a(n) + a(n+1) + a(n+2) = n^6, a(1)=a(2)=0.
- A152732 (program): a(n) + a(n+1) + a(n+2) = 2^n.
- A152733 (program): a(n) + a(n+1) + a(n+2) = 3^n.
- A152734 (program): 5 times pentagonal numbers: 5*n*(3*n-1)/2.
- A152738 (program): a(n) = floor((n^2)/phi).
- A152740 (program): 11 times triangular numbers.
- A152741 (program): 13 times triangular numbers.
- A152742 (program): 13 times the squares: a(n) = 13*n^2.
- A152743 (program): 6 times pentagonal numbers: a(n) = 3*n*(3*n-1).
- A152744 (program): 7 times pentagonal numbers: a(n) = 7*n*(3*n-1)/2.
- A152745 (program): 5 times hexagonal numbers: 5*n*(2*n-1).
- A152746 (program): Six times hexagonal numbers: 6*n*(2*n-1).
- A152749 (program): a(n) = (n+1)*(3*n+1)/4 for n odd, a(n) = n*(3*n+2)/4 for n even.
- A152750 (program): Eight times hexagonal numbers: 8*n*(2*n-1).
- A152751 (program): 3 times octagonal numbers: 3*n*(3*n-2).
- A152752 (program): Terms of A118962 that are == 9 (mod 10).
- A152753 (program): Last digit of even Catalan number A152670(n).
- A152756 (program): Bisection of A000533.
- A152757 (program): Numbers k such that the deficiency of k plus the number of proper divisors of k is a prime number (see A152864).
- A152758 (program): Numbers k such that the deficiency of k plus the number of proper divisors of k is not a prime number (see A152864).
- A152759 (program): 3 times 9-gonal (or nonagonal) numbers: 3n(7n-5)/2.
- A152760 (program): 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5).
- A152761 (program): Sum of divisors of Catalan number A000108(n).
- A152762 (program): Sum of proper divisors of Catalan number A000108(n).
- A152763 (program): Number of divisors of Catalan number A000108(n).
- A152764 (program): Bisection of A138144.
- A152765 (program): Smallest prime divisor of Catalan number A000108(n), with a(0) = a(1) = 1.
- A152766 (program): Largest proper divisor of the Catalan number A000108(n).
- A152767 (program): 3 times 10-gonal (or decagonal) numbers: 3n(4n-3).
- A152769 (program): Numbers n such that pi(n) is nonprime.
- A152770 (program): Sum of proper divisors minus the number of proper divisors of n: a(n) = sigma(n) - n - d(n) + 1.
- A152771 (program): a(n) = sigma(n) - 2*d(n) + 1.
- A152772 (program): a(n) = sigma(n) - 3*d(n) + 3.
- A152773 (program): 3 times heptagonal numbers: a(n) = 3n(5n-3)/2.
- A152775 (program): Numbers with 3n binary digits where every run length is 3, written in binary.
- A152776 (program): Numbers such that every run length in base 2 is 3.
- A152777 (program): 7 times heptagonal numbers: 7*n*(5*n-3)/2.
- A152785 (program): a(n)=Floor[(n^2)/Catalan].
- A152786 (program): Integers k such that (k^2)/2 is the arithmetic mean of a pair of twin primes.
- A152810 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence gives odd n such that e(n) > o(n) and e(n)-o(n) == 1 or 2 (mod 6).
- A152811 (program): a(n) = 2*(n^2 + 2*n - 2).
- A152813 (program): a(n) = 2*n^2 + 10*n + 3.
- A152815 (program): Triangle T(n,k), read by rows given by [1,0,-1,0,0,0,0,0,0,…] DELTA [0,1,-1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A152818 (program): Array read by antidiagonals: T(n,k) = (k+1)^n*(n+k)!/n!.
- A152822 (program): Periodic sequence [1,1,0,1] of length 4.
- A152823 (program): Largest divisor < n of n^2 + 1, a(1) = 1.
- A152827 (program): Partial products of PartitionsQ numbers (A000009).
- A152828 (program): Triangle read by rows, A007318 rows repeated three times .
- A152829 (program): Numbers k whose squares can be written in exactly one way as a sum of three squares: k^2 = a^2 + b^2 + c^2 with 1 <= a <= b <= c.
- A152830 (program): Triangle read by rows, A007318 rows repeated four times .
- A152831 (program): Triangle read by rows, A007318 repeated five times .
- A152832 (program): a(0) = -2; a(n) = n - a(n-1) for n > 0.
- A152833 (program): a(0) = -3; a(n) = n-a(n-1).
- A152834 (program): Numbers of form 6k+1 that use only digits 2 and 3.
- A152835 (program): a(0) = -22; a(n) = n-a(n-1).
- A152842 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,…] DELTA [3,-2,-1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A152843 (program): Numbers n such that both 2n+3 and 4n+7 are prime.
- A152847 (program): Triangle read by rows, A007318 rows repeated nine times .
- A152848 (program): Triangle read by rows, A007318 rows repeated ten times .
- A152849 (program): Triangle read by rows, A007318 rows repeated eleven times .
- A152854 (program): Numbers n such that either 2n+3 is not prime or 4n+7 is not prime.
- A152855 (program): Periodic sequence [1,2,0,2,0] of period 5
- A152856 (program): Periodic sequence [4,0,4,3,4] of period 5
- A152857 (program): Period 5: repeat [0, 2, 3, 0, 0].
- A152864 (program): Deficiency of n, plus the number of proper divisors of n: a(n) = 2n - sigma(n) + d(n) - 1.
- A152873 (program): Number of permutations of {1,2,…,n} (n>=2) having a single run of even entries. For example, the permutation 513284679 has a single run of even entries: 2846.
- A152875 (program): Number of permutations of {1,2,…,n} (n >= 2) with all odd entries preceding all even entries or all even entries preceding all odd entries.
- A152881 (program): Positions of those 1’s that are followed by a 0, summed over all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword.
- A152883 (program): Triangle read by rows: T(n,k) is the number of permutations of {1,2,…,n} in which k is an excedance (n >= 2, 1 <= k <= n-1). An excedance of a permutation p is a value j such that p(j) > j.
- A152885 (program): Number of descents beginning and ending with an odd number in all permutations of {1,2,…,n}.
- A152886 (program): Number of descents beginning and ending with an even number in all permutations of {1,2,…,n}.
- A152887 (program): Number of descents beginning with an even number and ending with an odd number in all permutations of {1,2,…,n}.
- A152888 (program): Partial sums of length of terms in A081368 where A081368(1) is set to 0.
- A152889 (program): Periodic sequence [1,0,4,0,0] of period 5
- A152890 (program): Periodic sequence [4,1,4,0,1] of period 5
- A152891 (program): a(1) = b(1) = 0; for n > 1, b(n) = b(n-1) + n-1 + a(n-1) and a(n) = a(n-1) + n-1 + b(n).
- A152892 (program): Period 5: repeat [0, 3, 1, 0, 1].
- A152893 (program): Periodic sequence [3, 3, 0, 0, 4] of period 5
- A152894 (program): Periodic sequence [0,0,1,4,0] of period 5.
- A152895 (program): Partial sums of A152891.
- A152896 (program): a=b=c=0;c(n)=c+n+a;b(n)=b+n+c;a(n)=a+n+b.
- A152897 (program): Partial sums of A152896.
- A152898 (program): Periodic sequence [1,4,0,0,0] of period 5
- A152902 (program): Convolution sequence, A000027 / A008683
- A152904 (program): Triangle read by rows: T(n,k) = A008683(n-k+1); 1<=k<=n; mu(n) “decrescendo”.
- A152906 (program): Irregular triangle read by rows, numbers in A007318 repeated three times .
- A152907 (program): Irregular triangle read by rows, numbers in A007318 repeated four times .
- A152912 (program): Primes p such that 2*p^2-1 is not prime.
- A152915 (program): Exponacci (or exponential Fibonacci) numbers.
- A152917 (program): A000169 prefixed by an initial 0.
- A152919 (program): a(1)=1, for n>1, a(n) = n^2/4 + n/2 for even n, a(n) = n^2/4 + n - 5/4 for odd n.
- A152920 (program): Triangle read by rows: triangle A062111 reversed.
- A152927 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 1 as k varies.
- A152928 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two m-gonal polygonal components chained with string components of length 1 as m varies.
- A152929 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two 4-gonal polygonal components chained with string components of length l as l varies.
- A152930 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 2 as k varies.
- A152933 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 6-gonal polygonal components chained with string components of length 2 as k varies.
- A152934 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two m-gonal polygonal components chained with string components of length 3 as m varies.
- A152947 (program): a(n) = 1 + (n-2)*(n-1)/2.
- A152948 (program): a(n) = (n^2 - 3*n + 6)/2.
- A152949 (program): a(n) = 3 + binomial(n-1,2).
- A152950 (program): a(n) = 3 + n*(n-1)/2.
- A152958 (program): Alladi’s third-order function phi_3(n).
- A152965 (program): Twice 12-gonal numbers: a(n) = 2*n*(5*n-4).
- A152966 (program): Twice repdigit numbers.
- A152967 (program): Partial sums of A152770.
- A152968 (program): a(n) = A139251(n+1)/2.
- A152978 (program): a(n) = A139251(n+2)/4 = A152968(n+1)/2.
- A152980 (program): First differences of toothpick corner sequence A153006.
- A152984 (program): Absolute values of A152864.
- A152985 (program): Sum of proper divisors minus the number of proper divisors of the square A000290(n).
- A152986 (program): Sum of proper divisors minus the number of proper divisors of pentagonal number A000326(n).
- A152987 (program): Sum of proper divisors minus the number of proper divisors of the number of partitions of n, A000041(n).
- A152989 (program): Sum of proper divisors minus the number of proper divisors of triangular number A000217(n).
- A152991 (program): a(n) = sigma(n) - pi(n).
- A152992 (program): a(n) = sigma(n) - d(n) - pi(n).
- A152993 (program): a(n) = n - d(n) - pi(n) + 1.
- A152994 (program): Nine times hexagonal numbers: a(n) = 9*n*(2*n-1).
- A152995 (program): Twice 11-gonal numbers: a(n) = n*(9*n-7).
- A152996 (program): 9 times pentagonal numbers: 9*n*(3*n-1)/2.
- A152997 (program): Twice 13-gonal numbers: a(n) = n*(11*n - 9).
- A152998 (program): Toothpick sequence on the semi-infinite square grid.
- A153000 (program): Toothpick sequence in the first quadrant.
- A153001 (program): Rows of A152980 when written as a triangle converge to this sequence.
- A153003 (program): Toothpick sequence in the first three quadrants.
- A153004 (program): First differences of toothpick numbers A153003.
- A153006 (program): Toothpick sequence starting at the outside corner of an infinite square from which protrudes a half toothpick.
- A153007 (program): Triangular number A000217(n) minus toothpick number A153006(n).
- A153008 (program): Catalan number A000108(n) minus Motzkin number A001006(n).
- A153010 (program): Indices of A153007 where the entry equals zero.
- A153011 (program): Sum of proper divisors, minus the number of proper divisors, minus cototient of n, plus 1.
- A153012 (program): Differences between adjacent digits of square root of 2.
- A153026 (program): a(1)=0, a(n) = n^3 - a(n-1).
- A153028 (program): Special values of the hypergeometric function of the type 4F0.
- A153030 (program): Positions of even digits of Pi.
- A153031 (program): Positions of prime digits of Pi.
- A153032 (program): Positions of digits of Pi that are divisible by 3.
- A153033 (program): Numbers with adjacent 1’s and no adjacent 0’s in binary expansion.
- A153034 (program): Numbers with adjacent 0’s and no adjacent 1’s in binary expansion.
- A153036 (program): Integer parts of the full Stern-Brocot tree.
- A153037 (program): a(n) = 2*n^2 + 16*n + 23.
- A153038 (program): Denominators of the fixed point a=(a_1,a_2,…) of the transformation x’= fix(x) where fix(x)_n = Sum_{d|n} d x_d, i.e., fix(a)=a.
- A153039 (program): Numbers n such that 2*n-7 is composite.
- A153040 (program): Numbers n>3 such that 2*n-5 is not a prime.
- A153041 (program): Numbers n >=10 such that 2*n-19 is not a prime.
- A153043 (program): Numbers n > 1 such that 2*n-3 is not a prime.
- A153044 (program): Numbers n such that 2*n-9 is not a prime.
- A153045 (program): Numbers k such that 2*k-11 is not a prime.
- A153047 (program): Numbers n such that 2*n-15 is not a prime.
- A153049 (program): Numbers n such that 2*n - 13 is not a prime.
- A153051 (program): Numbers n>=9 such that 2*n-17 is not a prime.
- A153052 (program): Numbers n such that 2*n + 5 is not a prime.
- A153053 (program): Numbers n such that 2*n + 7 is not a prime.
- A153056 (program): a(0)=2, a(n) = n^2+a(n-1).
- A153057 (program): a(0)=3; a(n) = n^2 + a(n-1) for n>0.
- A153058 (program): a(0)=4; a(n)=n^2+a(n-1) for n>0.
- A153059 (program): a(0) = 0, a(n) = a(n-1)^2 - n.
- A153062 (program): a(0)=1, a(n)=a(n-1)^2-n^2.
- A153071 (program): Decimal expansion of L(3, chi4), where L(s, chi4) is the Dirichlet L-function for the non-principal character modulo 4.
- A153079 (program): a(n) = 13^n + 2.
- A153080 (program): a(n) = 13*n + 2.
- A153081 (program): Nonnegative numbers n such that 2n + 13 is prime.
- A153082 (program): Numbers k such that 2*k + 13 is not prime.
- A153083 (program): Numbers such that 2*n + 11 is not prime.
- A153085 (program): Numbers k such that 4*k + 5 is not prime.
- A153086 (program): Numbers n such that 4*n+7 is not prime
- A153088 (program): Numbers k such that 5*k - 1 is not prime.
- A153110 (program): Period 6: repeat [1, 5, 7, 2, 4, 8].
- A153111 (program): Solutions of the Pell-like equation 1 + 6*A*A = 7*B*B, with A, B integers.
- A153122 (program): G.f.: 1/p(x) where p(x)=x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1.
- A153125 (program): Triangle read by rows: T(n,k) = maximal number of squares that can be covered by a queen on an n X k chessboard, 1<=k<=n.
- A153126 (program): Sums of rows of the triangle in A153125.
- A153127 (program): a(n) = (2*n + 1)*(5*n + 6).
- A153129 (program): Numbers n such that 8*n + 5 is not prime.
- A153130 (program): Period 6: repeat [1, 2, 4, 8, 7, 5].
- A153134 (program): Numbers n such that 6n - 7 is prime.
- A153135 (program): Primes p such that 6*p - 7 is also prime.
- A153141 (program): Permutation of nonnegative integers: A059893-conjugate of A153151.
- A153142 (program): Permutation of nonnegative integers: A059893-conjugate of A153152.
- A153143 (program): Nonnegative numbers n such that 2n + 19 is prime.
- A153144 (program): Numbers n such that 2*n+19 is not a prime.
- A153145 (program): Primes p such that 2*p + 19 is also prime.
- A153146 (program): Numbers n such that 2*n + 19 and 2*n - 19 are prime.
- A153147 (program): a(n) = A007916(n)^3.
- A153150 (program): Self-inverse permutation of natural numbers: A059893-conjugate of A056539.
- A153151 (program): Rotated binary decrementing: For n<2 a(n) = n, if n=2^k, a(n) = 2*n-1, otherwise a(n) = n-1.
- A153152 (program): Rotated binary incrementing: For n<2 a(n)=n, if n=(2^k)-1, a(n)=(n+1)/2, otherwise a(n)=n+1.
- A153153 (program): Permutation of natural numbers: A059893-conjugate of A003188.
- A153154 (program): Permutation of natural numbers: A059893-conjugate of A006068.
- A153157 (program): A007916(n)^4.
- A153158 (program): a(n) = A007916(n)^2.
- A153159 (program): A007916(n)^5.
- A153160 (program): A007916(n)^6.
- A153161 (program): Numerators of Stern-Brocot tree hanging between 1/3 and 2/3; denominators=A153162.
- A153162 (program): Denominators of Stern-Brocot tree hanging between 1/3 and 2/3; numerators=A153161.
- A153165 (program): Primes of form 6k+1 that use only digits 2 and 3.
- A153169 (program): a(n) = 4*n^2 + 12*n + 3.
- A153170 (program): Numbers k such that 3*k + 2 is not prime.
- A153171 (program): First differences of A046163.
- A153173 (program): a(n) = L(5*n)/L(n) where L(n) = Lucas number A000204(n).
- A153183 (program): Numbers k such that 3k-2 is prime.
- A153184 (program): Numbers n such that 3*n-2 is not prime.
- A153186 (program): Period 9: repeat 1,7,4,7,4,7,1,1,1.
- A153187 (program): Triangle sequence: T(n, k) = -Product_{j=0..k+1} ((n+1)*j - 1).
- A153188 (program): Triangle sequence: t(n,m)=Product[m*k, {k, 1, n}].
- A153189 (program): Triangle T(n,k) = Product_{j=0..k} n*j+1.
- A153190 (program): Triangle read by rows: t(n,m)=If[m == 0, 1, Product[m*k + 2, {k, 0, n}]].
- A153191 (program): a(n) = 9*a(n-1) + 6*a(n-2); a(0)=0, a(1)=1.
- A153192 (program): Numbers such that the numerator of floor(sqrt(n))/n, when reduced to its lowest terms, is equal to 2.
- A153193 (program): a(n) is the number of integers of the form n*(n+1)*k / (k - n*(n+1)) where k is an integer >= 1.
- A153194 (program): Numbers such that the numerator of floor(sqrt(n))/n, when reduced to its lowest terms, is equal to 3.
- A153196 (program): Numbers n such that 6*n+5 and 6*n+7 are twin primes.
- A153211 (program): Sum of digits of n, times digital reversal of sum of digits of n.
- A153217 (program): a(n)=n^(n+3)-(n+3)^n.
- A153218 (program): Numbers n such that 6n + 7 is prime.
- A153219 (program): Numbers n such that 6*n + 7 is not prime.
- A153229 (program): a(0) = 0, a(1) = 1, and for n>=2, a(n) = (n-1) * a(n-2) + (n-2) * a(n-1).
- A153231 (program): a(n) = 2^n * binomial(3n,n)/(2n+1).
- A153232 (program): a(n) = Sum((-1)^(n-i)*binomial(3i,i)*binomial(n+2i,3i)*2^i/(2i+1),i=0..n).
- A153234 (program): a(n) = floor(2^n/9).
- A153235 (program): Numbers n such that 8*n+7 is not prime.
- A153236 (program): Numbers n such that 8*n + 3 is not prime.
- A153237 (program): a(n) = A000079(n) - A153130(n).
- A153238 (program): Numbers k such that 2*k + 3 is composite.
- A153245 (program): Numbers n>1 such that 6*n-7 is not prime.
- A153246 (program): Number of fleeing trees computed for Catalan bijection A057164.
- A153257 (program): a(n) = n^3-(n+1)^2.
- A153258 (program): n^3 - (n+2)^2.
- A153259 (program): a(n)=n^3-(3*(n+3))^2.
- A153260 (program): a(n) = n^3 - 3*(n+3)^2.
- A153261 (program): Primes p such that 3*p-2 is not prime.
- A153263 (program): a(n) = A014217(n+3) - A014217(n).
- A153264 (program): Numbers n such that 16*n+15 is not prime.
- A153270 (program): Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 2, read by rows.
- A153271 (program): Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 3, read by rows.
- A153272 (program): Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 4, read by rows.
- A153273 (program): Triangle read by rows: T(n,k) = Product_{i=0..k-2} (i*n + n - 1).
- A153274 (program): Triangle, read by rows, T(n,k) = k^(n+1) * Pochhammer(1/k, n+1).
- A153275 (program): Numbers n such that 10*n+1 is not prime.
- A153276 (program): Numbers n >= 0 such that 5*n+6 is not prime.
- A153279 (program): Eigentriangle by rows, T(n,k) = A000079(n-k) * (diagonalized matrix of (1,1,3,9,27,81,…)).
- A153280 (program): Eigensequence of triangle A153279
- A153281 (program): Triangle read by rows, A130321 * A127647. Also, number of subsets of [n+2] with consecutive integers that start at k.
- A153282 (program): Numbers k such that 3*k + 4 is not prime.
- A153284 (program): a(n) = n + Sum_{j=1..n-1} (-1)^j * a(j) for n >= 2, a(1) = 1.
- A153285 (program): a(1)=1; for n > 1, a(n) = n^2 + Sum_{j=1..n-1} (-1)^j*a(j).
- A153286 (program): a(n) = n^3 + sum((-1)^j*a(j)); for j=1 to n-1; a(1)=1.
- A153287 (program): First differences of A152738.
- A153291 (program): G.f.: A(x) = F(x*F(x)) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764.
- A153299 (program): G.f.: A(x) = F(x*G(x)) where F(x) = G(x*F(x)) = 1 + x*F(x)^3 is the g.f. of A001764 and G(x) = F(x/G(x)) = 1 + x*G(x)^2 is the g.f. of A000108 (Catalan).
- A153307 (program): Numbers n such that 14*n+3 is not prime.
- A153308 (program): Numbers n such that 10*n+7 is not prime.
- A153309 (program): Numbers k such that 3*k + 1 is not prime.
- A153315 (program): Denominators of continued fraction convergents to sqrt(5/4).
- A153316 (program): Numerators of continued fraction convergents to sqrt(5/4).
- A153317 (program): Denominators of continued fraction convergents to sqrt(6/5).
- A153318 (program): Numerators of continued fraction convergents to sqrt(6/5).
- A153319 (program): Primes p such that 6*p-7 is not prime.
- A153327 (program): Numbers n such that 16*n+5 is not prime.
- A153329 (program): Numbers k such that 5*k + 1 is not prime.
- A153330 (program): Differences in adjacent elements of the sequence quantifying the steps needed for n to converge to 1 in the Collatz Conjecture.
- A153334 (program): Number of zig-zag paths from top to bottom of an n X n square whose color is that of the top right corner.
- A153335 (program): Number of zig-zag paths from top to bottom of an n X n square whose color is not that of the top right corner.
- A153336 (program): Number of zig-zag paths from top to bottom of a 2n by 2n square whose color is that of the top right corner
- A153337 (program): Number of zig-zag paths from top to bottom of a 2n-1 by 2n-1 square whose color is that of the top right corner
- A153338 (program): Number of zig-zag paths from top to bottom of a 2n-1 by 2n-1 square whose color is not that of the top right corner.
- A153339 (program): Number of zig-zag paths from top to bottom of a rectangle of width 5 with n rows whose color is that of the top right corner
- A153340 (program): Number of zig-zag paths from top to bottom of a rectangle of width 8 with n rows.
- A153342 (program): Binomial transform of triangle A046854 (shifted).
- A153343 (program): Numbers k such that 5*k + 4 is not prime.
- A153347 (program): Numbers n>0 such that 7*n-4 is not prime.
- A153348 (program): Numbers n such that 16*n+3 is not prime.
- A153349 (program): Period 6: repeat [1, 7, 4, 4, 7, 1].
- A153350 (program): Numbers n such that 7n+11 is not prime.
- A153351 (program): Numbers n such that 7*n+2 is not prime.
- A153355 (program): Numbers k such that 5k-1 is a prime.
- A153360 (program): Number of zig-zag paths from top to bottom of a rectangle of width 10 with n rows.
- A153362 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with n rows.
- A153363 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with n rows whose color is that of the top right corner
- A153364 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with n rows whose color is not that of the top right corner
- A153365 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with 2n rows whose color is that of the top right corner.
- A153366 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with 2n-1 rows whose color is that of the top right corner.
- A153367 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with 2n-1 rows whose color is not that of the top right corner.
- A153368 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows.
- A153369 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows whose color is that of the top right corner.
- A153370 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows whose color is not that of the top right corner.
- A153371 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n rows whose color is that of the top right corner.
- A153372 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n-1 rows whose color is that of the top right corner.
- A153373 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n-1 rows whose color is not that of the top right corner.
- A153380 (program): Numbers n such that 10*n+9 is not prime.
- A153381 (program): Numbers n such that 11*n+5 is not prime.
- A153382 (program): a(n)=a(n-1)+2a(n-2)-a(n-3)-a(n-4), a(0)=0,a(1)=8,a(2)=10,a(3)=18.
- A153383 (program): Numbers n such that 12*n+1 is not prime.
- A153384 (program): Numbers n such that 24*n+1 is not prime.
- A153388 (program): Second bisection of A153382.
- A153400 (program): Numbers n such that 18*n+1 is not prime.
- A153403 (program): Numbers n such that 10*n+3 is not prime.
- A153417 (program): Primes p such that p+14 is also prime.
- A153418 (program): Primes p such that p+18 is also prime.
- A153419 (program): Primes p such that p+20 is also prime.
- A153422 (program): Primes of the form n^2+15n+13
- A153423 (program): Primes of the form n^2+9n+241.
- A153424 (program): Primes of the form n^2+3n+223
- A153426 (program): a(n) = (n+1)! mod prime(n).
- A153435 (program): Numbers with 2n binary digits where every run length is 2, written in binary.
- A153448 (program): 3 times 12-gonal (or dodecagonal) numbers: 3*n*(5*n-4).
- A153449 (program): 11 times pentagonal numbers: 11*n*(3n-1)/2.
- A153464 (program): Numbers n such that 4*n+9 is not prime.
- A153465 (program): 9*4^n - 2.
- A153466 (program): a(n) = A027941(n) + A027941(n+6).
- A153478 (program): Sum of first n isolated (or single) primes A007510.
- A153480 (program): a(n) = 2*prime(n)^2 - 4.
- A153481 (program): a(n) = prime(n)^3 - 2.
- A153482 (program): a(n) = prime(n)^4 - 8.
- A153483 (program): a(n) = prime(n)^4 - 32.
- A153484 (program): a(n) = prime(n)^5 - 128.
- A153485 (program): Sum of all aliquot divisors of all positive integers <= n.
- A153486 (program): a(n) = prime(n)^6 - 512.
- A153490 (program): Sierpinski carpet, read by antidiagonals.
- A153491 (program): Triangle T(n,m)= 11*binomial(n,k) - 8 read by rows, 0<=k<=n.
- A153497 (program): a(n) is the number whose binary expansion is A153498(n).
- A153498 (program): Palindromes formed from concatenation of A147759(n) and the same string A147759(n) but without its initial digit.
- A153499 (program): a(n) is the number whose binary expansion is A153500(n).
- A153500 (program): First 3 terms coincide with A152756. For n>3, a(n) is the palindromic number formed from concatenation of 1, 0, A147759(n-3), 0, A147759(n-3), 0 and 1.
- A153502 (program): Primes of the form 3*n^2 - 3*n + 11.
- A153509 (program): Period 9: repeat [6, 6, 6, 3, 3, 3, 0, 0, 0].
- A153511 (program): a(n) = 4 * A051189(n).
- A153587 (program): a(n) = n mod (A062383(n) - n).
- A153590 (program): Primes p such that p^2 + 3p + 1 is also prime.
- A153591 (program): Primes p such that 6p^2+6p+1 is also prime.
- A153593 (program): a(n) = ((9 + sqrt(2))^n - (9 - sqrt(2))^n)/(2*sqrt(2)).
- A153594 (program): a(n) = ((4 + sqrt(3))^n - (4 - sqrt(3))^n)/(2*sqrt(3)).
- A153596 (program): a(n) = ((5 + sqrt(3))^n - (5 - sqrt(3))^n)/(2*sqrt(3)).
- A153597 (program): a(n) = ((6 + sqrt(3))^n - (6 - sqrt(3))^n)/(2*sqrt(3)).
- A153598 (program): a(n) = ((7 + sqrt(3))^n - (7 - sqrt(3))^n)/(2*sqrt(3)).
- A153599 (program): a(n) = ((8 + sqrt(3))^n - (8 - sqrt(3))^n)/(2*sqrt(3)).
- A153600 (program): a(n) = ((9 + sqrt(3))^n - (9 - sqrt(3))^n)/(2*sqrt(3)).
- A153638 (program): Odiousness of triangular numbers.
- A153639 (program): Evilness of triangular numbers.
- A153642 (program): a(n) = 4*n^2 + 24*n + 8.
- A153643 (program): Jacobsthal numbers A001045 incremented by 2.
- A153644 (program): a(n) = 4*n^2 + 28*n + 10.
- A153647 (program): a(n) = 3^n*(n + 2)!.
- A153659 (program): Triangle read by rows. A074206 interleaved with k-1 zeros in the k-th column.
- A153703 (program): Partial sums of A069996.
- A153709 (program): Expansion of (1 + 7*x)/(1 - 11*x - 26*x^2).
- A153726 (program): Initial digit of Catalan number A000108(n).
- A153727 (program): Period 3: repeat [1, 4, 2] ; Trajectory of 3x+1 sequence starting at 1.
- A153728 (program): Expansion of q^(-1/3) * (eta(q)^8 + 8 * eta(q^4)^8) in powers of q^2.
- A153729 (program): Expansion of q^(-1/3) * (eta(q)^8 + 32 * eta(q^4)^8) in powers of q.
- A153732 (program): Binomial transform of A109747.
- A153733 (program): Remove all trailing 1’s in the binary representation of n.
- A153757 (program): a(n) = Sum_{k=1..n} A003266(k).
- A153758 (program): a(n) = Sum_{k=1..n} A153757(k).
- A153760 (program): Number of degree-n permutations of order exactly 7.
- A153762 (program): Numbers n such that 8n + 9 is prime.
- A153763 (program): Numbers k >= 0 such that 8*k+9 is not prime.
- A153764 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,0,0,…] DELTA [0,1,0,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A153766 (program): Numbers n such that 8n-9 is prime.
- A153767 (program): Primes p such that 8*p - 9 is also prime.
- A153769 (program): Numbers n such that 8n-9 is not prime.
- A153772 (program): a(n) = (2^n + 2*(-1)^n - 6)/3.
- A153773 (program): a(2*n) = 3*a(2*n-1) - 1, a(2*n+1) = 3*a(2*n), with a(1)=1.
- A153774 (program): a(2*n) = 3*a(2*n-1), a(2*n+1) = 3*a(2*n) - 1, with a(1) = 1.
- A153775 (program): Sequence S such that 1 is in S and if x is in S, then 3x-1 and 3x are in S.
- A153776 (program): Sequence S such that 1 is in S and if x is in S, then 5x-3 and 5x-1 are in S.
- A153777 (program): Sequence S such that 1 is in S and if x is in S, then 5x-1 and 5x+1 are in S.
- A153778 (program): Binary sequence constructed like a Stern-Brocot tree between 0 and 1, where XOR is applied instead of the mediant operation.
- A153780 (program): 10 times pentagonal numbers: a(n) = 5*n*(3*n-1).
- A153781 (program): Numbers n such that n^2+13n+23 is prime.
- A153783 (program): 3 times 11-gonal (or hendecagonal) numbers: 3*n*(9*n-7)/2.
- A153784 (program): 4 times heptagonal numbers: 2n(5n-3).
- A153785 (program): 5 times heptagonal numbers: a(n) = 5*n*(5*n-3)/2.
- A153786 (program): 6 times heptagonal numbers: a(n) = 3*n*(5*n-3).
- A153788 (program): Number of proper divisors of the Catalan number A000108(n).
- A153792 (program): 12 times pentagonal numbers: a(n) = 6*n*(3*n-1).
- A153793 (program): 13 times pentagonal numbers: a(n) = 13*n*(3*n-1)/2.
- A153794 (program): 4 times octagonal numbers: a(n) = 4*n*(3*n-2).
- A153795 (program): 5 times octagonal numbers: a(n) = 5*n*(3*n-2).
- A153796 (program): 6 times octagonal numbers: a(n) = 6*n*(3*n-2).
- A153797 (program): 7 times octagonal numbers: a(n) = 7*n*(3*n-2).
- A153799 (program): Decimal expansion of 4 - Pi.
- A153805 (program): Decimal expansion of 3-e.
- A153808 (program): 8 times octagonal numbers: 8*n*(3*n-2).
- A153809 (program): Complement of A134928.
- A153814 (program): a(n) = 1001*n.
- A153817 (program): a(n)=Sum_{k=1..n} floor((n*k)/(n+k)).
- A153818 (program): a(n) = Sum_{k=1..n} floor(n^2/k^2).
- A153819 (program): Linear recurrence with a(n) = 3a(n-1) - a(n-2) + 2 = 4a(n-1) - 4a(n-2) + a(n-3). Full sequence for A153466.
- A153823 (program): Number of proper divisors of n!.
- A153824 (program): Sum of proper divisors of n!: a(n) = sigma(n!) - n!.
- A153836 (program): a(n) = 2^(n^2) - 2^(n^2 - n + 1) for n >= 1; a(0) = 0.
- A153839 (program): First Sunday in n-th month of 365-day year starting on Sunday
- A153840 (program): First Sunday in the n-th month of a 365-day year starting on Monday.
- A153841 (program): First Sunday in n-th month of 365-day year starting on Tuesday
- A153842 (program): First Sunday in n-th month of 365-day year starting on Wednesday
- A153843 (program): First Sunday in n-th month of 365-day year starting on Thursday
- A153844 (program): First Sunday in n-th month of 365-day year starting on Friday
- A153845 (program): First Sunday in n-th month of 365-day year starting on Saturday
- A153848 (program): Repeat 21.
- A153859 (program): Triangle read by rows, A007318 * (A007476 * 0 ^(n-k))
- A153860 (program): Triangle by columns: leftmost column = (1, 0, 1, -1, 1, -1, 1, …); columns >1 = (1, 1, 0, 0, 0, …).
- A153861 (program): Triangle read by rows, binomial transform of triangle A153860.
- A153869 (program): Triangle read by rows, A129186 * A128064(unsigned).
- A153873 (program): a(n) = 9*Fibonacci(2n+1) - 1.
- A153875 (program): 3 times 13-gonal (or tridecagonal) numbers: 3*n*(11*n - 9)/2.
- A153877 (program): Numbers n such that 5n-1 and 5n+1 are both prime.
- A153880 (program): Shift factorial base representation left by one digit.
- A153881 (program): 1 followed by -1, -1, -1, … .
- A153882 (program): a(n) = ((6 + sqrt(5))^n - (6 - sqrt(5))^n)/(2*sqrt(5)).
- A153883 (program): A153880(n)/2
- A153884 (program): a(n) = ((7 + sqrt(5))^n - (7 - sqrt(5))^n)/(2*sqrt(5)).
- A153885 (program): a(n) = ((8 + sqrt(5))^n - (8 - sqrt(5))^n)/(2*sqrt(5)).
- A153886 (program): a(n) = ((9 + sqrt(5))^n - (9 - sqrt(5))^n)/(2*sqrt(5)).
- A153893 (program): a(n) = 3*2^n - 1.
- A153894 (program): a(n) = 5*2^n - 1.
- A153972 (program): a(n) = 2^n + 6.
- A153973 (program): a(n) = 3*a(n-1) - 2*a(n-2), with a(1) = 9, a(2) = 12.
- A153974 (program): Numbers n such that n^3 - 3 is prime.
- A153976 (program): a(n) = n^3 + (n+2)^3.
- A153977 (program): One-fourth of partial sums of A153976.
- A153978 (program): a(n) = n*(n-1)*(n+1)*(3*n-2)/12.
- A153979 (program): Prime sums of prime factors of composite(k)=A002808(k).
- A153981 (program): a(n) = 36*Fibonacci(2*n+1) - 4.
- A153990 (program): Period 6: repeat [1, 2, 5, 4, 7, 8].
- A154021 (program): a(n+2) = 16*a(n+1) - a(n), with a(1)=0, a(2)=4.
- A154022 (program): a(n) = 5*A097780(n-2).
- A154023 (program): a(n+2) = 36*a(n+1) - a(n), a(1)=0, a(2)=6.
- A154024 (program): a(n+2) = 49*a(n+1) - a(n), a(1)=0, a(2)=7.
- A154025 (program): a(n+2) = 64*a(n+1) - a(n), a(1)=0, a(2)=8.
- A154026 (program): a(n+2) = 81*a(n+1) - a(n), a(1)=0, a(2)=9.
- A154027 (program): a(n+2) = 100*a(n+1) - a(n), a(1)=0, a(2)=10.
- A154028 (program): a(2n) = n*(n+1)/2, a(2n+1) = n!.
- A154029 (program): List of pairs of numbers: {n^2-1, (2*n-1)!!} such that F((2*n-1)!!) = n^2 - 1.
- A154030 (program): Sequence defined by a(2*n) = 2*(n^2 + 2*n) and a(2*n-1) = (2*n)!/n!.
- A154032 (program): Number of planar triangular n X n X n nonnegative integer grids symmetric under 120 degree rotation with every similarly oriented 2 X 2 X 2 subtriangle summing to 3.
- A154105 (program): a(n) = 12*n^2 + 18*n + 7.
- A154106 (program): a(n) = 12*n^2 + 22*n + 11.
- A154108 (program): A000110 / (1,2,3,…): (convolved with (1,2,3,…) = Bell numbers.
- A154112 (program): Numbers n such that (n+1)^3 - n^2 is prime.
- A154113 (program): Primes of the form (n+1)^3 - n^2.
- A154115 (program): Numbers n such that n + 3 is prime.
- A154117 (program): Expansion of (1 - x + 3*x^2)/((1-x)*(1-2*x)).
- A154118 (program): Expansion of (1 - x + 5x^2)/((1-x)*(1-2x)).
- A154120 (program): Array read by antidiagonals: T(n,k) = (k+1)^n*(n+k)!.
- A154127 (program): Period 6: repeat [1, 2, 5, 8, 7, 4].
- A154128 (program): a(n) = 5^n*(n+4)!/n!.
- A154129 (program): a(n) = (A132207(n)-1)/3.
- A154138 (program): Indices k such that 3 plus the k-th triangular number is a perfect square.
- A154139 (program): Indices k such that 4 plus the k-th triangular number is a perfect square.
- A154140 (program): Indices k such that 6 plus the k-th triangular number is a perfect square.
- A154141 (program): Indices k such that 8 plus the k-th triangular number is a perfect square.
- A154142 (program): Indices k such that 9 plus the k-th triangular number is a perfect square.
- A154143 (program): Indices k such that 10 plus the k-th triangular number is a perfect square.
- A154144 (program): Indices k such that 13 plus the k-th triangular number is a perfect square.
- A154146 (program): Numbers k such that 16 plus the k-th triangular number is a perfect square.
- A154147 (program): Indices k such that 19 plus the k-th triangular number is a perfect square.
- A154148 (program): Numbers k such that 21 plus the k-th triangular number is a perfect square.
- A154149 (program): Indices k such that 22 plus the k-th triangular number is a perfect square.
- A154150 (program): Numbers k such that 24 plus the k-th triangular number is a perfect square.
- A154151 (program): Indices k such that 25 plus the k-th triangular number is a perfect square.
- A154152 (program): Indices k such that 26 plus the k-th triangular number is a perfect square.
- A154153 (program): Numbers k such that 28 plus the k-th triangular number is a perfect square.
- A154154 (program): Numbers k such that 30 plus the k-th triangular number is a perfect square.
- A154221 (program): A simple Pascal-like triangle.
- A154222 (program): Row sums of number triangle A154221.
- A154223 (program): Diagonal sums of number triangle A154221.
- A154225 (program): List of pairs: {n*(n + 1)*(2*n + 1)/6, (n!)^2}.
- A154226 (program): List of pairs: {(n*(n+1)/2)^2, (n!)^3}.
- A154232 (program): a(2n) = (n^2-n-1) + a(2n-2), a(2n+1) = (n^2-n-1)*a(2n-1), with a(0)=0 and a(1)=1.
- A154234 (program): Triangle read by rows: T(n,k) = (n mod d(k)), where d(i) is the number of divisors of i.
- A154235 (program): a(n) = ( (4 + sqrt(6))^n - (4 - sqrt(6))^n )/(2*sqrt(6)).
- A154236 (program): a(n) = ( (5 + sqrt(6))^n - (5 - sqrt(6))^n )/(2*sqrt(6)).
- A154237 (program): a(n) = ( (6 + sqrt(6))^n - (6 - sqrt(6))^n )/(2*sqrt(6)).
- A154239 (program): a(n) = ( (7 + sqrt(6))^n - (7 - sqrt(6))^n )/(2*sqrt(6)).
- A154240 (program): a(n) = ( (8 + sqrt(6))^n - (8 - sqrt(6))^n )/(2*sqrt(6)).
- A154241 (program): a(n) = ( (9 + sqrt(6))^n - (9 - sqrt(6))^n )/(2*sqrt(6)).
- A154244 (program): a(n) = 6*a(n-1) - 2*a(n-2) for n>1; a(1)=1, a(2)=6.
- A154245 (program): a(n) = ( (4 + sqrt(7))^n - (4 - sqrt(7))^n )/(2*sqrt(7)).
- A154246 (program): a(n) = ( (5 + sqrt(7))^n - (5 - sqrt(7))^n )/(2*sqrt(7)).
- A154247 (program): a(n) = ( (6 + sqrt(7))^n - (6 - sqrt(7))^n )/(2*sqrt(7)).
- A154248 (program): a(n) = ( (7 + sqrt(7))^n - (7 - sqrt(7))^n )/(2*sqrt(7)).
- A154249 (program): a(n) = ( (8 + sqrt(7))^n - (8 - sqrt(7))^n )/(2*sqrt(7)).
- A154250 (program): a(n) = ( (9 + sqrt(7))^n - (9 - sqrt(7))^n )/(2*sqrt(7)).
- A154251 (program): Expansion of (1-x+7x^2)/((1-x)(1-2x)).
- A154252 (program): Expansion of (1-x+8x^2)/((1-x)(1-2x)) .
- A154253 (program): Primes of the form 9n^2-8n+2.
- A154254 (program): a(n) = 9n^2 - 8n + 2.
- A154260 (program): Numbers of the form m*(4*m +- 1)/2.
- A154261 (program): Primes of the form 9n^2-10n+3.
- A154262 (program): a(n) = 9*n^2 - 10*n + 3.
- A154264 (program): Nonnegative numbers n such that 9*n^2 - 10*n + 3 is prime.
- A154266 (program): a(n) = 27*n + 12.
- A154267 (program): a(n) = 27*n + 15.
- A154269 (program): Dirichlet inverse of A019590; Fully multiplicative with a(2^e) = (-1)^e, a(p^e) = 0 for odd primes p.
- A154271 (program): Dirichlet inverse of A154272; Fully multiplicative with a(3^e) = (-1)^e, a(p^e) = 0 for primes p <> 3.
- A154272 (program): 1,0,1 followed by 0,0,0,…
- A154276 (program): Primes of the form 81*n^2 - 72*n + 17.
- A154277 (program): a(n) = 81*n^2 - 72*n + 17.
- A154281 (program): 1,0,0,1 followed by 0,0,0…
- A154282 (program): Dirichlet inverse of A154281.
- A154286 (program): a(n) = E(k)*C(n+k,k) = Euler(k)*binomial(n+k,k) for k=4.
- A154287 (program): (L)-sieve transform of {1,4,9,16,…,n^2,…}=A000290.
- A154292 (program): Integers of the form m*(6*m -+ 1)/2.
- A154293 (program): Integers of the form t/6, where t is a triangular number (A000217).
- A154295 (program): a(n) = 81*n^2 - 90*n + 26.
- A154306 (program): a(n) = (n+1)^3*(3+n)!/6.
- A154307 (program): a(n) = (n+1)^4*(4+n)!/24.
- A154308 (program): a(n) = (n+1)^5*(5+n)!/120.
- A154312 (program): Triangle T(n,k), 0<=k<=n, read by rows, given by [0,1/2,-1/2,0,0,0,0,0,0,0,…] DELTA [2,-1/2,-1/2,2,0,0,0,0,0,0,0 …] where DELTA is the operator defined in A084938 .
- A154318 (program): Numbers n such that nonprime(prime(n))+1 is prime.
- A154319 (program): Primes p such that p^2 + 2*p - 4 is also prime.
- A154320 (program): Primes p such that p^2 + 8*p - 4 is also prime.
- A154322 (program): a(n) = 1 + n + binomial(n+3,5).
- A154323 (program): Central coefficients of number triangle A113582.
- A154324 (program): Diagonal sums of number triangle A113582.
- A154325 (program): Triangle with interior all 2’s and borders 1.
- A154327 (program): Diagonal sums of number triangle A132046.
- A154331 (program): Numbers m such that 12 m^2 is the average of a twin prime pair.
- A154333 (program): Difference between n^3 and the next smaller square
- A154334 (program): A triangular sequence of coefficients of polynomials: p(x,n) = ((x - 1)^n *(Sum_{k>=0} (((-1)^n*(2*k + 1)^(n - 1)))*x^k) + (x - 1)^(n + 1)*(Sum_{k>=0} ((-1)^(n + 1)*k^n)*x^k)/x)/2.
- A154335 (program): A triangular sequence of coefficients of polynomials: p(x,n) = (2*(x - 1)^n * (Sum_{k>=0} (((-1)^n*(2*k + 1)^(n - 1)))*x^k) - (x - 1)^(n + 1)*(Sum_{k>=0} ((-1)^(n + 1)*k^n)*x^k)/x).
- A154336 (program): A triangular sequence of coefficients of polynomials: p(x,n)=(3*(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k,0, Infinity}] -2*(x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x).
- A154337 (program): A triangular sequence of coefficients of polynomials: p(x,n)=(3*(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k,0, Infinity}] -(x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x)/2.
- A154338 (program): A triangular sequence of coefficients of polynomials: p(x,n)=(-(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k,0, Infinity}]+2*(x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x).
- A154340 (program): a(n) = ( (5 + 2*sqrt(2))^n - (5 - 2*sqrt(2))^n )/(4*sqrt(2)).
- A154346 (program): a(n) = 12*a(n-1) - 28*a(n-2) for n > 1, with a(0)=1, a(1)=12.
- A154347 (program): a(n) = ( (7 + 2*sqrt(2))^n - (7 - 2*sqrt(2))^n )/(4*sqrt(2)).
- A154348 (program): a(n) = 16*a(n-1) - 56*a(n-2) for n>1, with a(0)=1, a(1)=16.
- A154350 (program): a(n) = ( (9 + 2*sqrt(2))^n - (9 - 2*sqrt(2))^n )/(4*sqrt(2)).
- A154351 (program): a(n) = number of distinct values of A056239(m) when A153452(m) is equal to n.
- A154355 (program): a(n) = 25*n^2 - 36*n + 13.
- A154356 (program): Primes of the form 25n^2-14n+2 for n >= 0.
- A154357 (program): a(n) = 25*n^2 - 14*n + 2.
- A154358 (program): a(n) = 1250*n^2 - 1800*n + 649.
- A154359 (program): a(n) = 1250*n^2 - 700*n + 99.
- A154360 (program): a(n) = 250*n - 180.
- A154361 (program): a(n) = 250*n - 70.
- A154370 (program): Numbers k such that gpf(composite(k)) - lpf(composite(k)) is prime.
- A154371 (program): Composites with largest prime factor - smallest prime factor = prime.
- A154372 (program): Triangle T(n,k) = (k+1)^(n-k)*binomial(n,k).
- A154374 (program): a(n) = 1250*n^2 - 100*n + 1.
- A154375 (program): a(n) = 1250*n^2 + 100*n + 1.
- A154376 (program): a(n) = 25*n^2 - 2*n.
- A154377 (program): a(n) = 25*n^2 + 2*n.
- A154378 (program): a(n) = 250*n - 10.
- A154379 (program): a(n) = 250*n + 10.
- A154381 (program): Row sums of Bell related number triangle A154380.
- A154383 (program): Powers of 4 at even indices, two times powers of 4 at odd indices.
- A154384 (program): Odd nonprimes with odd sum of digits.
- A154387 (program): Composite numbers with even sum of digits.
- A154388 (program): Triangle T(n,k), 0<=k<=n, read by rows given by [0,1,-1,0,0,0,0,0,0,0,…] DELTA [1,-1,-1,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A154392 (program): Number of zeros of sin(x^2) in integer intervals starting with (0,1).
- A154402 (program): Inverse Moebius transform of Fredholm-Rueppel sequence, cf. A036987.
- A154405 (program): Primes of the form 20n^2+8n+1.
- A154406 (program): Larger twin primes in A061237.
- A154407 (program): a(n) = 5*2^(n-1) + 3*6^n/2.
- A154409 (program): Primes of the form 10n^2+6n+1.
- A154410 (program): a(n) = 5*(3*6^n + 2^n)/2.
- A154412 (program): Primes of the form 10n^2+14n+5, n >= 0.
- A154414 (program): Primes of the form 20n^2+32n+13.
- A154419 (program): Primes of the form 20*k^2 + 36*k + 17.
- A154420 (program): Maximal coefficient of MacMahon polynomial (cf. A060187) p(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; that is, a(n) = Max(coefficients(p(x,n)).
- A154426 (program): a(n) = n + (sum of preceding terms) mod n; a(0) = 0.
- A154428 (program): Primes of the form 50n^2 + 10n + 1.
- A154432 (program): Numbers k such that 5k^2-k+1 is prime.
- A154435 (program): Permutation of nonnegative integers induced by Lamplighter group generating wreath recursion, variant 3: a = s(b,a), b = (a,b), starting from the state a.
- A154436 (program): Permutation of nonnegative integers induced by Lamplighter group generating wreath recursion, variant 1: a = s(a,b), b = (a,b), starting from the state a.
- A154437 (program): Permutation of nonnegative integers: A059893-conjugate of A154435.
- A154438 (program): Permutation of nonnegative integers: A059893-conjugate of A154436.
- A154503 (program): Numbers n of A144571
- A154506 (program): Primes of the form concatenation(A141468(k), k).
- A154508 (program): Numbers k such that appending k to the k-th nonprime yields a prime.
- A154510 (program): Primes of the form 648*n^2 + 72*n + 1.
- A154511 (program): Primes of the form 648n^2 - 72n + 1.
- A154514 (program): a(n) = 648*n^2 - 72*n + 1.
- A154515 (program): a(n) = 648*n^2 + 72*n + 1.
- A154516 (program): a(n) = 9n^2 - n.
- A154517 (program): a(n) = 9*n^2 + n.
- A154518 (program): a(n) = 216*n - 12.
- A154519 (program): a(n) = 216*n + 12.
- A154529 (program): A090040 mod 9.
- A154533 (program): Number of constants of the form a^3*u + b*c*v, where a, b, c are linear, u of order n-3 and v of order n-2.
- A154546 (program): Numbers n in A154276.
- A154549 (program): a(n) = 111111*n.
- A154554 (program): Primes p such that m=p-1 is the least number such that p divides m!+1.
- A154556 (program): Exponential Riordan array [exp(-x), x(1+x/2)]
- A154557 (program): Production array of A122848, read by row.
- A154558 (program): Triangle read by rows, A007318 * (A001006 * 0^(n-k))
- A154560 (program): (n+3)^2*n/2 + 1.
- A154563 (program): Averages of twin prime pairs of A074378.
- A154565 (program): One-half of averages of twin prime pairs of A001318.
- A154569 (program): Partial sums of (2n-1)^(2n+1)+(2n+1)^(2n-1).
- A154570 (program): The main diagonal of the successive differences of A154127.
- A154571 (program): Numbers that are congruent to {0, 3, 4, 5, 7, 8} mod 12.
- A154575 (program): a(n) = 2*n^2 + 12*n + 4.
- A154576 (program): a(n) = 2*n^2 + 14*n + 5.
- A154577 (program): Primes of the form 2n^2+14n+5.
- A154585 (program): a(n) = abs(Sum_{k=1..n} (-1)^k * (n-k+1 mod k)).
- A154589 (program): a(n)=A154570(n)+A154570(n+1).
- A154590 (program): 2n^2+16n+6.
- A154591 (program): a(n) = 2*n^2 + 18*n + 7.
- A154592 (program): Primes of the form 2n^2+18n+7, n>=0.
- A154595 (program): Period 6: repeat [1, 3, 3, -1, -3, -3].
- A154597 (program): a(n) = 15*a(n-1) + a(n-2) with a(0) = 0, a(1) = 1.
- A154599 (program): a(n) = 2*n^2 + 20*n + 8.
- A154600 (program): a(n) = 2*n^2 + 22*n + 9.
- A154601 (program): Primes of the form 2*n^2 + 22*n + 9.
- A154603 (program): Binomial transform of reduced tangent numbers (A002105).
- A154604 (program): Hankel transform of reduced tangent numbers.
- A154605 (program): Decimal expansion of 2/(4th root of 3).
- A154607 (program): Numbers n such that 11*n + 4 is prime.
- A154608 (program): Primes p such that 11*p + 4 is also prime.
- A154609 (program): a(n) = 13*n + 5.
- A154610 (program): Numbers n such that 13n + 5 is prime.
- A154611 (program): Numbers n such that 7*n+3 is not prime.
- A154612 (program): 17n + 7.
- A154613 (program): Prime p such that 23p + 10 is prime.
- A154614 (program): Triangle read by rows where T(m,n) = m*n + m + n - 1, 1<=n<=m.
- A154615 (program): a(n) = A022998(n)^2.
- A154616 (program): Primes of the form (4*n^2-8*n-9)/3.
- A154617 (program): Eleven times hexagonal numbers: 11*n*(2*n-1).
- A154618 (program): Triangle read by rows: integer values of T(n,m) = (4*m*n+2*m+2*n-3)/3.
- A154619 (program): Primes of the form (4k^2 + 4k - 5)/5.
- A154620 (program): Primes p such that 31p+14 is prime.
- A154621 (program): Primes congruent to 32 mod 67.
- A154623 (program): Sequence with g.f. 1+(x/(1-5*x))*c(x/(1-5*x)), c(x) the g.f. of A000108.
- A154624 (program): Primes congruent to 34 mod 71.
- A154626 (program): a(n) = 2^n*A001519(n).
- A154627 (program): Expansion of (1-5x)/(1-8x+4x^2).
- A154628 (program): Primes congruent to 35 mod 73
- A154629 (program): Period 9: repeat [9, 3, 1, 3, 3, 1, 3, 9, 1].
- A154631 (program): Triangle read by rows: T(m,n) = 2mn + m + n + 5.
- A154633 (program): a(n) = (4*n+1)*(4*n+3)*(4*n+5)*(4*n+7).
- A154635 (program): Ratio of the sum of the bends of the 5-dimensional spheres added in the n-th generation of Apollonian packing to the sum of the bends of the initial configuration of seven mutually tangent spheres.
- A154636 (program): a(n) is the ratio of the sum of the bends of the circles that are drawn in the n-th generation of Apollonian packing to the sum of the bends of the circles in the initial configuration of 3 circles.
- A154637 (program): a(n) is the ratio of the sum of squares of the bends of the circles that are added in the n-th generation of Apollonian packing, to the sum of squares of the bends of the initial three circles.
- A154638 (program): a(n) is the number of distinct reduced words of length n in the Coxeter group of “Apollonian reflections” in three dimensions.
- A154648 (program): Primes of the form n^2 - 13.
- A154669 (program): Averages k of twin prime pairs such that 2*k^3 + 12*k^2 is a square.
- A154670 (program): Averages of twin prime pairs k such that k*2 and k/2 are squares.
- A154671 (program): Averages of twin prime pairs k such that k*3 and k/3 are squares.
- A154680 (program): Triangle read by rows where T(m,n)=2*m*n + m + n - 2.
- A154681 (program): Triangle read by rows where T(m,n) = 2*m*n + m + n +3.
- A154682 (program): (2n-1)^(2n+1) + (2n+1)^(2n-1).
- A154684 (program): Triangle read by rows where T(m,n)=2mn + m + n - 3, 1<=n<=m.
- A154685 (program): Triangle read by rows where T(m,n)=2mn+m+n+4
- A154686 (program): Numbers k such that k^3 + 2*k^2 + k + 1 is prime.
- A154687 (program): Period 6: repeat [1, 4, 7, 8, 5, 2].
- A154690 (program): Triangle read by rows: T(n,m) = (2^(n-m) + 2^m)*binomial(n,m), 0 <= m <= n.
- A154691 (program): Expansion of (1+x+x^2) / ((1-x-x^2)*(1-x)).
- A154693 (program): Triangle T(n,m) = ( 2^(n-m)+2^m )*A008292(n+1,m+1) read by rows.
- A154695 (program): Generalized Sierpinski-Pascal-MacMahon gasket triangular sequence defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n), where b(n) = coefficients of p(x, n) = 2^n*(1-x)^(n+1) * LerchPhi(x, -n, 1/2), and r=2, q=1.
- A154699 (program): Terms in A014217 pairwise swapped.
- A154708 (program): Numbers a such that b and c exist with b <= a < c and a*(a+1) + b^2 = c^2.
- A154715 (program): Triangle interpolating between the subsets of an n-set (A000079) and the trees on n labeled nodes (A000272) (read by rows).
- A154728 (program): Products of three consecutive primes of the form 6n+1 (see A002476).
- A154736 (program): Define k(0) = 2 and k(m) = m^2-k(m-1) for m >= 1. This is a list of those m for which k(m)+1 and k(m)-1 are both prime.
- A154739 (program): Decimal expansion of sqrt(1 - 1/sqrt(2)), the abscissa of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant.
- A154743 (program): Decimal expansion of 2^(1/4) - 2^(-1/4), the ordinate of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant.
- A154747 (program): Decimal expansion of sqrt(sqrt(2) - 1), the radius vector of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant.
- A154760 (program): Final digit of n!! (A006882).
- A154764 (program): Primes with exactly one odd decimal digit.
- A154766 (program): Numbers n with exactly one even decimal digit in prime(n).
- A154777 (program): Numbers of the form x^2 + 2*y^2 with positive integers x and y.
- A154778 (program): Numbers of the form a^2 + 5b^2 with positive integers a,b.
- A154783 (program): Row sums of triangle in A154720.
- A154784 (program): Row sums of triangle in A154721.
- A154785 (program): Row sums of triangle in A154724.
- A154786 (program): Row sums of triangle in A154725.
- A154787 (program): a(n) = A061357(n)*n = A154786(n)/2.
- A154804 (program): Number of ways to represent 2n as the sum of two distinct primes (counting 1 as a prime).
- A154806 (program): Numbers such that every run length in base 2 is 4.
- A154808 (program): Numbers such that every run length in base 2 is 5.
- A154809 (program): Numbers whose binary expansion is not palindromic.
- A154810 (program): Nonpalindromic numbers with binary digits only.
- A154811 (program): a(n) = Fibonacci(2n+1) mod 9.
- A154815 (program): Period 6: repeat [8, 7, 4, 5, 2, 1].
- A154817 (program): Triangle T(n,k) = A060187(n+2,k+2), 1<=k<=n.
- A154825 (program): Reversion of x*(1-2*x)/(1-3*x).
- A154840 (program): Distance to nearest cube different from n.
- A154870 (program): Period 6: repeat [7, 5, 1, -7, -5, -1].
- A154879 (program): Third differences of the Jacobsthal sequence A001045.
- A154890 (program): Jacobsthal numbers A001045 alternatingly incremented by 3 and 5.
- A154893 (program): Numbers whose number of proper divisors is not a prime number.
- A154920 (program): Denominators of a ternary BBP-type formula for log(3).
- A154921 (program): Triangle read by rows, T(n,k) = C(n,k)*Sum_{j=0..n-k} E(n-k,j)*2^j, where E(n,k) are the Eulerian numbers A173018(n,k), n >= 0, 0 <= k <= n.
- A154926 (program): Signed version of Pascal’s triangle. Diagonal positive, rest negative.
- A154929 (program): A Fibonacci convolution triangle.
- A154930 (program): Inverse of Fibonacci convolution array A154929.
- A154931 (program): Third column of A154921.
- A154948 (program): Riordan array ((1+x)/(1-x^2)^2, x(1+x)/(1-x)).
- A154949 (program): Diagonal sums of Riordan array A154948.
- A154955 (program): a(1) = 1, a(2) = -1, followed by 0, 0, 0, … .
- A154957 (program): A symmetric (0,1)-triangle.
- A154958 (program): Antidiagonal sums of number triangle A154957 regarded as a lower triangular infinite matrix.
- A154964 (program): a(n) = 3*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=1, a(2)=5.
- A154968 (program): a(n) = 4*a(n-1) + 12*a(n-2), n>2 with a(0)=1, a(1)=1, a(2)=7.
- A154990 (program): Triangle read by rows. Main diagonal is positive. The rest of the terms are negative.
- A154992 (program): A048473 prefixed by two zeros.
- A154996 (program): a(n) = 5*a(n-1) + 20*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=9.
- A154997 (program): a(n) = 6*a(n-1) + 30*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=11.
- A154999 (program): a(n) = 7*a(n-1) + 42*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=13.
- A155000 (program): a(n) = 8*a(n-1) + 56*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=15.
- A155001 (program): a(n) = 9*a(n-1) + 72*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=17.
- A155013 (program): Integer part of square root of A000584.
- A155014 (program): a(n) = floor(sqrt(n^7)).
- A155015 (program): Integer part of square root of n^11 = A008455(n).
- A155016 (program): Integer part of square root of A010801.
- A155017 (program): a(n) = 10*a(n-1) + 90*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=19 .
- A155018 (program): Integer part of square root of n^15 = A010803(n).
- A155019 (program): Integer part of square root of n^17 = A010805(n).
- A155020 (program): a(n) = 2*a(n-1) + 2*a(n-2) for n>2, a(0)=1, a(1)=1, a(2)=3.
- A155029 (program): Complement to A051731 with the identity matrix A023531 included.
- A155031 (program): Triangle T(n, k) = 0 if n==0 (mod k) otherwise -1 with T(n, n) = 1 and T(n, 0) = 0, read by rows.
- A155037 (program): Numbers n such that n^3+2*n^2+1 is prime.
- A155038 (program): Triangle read by rows: T(n,k) is the number of compositions of n with first part k.
- A155040 (program): A symmetric (1,-1)-triangle.
- A155041 (program): Diagonal sums of symmetric (1,-1)-triangle A155040.
- A155043 (program): a(0)=0; for n >= 1, a(n) = 1 + a(n-d(n)), where d(n) is the number of divisors of n (A000005).
- A155046 (program): List of pairs: first pair is (1,1); then follow (x,y) with (x+2y, x+y).
- A155047 (program): a(1) = 1, a(2) = 2, then a(n) = largest prime factor of the partial sum up to a(n-1).
- A155049 (program): Expansion of (1+5*x)/(1-13*x+10*x^2).
- A155050 (program): A symmetric Catalan based triangle.
- A155051 (program): Expansion of c(x^2)*(1+x)/(1-x), c(x) the g.f. of A000108.
- A155058 (program): Primes with odd largest digit.
- A155067 (program): First differences of A031368.
- A155069 (program): Expansion of (3 - x - sqrt(1 - 6*x + x^2))/2.
- A155071 (program): Primes with two odd digits.
- A155072 (program): Positive integers n such that the base-2 MR-expansion of 1/n is periodic with period (n-1)/4.
- A155073 (program): Expansion of (1+6*x)/(1-12*x-8*x^2).
- A155076 (program): Triangle read by rows. The main diagonal is positive. If rowindex >= 2*columnindex then -1 else 0.
- A155084 (program): A Catalan transform of x^n (A002605).
- A155085 (program): a(n) = n + sum of divisors of n.
- A155086 (program): Numbers n such that n^2 == -1 (mod 13).
- A155090 (program): Composites k such that composite(k) is odd.
- A155091 (program): Triangle read by rows. Signed version of A145362. Main diagonal positive, rest of the nonzero terms negative.
- A155095 (program): Numbers k such that k^2 == -1 (mod 17).
- A155096 (program): Numbers k such that k^2 == -1 (mod 29).
- A155097 (program): Numbers k such that k^2 == -1 (mod 37).
- A155098 (program): Numbers k such that k^2 == -1 (mod 41).
- A155099 (program): Third column of A155092.
- A155102 (program): Triangle T(n,k) read by rows. If n=k then T(n,k)=1, elseif n=2*k then T(n,k)=-(k+1), else T(n,k)=0.
- A155104 (program): Numbers appearing in the fourth column of A155103.
- A155107 (program): Numbers that are 23 or 30 (mod 53).
- A155108 (program): Primes k such that the k-th composite is even.
- A155110 (program): a(n) = 8*Fibonacci(2n+1).
- A155111 (program): Odd numbers k such that composite(k) is odd.
- A155112 (program): Triangle T(n,k), 0<=k<=n, read by rows given by [0,2,-1/2,-1/2,0,0,0,0,0,0,0,0,…] DELTA [1,0,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A155116 (program): a(n) = 3*a(n-1) + 3*a(n-2), n>2, a(0)=1, a(1)=2, a(2)=8.
- A155117 (program): a(n) = 4*a(n-1) + 4*a(n-2), n>2, a(0)=1, a(1)=3, a(2)=15.
- A155118 (program): Array T(n,k) read by antidiagonals: the k-th term of the n-th iterated differences of A140429.
- A155119 (program): a(n) = 5*a(n-1) + 5*a(n-2), n > 2, a(0)=1, a(1)=4, a(2)=24.
- A155120 (program): a(n) = 2*(n^3 + n^2 + n - 1).
- A155121 (program): a(n) = 2*n*(1 + n + n^2 + n^3) - 3.
- A155122 (program): a(n) = 4*(3*n+2)*(2*n+1)*(n+2)*(n+1).
- A155124 (program): Triangle T(n, k) = 1-n if k=0 else 2, read by rows.
- A155127 (program): a(n) = 6*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=5, a(2)=35.
- A155130 (program): a(n) = 7*a(n-1) + 7*a(n-2), n>2, a(0)=1, a(1)=6, a(2)=48.
- A155132 (program): a(n) = 8*a(n-1) + 8*a(n-2), n > 2, a(0)=1, a(1)=7, a(2)=63.
- A155133 (program): Numbers n >= 0 such that 5n^2+4n+1 is prime.
- A155135 (program): Integers n such that n^3+28*n^2 is a square.
- A155136 (program): Integers n such that n+28 is a square.
- A155138 (program): a(n) = nonnegative value y such that (A155136(n), y) is a solution to the Diophantine equation x^3+28*x^2 = y^2.
- A155144 (program): a(n) = 9*a(n-1) + 9*a(n-2), n>2; a(0)=1, a(1)=8, a(2)=80.
- A155148 (program): Numbers n such that n^4 has exactly 2 different decimal digits.
- A155151 (program): Triangle T(n, k) = 4*n*k + 2*n + 2*k + 2, read by rows.
- A155152 (program): Numbers n such that 13n^2+3n+1 is prime.
- A155155 (program): a(n) = 2*(10*3^n - 1).
- A155156 (program): Triangle T(n, k) = 4*n*k + 2*n + 2*k, read by rows.
- A155157 (program): a(n) = 10*a(n-1) + 10*a(n-2), with a(0)=1, a(1)=9, a(2)=99.
- A155158 (program): Period 4: repeat [1, 5, 7, 3].
- A155159 (program): a(n) = 1 + 2*n*n!.
- A155160 (program): a(n) = 2^n * (n + 3)!!.
- A155161 (program): A Fibonacci convolution triangle: Riordan array (1, x/(1 - x - x^2)). Triangle T(n,k), 0 <= k <= n, read by rows.
- A155167 (program): (L)-sieve transform of A004767 = {3,7,11,15,…,4n-1,…}.
- A155171 (program): Numbers p such that if q = p+1 then (a = q^2-p^2, b = 2*p*q, c = q^2 + p^2) is a primitive Pythagorean triple with s-1 and s+1 primes, where s = a+b+c.
- A155173 (program): Short leg A of primitive Pythagorean triangles such that perimeter s is average of twin prime pairs, q=p+1, A=q^2-p^2, C=q^2+p^2, B=2*p*q, s=A+B+C; s -/+ 1 are primes.
- A155174 (program): Long leg B of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, s=a+b+c, s-+1 are primes.*)
- A155175 (program): Hypotenuse C of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, s=a+b+c, s-+1 are primes.
- A155176 (program): Perimeter s/6 (divided by 6) of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, s=a+b+c, s-+1 are primes.
- A155177 (program): Area ar/6 (divided by 6) of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes.
- A155179 (program): a(n)=4*a(n-1)+a(n-2), n>2; a(0)=1, a(1)=3, a(2)=12.
- A155181 (program): a(n)=5*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=4, a(2)=20 .
- A155189 (program): Square-weak primes.
- A155195 (program): a(n)=6*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=5, a(2)=30 .
- A155196 (program): a(n)=7*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=6, a(2)=42 .
- A155197 (program): a(n) = 8*a(n-1) + a(n-2) for n>2, with a(0)=1, a(1)=7, a(2)=56.
- A155198 (program): a(n)=9*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=8, a(2)=72 .
- A155199 (program): a(n)=10*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=9, a(2)=90 .
- A155200 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2) * x^n/n ), a power series in x with integer coefficients.
- A155201 (program): G.f.: A(x) = exp( Sum_{n>=1} (2^n + 1)^n * x^n/n ), a power series in x with integer coefficients.
- A155202 (program): G.f.: A(x) = exp( Sum_{n>=1} (2^n - 1)^n * x^n/n ), a power series in x with integer coefficients.
- A155203 (program): G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2) * x^n/n ), a power series in x with integer coefficients.
- A155204 (program): G.f.: A(x) = exp( Sum_{n>=1} (3^n + 1)^n * x^n/n ), a power series in x with integer coefficients.
- A155207 (program): G.f.: A(x) = exp( Sum_{n>=1} 4^(n^2) * x^n/n ), a power series in x with integer coefficients.
- A155209 (program): G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n * x^n/n ), a power series in x with integer coefficients.
- A155210 (program): G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n/3^(n-1) * x^n/n ), a power series in x with integer coefficients.
- A155211 (program): Numbers n such that n^4+(n+1)^4 is a prime.
- A155212 (program): a(n) = (n^2 + 9*n + 4)/2.
- A155213 (program): a(n) = floor(prime(n)/9).
- A155449 (program): Numbers k == 6 or 11 (mod 17).
- A155450 (program): Numbers equal to 5 or 18 mod 23.
- A155455 (program): a(n)=5*a(n-1)+16*a(n-2), n>1 ; a(0)=0, a(1)=1.
- A155456 (program): Write (1+1/x)*log(1+x) = Sum c(n)*x^n; then a(n) = (n+1)!*c(n).
- A155457 (program): a(n) = exp(Lambda(n)), where Lambda(n) is the von Mangoldt function for odd (!) primes.
- A155458 (program): a(n)=6*a(n-1)+25*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=6 .
- A155459 (program): a(n)=7*a(n-1)+36*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=7 .
- A155460 (program): a(n)=8*a(n-1)+49*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=8 .
- A155461 (program): a(n) = n^2 + 52*n + 30.
- A155462 (program): Frequency of n in A155213.
- A155464 (program): a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 0, a(1) = 51, a(2) = 340.
- A155465 (program): a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 7, a(1) = 88, a(2) = 555.
- A155466 (program): a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 28, a(1) = 207, a(2) = 1248.
- A155469 (program): Numbers that are the sum of 2 (not-distinct) numbers; nonzero square and cube, including repetitions.
- A155477 (program): a(n) = 43^(2*n+1).
- A155482 (program): Signed-digit binary expansion of Pi/4
- A155483 (program): a(n)=A000040(A043489(n+1)).
- A155485 (program): a(n) = 5^n + (1 - 4^n)/3.
- A155487 (program): Difference between n-th composite number and twice its least prime factor.
- A155494 (program): Triangle T(n, k) = (k+1)*(n-k+1)*binomial(n,k) with T(n, 0) = T(n, n) = 1, read by rows.
- A155495 (program): Triangle read by rows: t(n,m) = binomial(2*n,2*m) * binomial(n,m).
- A155497 (program): Triangle T(n, k) = binomial(n, k)*binomial(n+1, k+1)*binomial(2*n, 2*k)/(n-k+1), read by rows.
- A155498 (program): Number of odd digits in the concatenation of first n primes.
- A155499 (program): a(n) = n + (n+1)^(n+2).
- A155504 (program): Numbers of the form (3h+1)*3^(k+1) listed in increasing order.
- A155516 (program): Triangle T(n, k) = binomial(2*n, 2*k)*binomial(2*n+1, 2*k+1)/(2*n-2*k+1), read by rows.
- A155519 (program): a(n) = Sum (J(p): p is a permutation of {1,2,…,n}), where J(p) is the number of j <= ceiling(n/2) such that p(j) + p(n+1-j) = n+1.
- A155521 (program): Smallest fixed point summed over all non-derangement permutations of {1,2,…,n}.
- A155537 (program): Triangle T(n,k,p,q) = (p^n + q^n)*A001263(n, k) with p=2 and q=1, read by rows.
- A155538 (program): Take square root of previous term.
- A155539 (program): a(n) = n^(n+3) + (n+3)^n.
- A155542 (program): Expansion of (2+2*x)/(1-8*x-25*x^2).
- A155543 (program): a(n)=2*A081294(n).
- A155546 (program): Triangle read by rows where T(m,n)=2mn + m + n - 5, 1<=n<=m.
- A155547 (program): a(n) = prime(n) without prime digits in n.
- A155550 (program): Triangle read by rows where T(m,n)=2*m*n + m + n - 6.
- A155551 (program): Triangle read by rows where T(m,n)=2*m*n + m + n - 9.
- A155557 (program): A proximate-prime polynomial sequence generated by 2*n^2 - 2*n + 53089.
- A155559 (program): a(n) = 2*A131577(n).
- A155579 (program): Recursive sequence (n+1)*a(n) = 3*(3*n-2)*a(n-1).
- A155585 (program): a(n) = 2^n*E(n, 1) where E(n, x) are the Euler polynomials.
- A155586 (program): A modified Catalan sequence array.
- A155587 (program): Expansion of (1 + x*c(x))/(1 - x), where c(x) is the g.f. of A000108.
- A155588 (program): a(n) = 5^n + 2^n - 1^n.
- A155589 (program): 6^n+2^n-1.
- A155590 (program): a(n) = 7^n+2^n-1^n.
- A155592 (program): 8^n+2^n-1^n.
- A155593 (program): a(n) = 9^n + 2^n - 1.
- A155594 (program): 10^n+2^n-1.
- A155595 (program): 11^n+2^n-1.
- A155596 (program): a(n) = 5^n - 2^n + 1^n.
- A155597 (program): a(n) = 6^n - 2^n + 1.
- A155598 (program): a(n) = 7^n-2^n+1.
- A155599 (program): a(n) = 8^n - 2^n + 1^n.
- A155600 (program): a(n) = 9^n-2^n+1^n.
- A155601 (program): a(n) = 10^n - 2^n + 1^n.
- A155602 (program): 4^n + 3^n - 1.
- A155603 (program): a(n) = 5^n+3^n-1.
- A155604 (program): 6^n+3^n-1.
- A155605 (program): 7^n+3^n-1.
- A155606 (program): a(n) = 8^n + 3^n - 1.
- A155607 (program): 9^n+3^n-1.
- A155608 (program): 10^n + 3^n - 1.
- A155609 (program): a(n) = 4^n - 3^n + 1.
- A155610 (program): 5^n - 3^n + 1.
- A155611 (program): 6^n - 3^n + 1.
- A155612 (program): 7^n - 3^n + 1.
- A155613 (program): 8^n - 3^n + 1.
- A155614 (program): 9^n - 3^n + 1.
- A155615 (program): 10^n - 3^n + 1.
- A155616 (program): 5^n + 4^n - 1.
- A155617 (program): 6^n + 4^n - 1.
- A155618 (program): a(n) = 7^n+4^n-1^n.
- A155619 (program): 8^n+4^n-1^n
- A155620 (program): 9^n+4^n-1.
- A155621 (program): 10^n+4^n-1^n
- A155622 (program): a(n) = 11^n - 2^n + 1.
- A155623 (program): a(n) = 11^n + 3^n - 1.
- A155624 (program): 11^n-3^n+1.
- A155625 (program): 11^n+4^n-1.
- A155626 (program): a(n) = 5^n-4^n+1.
- A155627 (program): a(n) = 6^n - 4^n + 1.
- A155628 (program): a(n) = 7^n-4^n+1^n.
- A155629 (program): a(n) = 8^n-4^n+1^n.
- A155630 (program): a(n) = 9^n-4^n+1^n.
- A155631 (program): 10^n-4^n+1^n
- A155632 (program): a(n) = 11^n - 4^n + 1^n.
- A155633 (program): 6^n+5^n-1.
- A155634 (program): 7^n + 5^n - 1.
- A155635 (program): 8^n+5^n-1.
- A155636 (program): 9^n+5^n-1.
- A155637 (program): 10^n+5^n-1.
- A155638 (program): a(n) = 11^n+5^n-1^n.
- A155639 (program): a(n) = 6^n-5^n+1^n.
- A155640 (program): a(n) = 7^n - 5^n + 1^n.
- A155641 (program): 8^n-5^n+1^n.
- A155642 (program): 9^n - 5^n + 1.
- A155643 (program): 10^n-5^n+1.
- A155644 (program): 11^n-5^n+1.
- A155645 (program): 7^n+6^n-1.
- A155646 (program): a(n) = 8^n + 6^n - 1.
- A155647 (program): a(n) = 9^n+6^n-1^n.
- A155648 (program): a(n) = 10^n + 6^n - 1.
- A155649 (program): a(n) = 11^n+6^n-1^n.
- A155650 (program): 7^n - 6^n + 1.
- A155651 (program): 8^n-6^n+1^n
- A155652 (program): 9^n-6^n+1.
- A155653 (program): 10^n-6^n+1.
- A155654 (program): 11^n - 6^n + 1.
- A155655 (program): 8^n+7^n-1^n.
- A155656 (program): 9^n+7^n-1.
- A155657 (program): 10^n+7^n-1.
- A155658 (program): a(n) = 11^n + 7^n - 1.
- A155659 (program): 8^n-7^n+1.
- A155660 (program): 9^n-7^n+1.
- A155661 (program): 10^n-7^n+1.
- A155662 (program): 11^n-7^n+1.
- A155663 (program): 9^n+8^n-1.
- A155664 (program): 10^n+8^n-1
- A155665 (program): 11^n+8^n-1.
- A155666 (program): 9^n-8^n+1.
- A155667 (program): 10^n-8^n+1.
- A155668 (program): 11^n-8^n+1.
- A155669 (program): 10^n+9^n-1.
- A155670 (program): 11^n+9^n-1^n
- A155671 (program): a(n) = 10^n - 9^n + 1^n.
- A155672 (program): 11^n-9^n+1^n
- A155673 (program): 11^n+10^n-1^n
- A155674 (program): 11^n-10^n+1^n
- A155689 (program): a(n) = Sum_{k >= 1} floor(n * sqrt(2) / 2^k).
- A155698 (program): a(n)=a(n-1)+a(n-2)^a(n-3); a(1)=a(2)=a(3)=1.
- A155701 (program): a(n) = (4^n + 8)/3.
- A155702 (program): Primes of the form 2n^2-9.
- A155704 (program): Triangle read by rows where T(m,n)=2*m*n + m + n + 10.
- A155705 (program): Triangle read by rows where T(m,n) = 2*m*n + m + n + 2.
- A155706 (program): A119468 made symmetrical using a matrix polynomial system: A(n,m,k)=If[m less than n, 1, -1]; p(x,k)=(-1)^n*CharacteristicPolynomial[A[n,m,k],x]; t(n,m)=coefficients(p(x,n)+x^n*p(1/x,n))
- A155716 (program): Numbers of the form N = a^2 + 6b^2 for some positive integers a,b.
- A155721 (program): Positions of parity change in A033035.
- A155722 (program): Numbers k such that 2*k + 9 is prime.
- A155723 (program): Numbers k such that 2*k + 9 is not prime.
- A155724 (program): Triangle read by rows: T(m,n) = 2mn + m + n - 4.
- A155726 (program): Production matrix for Fibonacci numbers, read by row.
- A155727 (program): Production matrix of the Jacobsthal numbers, read by row.
- A155728 (program): INVERTi transform of A054765: (1, 3, 19, 160, 1744, …).
- A155730 (program): Indices of Bell numbers divisible by 5.
- A155734 (program): Binomial transform of A154879.
- A155736 (program): Numbers n such that 4*n^2+2*n-1 is a prime.
- A155737 (program): Primes of the form 4*n^2 + 2*n -1.
- A155738 (program): Primes p such that 4*p^2+2*p-1 is also prime
- A155750 (program): First differences of A031215.
- A155752 (program): Where 2’s occur in the prime differences A001223.
- A155753 (program): a(n) = (n^3 - n + 9)/3.
- A155754 (program): A variation on 10^n mod 19
- A155757 (program): (n^3 - n + 15)/3.
- A155761 (program): Riordan array (c(2*x^2), x*c(2*x^2)) where c(x) is the g.f. of A000108.
- A155769 (program): a(n) = 2n^2 + 2n - 41.
- A155770 (program): Primes of form: 2*n^2+2*n-41.
- A155771 (program): Numbers n such that 2*n^2+2*n-41 is a prime.
- A155794 (program): Triangle read by rows: t(n,m)=(m*(m-n))!
- A155795 (program): Triangle read by rows: t(n,k)=n!/(n - k*(n - k)).
- A155797 (program): Triangle read by rows: t(n,k)=Binomial[k*(n - k), n]
- A155798 (program): Triangle read by rows: t(n,k)=Binomial[n, k] + Binomial[k*(n - k), n]
- A155803 (program): A023001 interleaved with 2*A023001 and 4*A023001.
- A155816 (program): First nonzero digit in the decimal expansion of (cos Pi/4)^n
- A155819 (program): a(n) = p(n+1)^2 + 2*p(n) + 1; p(n) is the n-th prime number and n >= 1.
- A155820 (program): Primes of the form prime(k)^2 + 2*prime(k-1) where prime(k) is the k-th prime number.
- A155822 (program): Number of compositions of n with no part greater than 3 such that no two adjacent parts are equal.
- A155828 (program): Number of integers k in {1,2,3,..,n} such that kn+1 is a square.
- A155836 (program): 2^(2^n) mod n.
- A155851 (program): n is prime and is the sum of the first k primes for some k, start from 5.
- A155853 (program): Numbers n such that 13*n + 3 is a prime.
- A155854 (program): Numbers n such that 13*n + 3 is not prime.
- A155856 (program): Triangle T(n,k) = binomial(2*n-k, k)*(n-k)!, read by rows.
- A155857 (program): Row sums of triangle A155856.
- A155859 (program): a(n) = (1/162)*(61*10^n + 18*n + 20).
- A155862 (program): A ‘Morgan Voyce’ transform of A007854.
- A155863 (program): Triangle T(n,k) = n*(n^2 - 1)*binomial(n-2, k-1) for 1 <= k <= n-1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, read by rows.
- A155864 (program): Triangle T(n,k) = n*(n-1)*binomial(n-2, k-1) for 1 <= k <= n-1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, read by rows.
- A155865 (program): Triangle T(n,k) = (n-1)*binomial(n-2, k-1) for 1 <= k <= n-1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, read by rows.
- A155866 (program): A ‘Morgan Voyce’ transform of the Bell numbers A000110.
- A155867 (program): A ‘Morgan Voyce’ transform of the large Schroeder numbers A006318.
- A155872 (program): a(n) = 10^n + 11^n.
- A155874 (program): Smallest positive composite number such that a(n)+n is also composite.
- A155875 (program): Smallest positive composite number such that a(n) - n is also composite.
- A155879 (program): a(0) = 4; for n > 0, a(n) is the smallest composite number c > a(n-1) such that c - n is also composite.
- A155883 (program): a(n) = 14*n^3 - 30*n^2 + 24*n - 7.
- A155887 (program): Riordan array (1, (1/(1-x))c(x/(1-x))), c(x) the g.f. of A000108.
- A155888 (program): a(n) = dimension of the space of n-boxes in the unshaded subfactor planar algebra of type E8.
- A155902 (program): Arises in Connell’s game, a variation of Wythoff’s Nim game.
- A155912 (program): Let d(i) be the i-th digit of the decimal expansion of Pi = 3.1415926535897932384626433832795…, so that d(0) = 3, d(1) = 1, d(2) = 4, etc. Then a(0) = 3, a(n) = d(d(n)) for n>0.
- A155919 (program): Number of squared hypotenuses mod n in three dimensions.
- A155933 (program): Primes of the form n^2 + (n+1)^3.
- A155934 (program): The sequence k(m) defined in A005991.
- A155935 (program): Numbers n such that 13*n + 5 is not prime.
- A155937 (program): Numbers n such that 13*n + 8 is a prime.
- A155938 (program): Primes p such that 13*p + 8 is also prime.
- A155939 (program): Numbers n such that 13*n + 8 is not a prime.
- A155941 (program): Numbers n such that 16*n+1 is not prime.
- A155942 (program): Numbers n such that 16n+1 is a prime.
- A155943 (program): Primes p such that 16*p + 1 is also prime.
- A155944 (program): Jacobsthal numbers A001045, every second term incremented by 1.
- A155945 (program): Numbers n such that 24*n + 13 is not prime.
- A155946 (program): Numbers d for which the volume of the regular d-dimensional simplex of unit edge is rational.
- A155954 (program): a(0)=2, a(1)=3, a(2)=5, a(n) = smallest prime greater than or equal to a(n-1) + a(n-2) + a(n-3).
- A155955 (program): Triangle read by rows: T(n,k) = (k*n)^k, 0 <= k <= n.
- A155956 (program): a(n) = Sum_{k=0..n} (k*n)^k.
- A155957 (program): a(n) = (2*n^2)^n.
- A155965 (program): a(n) = n*(n^2+4).
- A155966 (program): a(n) = 2*n^2 + 8.
- A155972 (program): The Partition Ruler
- A155977 (program): a(n) = n^5 + n^3.
- A155978 (program): The primes (p-11)/10 arising in A089442.
- A155980 (program): First differences of A135351.
- A155988 (program): a(n) = (2*n+1)*9^n.
- A155989 (program): List of numbers prime(k) as k runs through the numbers with a single prime digit.
- A155990 (program): Numbers prime(k) as k runs through the numbers whose digits are all prime.
- A155996 (program): Nearest integer to 2^n*Pi/4.
- A155997 (program): Triangle read by rows: T(n, k) = f(n, k) + f(n, n-k), where f(n, k) = binomial(n, k)*(1 + (-1)^k)/2.
- A155998 (program): Triangle read by rows: T(n, k) = f(n, k) + f(n, n-k), where f(n, k) = binomial(n, k)*(1 - (-1)^k)/2.
- A156002 (program): Partial sums of round(7^n/9).
- A156004 (program): Primes p such that 8*p+21 is prime.
- A156005 (program): Primes p such that 16*p+45 is prime.
- A156016 (program): Expansion of (1-x-sqrt(1-6x-3x^2))/(2x).
- A156017 (program): Schroeder paths with two rise colors and two level colors.
- A156018 (program): Primes of the form k^3 + k^2 + k - 1.
- A156022 (program): Maximum number of positive numbers represented by substrings of an n-bit number’s binary representation
- A156023 (program): n(n+1)/2 - A112509(n)
- A156024 (program): n(n+1)/2 - A156022(n)
- A156033 (program): Numerator of (Sum_{k=1..n} k^3)/n!.
- A156034 (program): Denominator of (Sum_{k=1..n} k^3)/n!.
- A156035 (program): Decimal expansion of 3 + 2*sqrt(2).
- A156036 (program): Numerators in expansion of log(z^2/(cosh(z)-cos(z))).
- A156037 (program): Largest nonprime < n-th prime.
- A156039 (program): Number of compositions (ordered partitions) of n into 4 parts, where the first is at least as great as each of the others.
- A156040 (program): Number of compositions (ordered partitions) of n into 3 parts (some of which may be zero), where the first is at least as great as each of the others.
- A156056 (program): n-th triangular number modulo n-th prime.
- A156057 (program): Decimal expansion of log(3)/2.
- A156058 (program): a(n) = 5^n * Catalan(n).
- A156060 (program): Jacobsthal numbers A001045 mod 9.
- A156061 (program): a(n) = product of indices of distinct prime factors of n, where index(prime(k)) = k.
- A156062 (program): Riordan array (1/(1-x^4), x/(1-x^4)).
- A156065 (program): Diagonal sums of inverse of Riordan array (1/(1-x^4),x/(1-x^4)).
- A156066 (program): Numbers n with property that n^2 is a square arising in A154138.
- A156067 (program): a(0)=1. a(n)= -2^(n-1)-3*(-1)^n, n>1.
- A156077 (program): a(n) = #{1<=k<=n : A000002(k)=1}.
- A156078 (program): a(n) = #{1 <= k <= ceiling(n/2) : A000002(2k) = 1}.
- A156079 (program): a(n) = #{1 <= k <= ceiling(n/2) : A000002(2k) = 2}.
- A156080 (program): a(n) = #{1 <= k <= ceiling(n/2) : A000002(2k-1) = 2}.
- A156081 (program): a(n) = #{1 <= k <= ceiling(n/2) : A000002(2k-1) = 1}.
- A156084 (program): Sum of the squares of the first n Fibonacci numbers with index divisible by 3.
- A156085 (program): One fourth of the sum of the squares of the first n Fibonacci numbers with index divisible by 3.
- A156086 (program): Sum of the squares of the first n Fibonacci numbers with index divisible by 4.
- A156087 (program): One ninth of the sum of the squares of the first n Fibonacci numbers with index divisible by 4.
- A156088 (program): Alternating sum of the squares of the first n even-indexed Fibonacci numbers.
- A156089 (program): Alternating sum of the squares of the first n odd-indexed Fibonacci numbers.
- A156090 (program): Alternating sum of the squares of the first n Fibonacci numbers with index divisible by 3.
- A156091 (program): One fourth of the alternating sum of the squares of the first n Fibonacci numbers with index divisible by 3.
- A156092 (program): Alternating sum of the squares of the first n Fibonacci numbers with index divisible by 4.
- A156093 (program): One ninth of the alternating sum of the squares of the first n Fibonacci numbers with index divisible by 4.
- A156094 (program): 5 F(2n) (F(2n) - 1) + 1 where F(n) denotes the n-th Fibonacci number.
- A156095 (program): 5 F(2n) (F(2n) + 1) + 1 where F(n) denotes the n-th Fibonacci number.
- A156096 (program): Inverse binomial transform of A030186.
- A156104 (program): Primes p such that p+36 is also prime.
- A156105 (program): Primes p such that p + 72 is also prime.
- A156107 (program): Primes p such that p + 144 is also prime.
- A156125 (program): a(n)=10^n*C(2n,n)/C(n+3,3).
- A156126 (program): Sequence related to Hankel transform of super-ballot numbers.
- A156127 (program): a(n) = 7*2^n - 3.
- A156128 (program): a(n) = 6^n * Catalan(n).
- A156136 (program): A triangle of polynomial coefficients related to Mittag-Leffler polynomials: p(x,n)=Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x).
- A156143 (program): P_n(1)*Q_n(1) (see A155100 and A104035), defining Q_{-1} = 0.
- A156156 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 13, a(2) = 53.
- A156157 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 17, a(2) = 85.
- A156158 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 25, a(2) = 137.
- A156160 (program): a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=169, a(2)=2809.
- A156161 (program): a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=289, a(2)=7225.
- A156162 (program): a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=625, a(2)=18769.
- A156163 (program): Decimal expansion of (19+6*sqrt(2))/17.
- A156164 (program): Decimal expansion of 17 + 12*sqrt(2).
- A156168 (program): A bisection of A002437.
- A156169 (program): A bisection of A002437.
- A156171 (program): G.f.: A(x) = exp( Sum_{n>=1} x^n/(1 - 2^n*x)^n / n ), a power series in x with integer coefficients.
- A156172 (program): Twice A002437.
- A156173 (program): A q-factorial type triangle sequence: t(n,m)=Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}].
- A156174 (program): Period 5: repeat [1,-1,1,-1,0].
- A156177 (program): A bisection of A000436.
- A156178 (program): A bisection of A000436.
- A156180 (program): Denominator of Euler(n,1/3).
- A156183 (program): Denominator of Euler(n, 1/5).
- A156189 (program): Denominator of Euler(n, 1/6).
- A156192 (program): Denominator of Euler(n, 1/7).
- A156194 (program): Period 12: 1,2,7,1,7,2,1,1,4,2,4,1 repeated.
- A156195 (program): a(2n+2) = 6*a(2n+1), a(2n+1) = 6*a(2n) - 5^n*A000108(n), a(0)=1.
- A156198 (program): a(n) = 2*a(n-1)+3 with n>1, a(1)=8.
- A156199 (program): Period 12: repeat 1, 1, 4, 2, 4, 1, 1, 2, 7, 1, 7, 2 .
- A156201 (program): Numerator of Euler(n, 1/8).
- A156202 (program): a(n) = 2*a(n-1)+3 for n > 1, a(1) = 10.
- A156203 (program): a(n) = 2*a(n-1) + 3 for n>1, a(1)=14.
- A156207 (program): Sum of the products of the digits in n and their position m in n.
- A156208 (program): Primes appearing as the products of digits and positions in A156207(i) in the order of appearance.
- A156213 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*C(2*n-1,n)*x^n/n ), a power series in x with integer coefficients.
- A156216 (program): G.f.: A(x) = exp( Sum_{n>=1} A000204(n)^n * x^n/n ), a power series in x with integer coefficients.
- A156217 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)^n*x^n/n ), a power series in x with integer coefficients.
- A156218 (program): Denominator of Euler(n, 1/9).
- A156226 (program): Primes of the form 9*n^2 + 1.
- A156227 (program): Period 12: repeat [0,1,3,8,3,1,0,8,6,1,6,8].
- A156229 (program): Partial sums of A052343.
- A156230 (program): Sum of the products of the digits of n and the positions of the digits m in n starting from the last digit.
- A156232 (program): a(n) is the number of induced subgraphs with odd number of edges in the cycle graph C(n).
- A156234 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*A000204(n)*x^n/n ).
- A156242 (program): Bisection of A054353.
- A156243 (program): Bisection of A054353.
- A156244 (program): Bisection of A078649.
- A156245 (program): Bisection of A078649.
- A156246 (program): a(n)=sum(k=1,n,A000002(2*k-1))
- A156247 (program): a(n)=sum(k=1,n,A000002(2*k))
- A156248 (program): a(n)=sum(k=1,n,(-1)^k*A000002(2*k))
- A156249 (program): a(n)=sum(k=1,n,(-1)^k*A000002(2*k-1))
- A156250 (program): Least k such that A078649(k)>= A054353(n).
- A156251 (program): Least k such that A078649(k)>=n
- A156252 (program): Primes of the form 4*n^2+6*n+43.
- A156253 (program): Least k such that A054353(k) >= n.
- A156256 (program): Number of 1’s separating successive 2’s in the Kolakoski sequence A000002.
- A156257 (program): Digit of runs of length 2 in the Kolakoski sequence A000002: a(n) = A000002(A078649(n)).
- A156258 (program): a(n)=(1/2)*(A000002(A078649(n))-A000002(A078649(n)+2)+1)
- A156259 (program): a(n)=(1/2)*(A000002(A078649(n)+2)-A000002(A078649(n))+1)
- A156260 (program): Row sums of A156254.
- A156261 (program): a(n)=n/2+(1/2)*sum(k=1,n,A000002(A078649(k)+2)-A000002(A078649(k)))
- A156262 (program): a(n)=n/2-(1/2)*sum(k=1,n,A000002(A078649(k)+2)-A000002(A078649(k)))
- A156263 (program): a(n)=A000002(3*n-1)
- A156264 (program): a(n) = A000002(3*n-2), where A000002 is the Kolakoski sequence.
- A156265 (program): a(n)=3*n-A078649(n)
- A156266 (program): a(n) = 7^n*Catalan(n).
- A156267 (program): a(n)=A054353(2*n)-A078649(n)
- A156270 (program): a(n) = 8^n*Catalan(n).
- A156271 (program): a(n)=sum(k=1,n,A000002(A078649(k)))
- A156273 (program): a(n) = 9^n*Catalan(n).
- A156275 (program): a(n) = 10^n*Catalan(n).
- A156276 (program): Denominator of Euler(n, 1/10).
- A156277 (program): Numbers appearing at every third row in the third column of A156241.
- A156279 (program): 4 times the Lucas number A000032(n).
- A156283 (program): Period 6: repeat [1, 2, 4, -4, -2, -1].
- A156286 (program): Triangle T(n, k) = (1/k^n)*Product_{j=1..n} ( (k-1)*(k+1)^j + 1 ), read by rows.
- A156287 (program): Numbers k such that 4*k-5 is a prime number.
- A156288 (program): Numbers n such that 4*n-5 is not a prime number.
- A156290 (program): Triangle read by rows: alternating binomial coefficients with signs.
- A156293 (program): Denominator of Euler(n, 1/11).
- A156294 (program): Sum of products of the digits of prime numbers and the position of the digits in the prime numbers.
- A156296 (program): a(1)=1, a(n) = 2 * Sum_{k=1..n-1} (3^k-1)/2 * a(k) for n>=2.
- A156297 (program): Triangle T(n,k) read by rows. If n = k^2 then 1 else 0.
- A156300 (program): Primes p such that 4*p - 5 is also prime.
- A156301 (program): a(n) = ceiling( n * (log_3 2)) = ceiling(n * 0.6309297535714574371…).
- A156302 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)^2*x^n/n ), a power series in x with integer coefficients.
- A156303 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n^2)*x^n/n ), a power series in x with integer coefficients.
- A156304 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n^3)*x^n/n ), a power series in x with integer coefficients.
- A156308 (program): Inverse of triangle S(n,m) defined by sequence A156290, n >= 1, 1 <= m <= n.
- A156309 (program): Decimal expansion of the absolute value of the larger solution of (n^2+n)/2 = -1/12. (Real root q of 6n^2 + 6n + 1, the other root being p = -1-q.)
- A156319 (program): Triangle by columns: (1, 2, 0, 0, 0, …) in every column.
- A156320 (program): List of prime pairs of the form (p, p+8).
- A156324 (program): a(1)=0, a(n+1) is smallest nonprime >= a(n)+n.
- A156330 (program): Numerator of Euler(n, 1/12).
- A156331 (program): a(n)=8*A154811(n).
- A156334 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^[n^2/2+1]*x^n/n ), a power series in x with integer coefficients.
- A156335 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.
- A156337 (program): G.f.: A(x) = exp( Sum_{n>=1} 4^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.
- A156339 (program): Denominator of Euler(n, 1/13).
- A156340 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2-n+1) * x^n/n ), a power series in x with integer coefficients.
- A156341 (program): Expansion of (2-6*x)/(1-12*x+11*x^2).
- A156346 (program): Palindromic period of length 12: repeat 1,2,-4,4,-2,-1,-1,-2,4,-4,2,1.
- A156348 (program): Triangle T(n,k) read by rows. Column of Pascal’s triangle interleaved with k-1 zeros.
- A156349 (program): a(n)=sum_{k=1..n} r(k) where r(k)=A000002(k) if A000002(k+1)=2 and r(k)=0 if A000002(k+1)=1
- A156351 (program): a(n) = Sum_{k=1..n} (-1)^K(k+1)*(K(k+1)-K(k)) where K(k) = A000002(k).
- A156352 (program): a(n)=A078649(A054353(n)-n+1)-A054353(n)
- A156353 (program): A symmetrical powers triangle sequence: t(n,m) = (m^(n - m) + (n - m)^m).
- A156354 (program): Triangle T(n, k) = k^(n-k) + (n-k)^k with T(0, 0) = 1, read by rows.
- A156359 (program): Denominator of Euler(n, 1/14).
- A156360 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma_n(2n)*x^n/n ), where sigma_n(2n) is the sum of the n-th powers of the divisors of 2*n.
- A156361 (program): a(2*n+2) = 7*a(2*n+1), a(2*n+1) = 7*a(2*n) - 6^n*A000108(n), a(0) = 1.
- A156362 (program): a(2*n+2) = 8*a(2*n+1), a(2*n+1) = 8*a(2*n) - 7^n*A000108(n), a(0)=1.
- A156365 (program): T(n, k) = E(n, k)*2^k where E(n,k) are the Eulerian numbers A173018, for n > 0 and 0 <= k <= n-1, additionally T(0,0) = 1.
- A156367 (program): Triangle T(n, k) = binomial(n+k, 2*k)*k!, read by rows.
- A156372 (program): Denominator of Euler(n, 1/15).
- A156376 (program): a(n) = 30*n + 19.
- A156377 (program): Numerator of Euler(n, 1/16).
- A156384 (program): The number of solutions to x^2 + y^2 + 2*z^2 = n in nonnegative integers x,y,z.
- A156531 (program): Denominator of Euler(n, 1/17).
- A156536 (program): Period length 12: repeat 7,5,-1,1,-5,-7,-7,-5,1,-1,5,7.
- A156540 (program): Array A(n, k) = Product_{j=1..n} ( (k+1)^j - 1 ) with A(n, 0) = n!, read by antidiagonals.
- A156542 (program): Number of distinct Sophie Germain prime factors of n.
- A156543 (program): Multiplicative closure of primes that are not Sophie Germain primes (A053176).
- A156548 (program): Decimal expansion of the real part of the limit of f(f(…f(0)…)) where f(z)=sqrt(i+z).
- A156550 (program): a(n) = 5*(-1)^n*A078008(n).
- A156551 (program): Period 10: repeat [8,6,0,4,2,2,4,0,6,8].
- A156552 (program): Unary-encoded compressed factorization of natural numbers.
- A156554 (program): The number of integer sequences of length d = 2n+1 such that the sum of the terms is 0 and the sum of the absolute values of the terms is d-1.
- A156558 (program): a(n) = Sum_{k=1..n} (n^k mod (n-k+1)).
- A156561 (program): Floor(Fibonacci(2n+1)/9).
- A156562 (program): a(n) = (-1)^n*Sum_{k=1..n} A054353(k)*(-1)^k.
- A156563 (program): a(n) = (-1)^n*Sum_{k=1..n} A078649(k)*(-1)^k.
- A156566 (program): a(2n+2) = 9*a(2n+1), a(2n+1) = 9*a(2n) - 8^n*A000108(n), a(0)=1.
- A156568 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=23, a(2)=115.
- A156569 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=37, a(2)=205.
- A156570 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=17, a(2)=65.
- A156571 (program): Decimal expansion of (27 + 10*sqrt(2))/23.
- A156573 (program): a(n) = 34*a(n-1) - a(n-2) - 4232 for n > 2; a(1)=529, a(2)=13225.
- A156574 (program): a(n) = 34*a(n-1) - a(n-2) - 4232 for n > 2; a(1)=1369, a(2)=42025.
- A156575 (program): a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=289, a(2)=4225.
- A156577 (program): a(2*n+2) = 10*a(2*n+1), a(2*n+1) = 10*a(2*n) - 9^n*A000108(n), a(0) = 1.
- A156578 (program): Triangle of coefficients of 1 - (n+1)*x^n + n*x^(n+1), read by rows.
- A156581 (program): Triangle T(n, k, m) = (m+2)^(k*(n-k)) with m = 15, read by rows.
- A156589 (program): a(n) = 4^n - 2^n - 1.
- A156590 (program): Decimal expansion of the imaginary part of the limit of f(f(…f(0)…)) where f(z)=sqrt(i+z).
- A156591 (program): First differences of A154570.
- A156592 (program): Product p*q of two primes with q = 2*p + 1.
- A156595 (program): Fixed point of the morphism 0->011, 1->010.
- A156596 (program): Infinite Fibonacci word fractal sequence.
- A156605 (program): a(n) = (4^n + 20)/3.
- A156611 (program): a(1) = 2, a(n+1) is smallest prime >= a(n)+2*n.
- A156615 (program): a(1)=2, a(n+1) is the smallest prime > n*final digit of a(n).
- A156616 (program): G.f.: Product_{n>0} ((1+x^n)/(1-x^n))^n.
- A156619 (program): Numbers congruent to {7, 18} mod 25.
- A156622 (program): Values of register a when register b becomes 0 for the two-register machine {i[1], i[1], i[1], d[2,1], d[1,6], i[2], d[1,5], d[2,3]}.
- A156623 (program): Values of register b when register a becomes 0 for the two register machine {i[1], i[1], i[1], d[2,1], d[1,6], i[2], d[1,5], d[2,3]}
- A156626 (program): a(0)=1; a(1)=2; a(2)=6; a(n+1) = 2*(n+1)*a(n) - n^2*a(n-1), n > 1.
- A156627 (program): a(n) = 4394*n - 1820.
- A156634 (program): Denominator of Euler(n, 1/18).
- A156635 (program): 144*n^2 - n.
- A156636 (program): a(n) = 4394*n + 1820.
- A156637 (program): Pell numbers A000129 mod 9. Period 24: repeat 0,1,2,5,3,2,7,7,3,4,2,8,0,8,7,4,6,7,2,2,6,5,7,1.
- A156638 (program): Numbers k such that k^2 + 2 == 0 (mod 9).
- A156639 (program): a(n) = 169*n^2 - 140*n + 29.
- A156640 (program): a(n) = 169*n^2 + 140*n + 29.
- A156641 (program): a(n) = 13*(100^(n+1) - 1)/99.
- A156642 (program): Number of decompositions of 4n+2 into unordered sums of two primes of the form 4k+3.
- A156644 (program): Mirror image of triangle A080233.
- A156649 (program): Decimal expansion of (9+4*sqrt(2))/7.
- A156655 (program): Primes of the form 1000*k + 1.
- A156657 (program): Numbers that are not safe primes.
- A156659 (program): Characteristic function of safe primes.
- A156660 (program): Characteristic function of Sophie Germain primes.
- A156661 (program): Denominator of Euler(n, 1/19).
- A156663 (program): Triangle by columns, powers of 2 interleaved with zeros.
- A156664 (program): Binomial transform of A052551.
- A156665 (program): Triangle read by rows, A156663 * A007318
- A156672 (program): a(1)=2, a(n+1) is the smallest prime >= a(n) + sum of digits of a(n).
- A156674 (program): Numbers k such that k^2 - 2 == 0 (mod 49).
- A156675 (program): a(n) = 17*((100^(n+1) - 1)/99).
- A156676 (program): a(n) = 81*n^2 - 44*n + 6.
- A156677 (program): a(n) = 81n^2 - 118n + 43.
- A156683 (program): Integers that can occur as either leg in more than one primitive Pythagorean triple
- A156685 (program): Number of primitive Pythagorean triples A^2 + B^2 = C^2 with 0 < A < B < C and gcd(A,B)=1 that have a hypotenuse C that is less than or equal to n.
- A156686 (program): The ordered set of a + b - c as (a,b,c) runs through all Pythagorean triples with a<b<c.
- A156688 (program): The total number of distinct Pythagorean triples with an area numerically equal to n times their perimeters
- A156701 (program): a(n) = 4*n^4 + 17*n^2 + 4.
- A156702 (program): Numbers k such that k^2 - 1 == 0 (mod 24^2).
- A156706 (program): For all numbers k(n) congruent to +1 or -1 (mod 6) starting with k(n) = {5,7,11,13,…}, a(k(n)) is the congruence (mod 6) if k(n) is prime and 0 if k(n) is composite.
- A156707 (program): For all numbers k(n) congruent to +1 or -1 (mod 4) starting with k(n) = {3,5,7,9,11,…}, a(k(n)) is the congruence (mod 4) if k(n) is prime and 0 if k(n) is composite.
- A156708 (program): Triangle read by rows, binomial transform of A154325
- A156709 (program): For all numbers k(n) congruent to -1 or +1 (mod 6) starting with k(n) = {5,7,11,13,…}, a(k(n)) is incremented by the congruence (mod 6) if k(n) is prime and by 0 if k(n) is composite.
- A156711 (program): a(n) = 144*n^2 - 161*n + 45.
- A156712 (program): Star numbers (A003154) that are also triangular numbers (A000217).
- A156717 (program): Triangle read by rows: T(n,m) = binomial(n + m - 1, 2*m) + binomial(2*n - m - 2, 2*(n - m - 1)).
- A156718 (program): Numbers k such that k^2 == -1 (mod 13^2).
- A156719 (program): a(n) = 144*n^2 - 127*n + 28.
- A156721 (program): a(n) = 57122*n^2 - 47320*n + 9801.
- A156723 (program): a(n)=A156253(n)-A156251(n)
- A156724 (program): a(n)=A156253(2n)-A156251(2n)
- A156726 (program): a(n)=A156253(2n-1)-A156251(2n-1)
- A156728 (program): a(n) = abs(A054354(n)).
- A156729 (program): a(n)=(v(2*n+2)-v(2*n))/2 where v(n)=A156253(n)-A156251(n).
- A156731 (program): a(n)=(v(2*n+1)-v(2*n-1))/2 where v(n)=A156253(n)-A156251(n).
- A156732 (program): Triangle T(n, k) = ((n-2*k)^2/(n-k+1))*binomial(n+1, k+1), read by rows.
- A156733 (program): Euler transform of n*A065958(n).
- A156734 (program): Square array read by antidiagonals up. T(n,k) = if k divides n then +1 else -1.
- A156735 (program): a(n) = 57122*n^2 + 47320*n + 9801.
- A156745 (program): a(n) = Sum_{k=1..n} floor((n+k)/k) = n + Sum_{k=1..n} sigma_0(k), where sigma_0(k) is A000005(k). Also a(n) = n + A006218(n).
- A156746 (program): Numerator of Euler(n, 1/20).
- A156749 (program): For all numbers k(n) congruent to -1 or +1 (mod 4) starting with k(n) = {3,5,7,9,11,…}, a(k(n)) is incremented by the congruence (mod 4) if k(n) is prime and by 0 if k(n) is composite.
- A156752 (program): a(n) = floor(Catalan(n+1)/Catalan(n)).
- A156755 (program): Period 9: repeat 1,1,2,1,1,2,2,2,3.
- A156760 (program): 5*4^n-1.
- A156762 (program): Denominator of Euler(n, 1/21).
- A156763 (program): Triangle T(n, k) = binomial(2*k, k)*binomial(n+k, n-k) + binomial(2*n-k, k)*binomial(2*(n-k), n-k), read by rows.
- A156769 (program): a(n) = denominator(2^(2*n-2)/factorial(2*n-1)).
- A156771 (program): a(n) = 729*n - 531.
- A156772 (program): a(n) = 729*n - 198.
- A156773 (program): a(n) = 6561*n^2 - 9558*n + 3482.
- A156774 (program): a(n) = 6561*n^2 - 3564*n + 485.
- A156778 (program): n*A007504(n)/2 = n*(sum of first n primes)/2
- A156779 (program): Sum( d | n, sp(d)), where sp(d) = A034387(d) = sum of primes <= d.
- A156780 (program): sp(n)*pi(n) = A034387(n)*A000720(n) = (sum of primes <= n)*(number of primes <= n).
- A156789 (program): Irregular triangle, read by rows, T(n, k) = binomial(2*n, k)*binomial(2*k, k).
- A156795 (program): a(n) = 81*n - 59.
- A156796 (program): a(n) = 81*n - 22.
- A156797 (program): Numbers k such that k^2 + 2 == 0 (mod (9^2)).
- A156798 (program): a(n) = n^4 + 5*n^2 + 4.
- A156810 (program): a(n) = 225*n^2 - 251*n + 70.
- A156812 (program): a(n) = 225*n^2 - 199*n + 44.
- A156813 (program): a(n) = 225*n^2 - n.
- A156814 (program): a(n) = 225*n^2 + n.
- A156815 (program): Triangle T(n, k) = n!*StirlingS2(n, k)/binomial(n, k), read by rows.
- A156820 (program): T(n,m) = Sum_{j=0..m} (-1)^(j + m)*(j + 1)^n*binomial(m, j) + Sum_{j=0..(n-m) (-1)^(j - m + n )*(1 + j)^n*binomial(n-m, j).
- A156821 (program): Prime factors of 13! listed with multiplicity.
- A156827 (program): A001792*A008683.
- A156828 (program): a(1) = 2. a(n) = the smallest prime >= a(n-1) + 4.
- A156829 (program): a(1) = 2. a(n) = the smallest prime >= a(n-1) + 6.
- A156834 (program): A156348 * A000010
- A156836 (program): Triangle read by rows, A156348 * A130207
- A156838 (program): Row sums of triangle A156837
- A156840 (program): Numbers k >= 1 such that k^2 == 1 (mod 900).
- A156841 (program): 529n^2 - 312n + 46.
- A156842 (program): 529n^2 - 746n + 263.
- A156843 (program): 279841n^2 - 165048n + 24335.
- A156844 (program): 279841n^2 - 394634n + 139128.
- A156845 (program): 12167n - 8579.
- A156846 (program): 12167n - 3588.
- A156849 (program): Numbers k such that k^2 == 2 (mod 23^2).
- A156850 (program): a(1)=2, a(n+1) is the smallest prime > (a(n) + sum of digits of a(n)).
- A156853 (program): a(n) = 2025*n^2 - 649*n + 52.
- A156854 (program): a(n) = 2025*n^2 - 3401*n + 1428.
- A156855 (program): a(n) = 2025*n^2 - n.
- A156856 (program): a(n) = 2025*n^2 + n.
- A156857 (program): Expansion of (1+2*x)/(1+x+4*x^2)^2.
- A156859 (program): The main column of a version of the square spiral.
- A156861 (program): Triangle read by rows: T(n, k) = 2^k - binomial(n, k+1).
- A156862 (program): Triangle read by rows: T(n, k) = 2^k - binomial(n, k+1) + 2^(n-k) - binomial(n, n-k+1).
- A156863 (program): Denominator of Euler(n, 1/22).
- A156864 (program): Triangle read by rows: T(n, k) = 2^k - binomial(n+1, k+1) - ((2*k-n)/(k+1)) * binomial(n+1, k).
- A156865 (program): a(n) = 729000*n - 612180.
- A156866 (program): a(n) = 729000*n - 116820.
- A156867 (program): a(n) = 729000*n - 180.
- A156868 (program): a(n) = 729000*n + 180.
- A156872 (program): Period 12: 1,3,-1,3,1,0,-1,-3,1,-3,-1,0 repeated.
- A156874 (program): Number of Sophie Germain primes <= n.
- A156875 (program): Number of safe primes <= n.
- A156877 (program): Number of primes <= n that are safe primes and also Sophie Germain primes.
- A156886 (program): a(n) = Sum_{k=0..n} C(n,k)*C(3*n+k,k)
- A156887 (program): a(n) = Sum_{k=0..n} C(n,k)*C(4*n+k,k).
- A156892 (program): Denominator of Euler(n, 1/23).
- A156894 (program): a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2*n+k-1,k).
- A156898 (program): a(n) = the smallest squarefree integer >= the n-th prime power.
- A156899 (program): a(n) = the largest prime power <= the n-th positive squarefree integer.
- A156900 (program): a(n) = the smallest prime power >= the n-th positive squarefree integer.
- A156906 (program): Transform of Fibonacci(n+1) with Hankel transform (-1)^binomial(n+1,2) * Fibonacci(n+1).
- A156909 (program): G.f.: A(x) = 1 + x*exp( Sum_{k>=1} [A(-(-1)^k*x) - 1]^k/k ).
- A156910 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)/(1 - 2^n*x)^n * x^n/n ).
- A156911 (program): G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2)/(1 - 3^n*x)^n * x^n/n ).
- A156922 (program): Third right hand column (n-m=2) of the A156920 triangle
- A156926 (program): Row sums of the FP2 polynomials of A156925.
- A156928 (program): G.f. of the z^1 coefficients of the FP1 in the second column of the A156921 matrix.
- A156934 (program): G.f. of the z^1 coefficients of the FP2 in the second column of the A156925 matrix
- A156944 (program): Let d(i) be the i-th digit of the decimal expansion of e = 2.71828182845…, so that d(1) = 2, d(2) = 7, d(3) = 1, etc. Then a(n) = d(10 - d(n)).
- A156959 (program): Numerator of Euler(n, 1/24).
- A156965 (program): Denominator of Euler(n, 1/25).
- A156991 (program): Triangle T(n,k) read by rows: T(n,k) = n! * binomial(n + k - 1, n).
- A156992 (program): Triangle T(n,k) = n!*binomial(n-1, k-1) for 1 <= k <= n, read by rows.
- A156995 (program): Triangle T(n, k) = 2*n*binomial(2*n-k, k)*(n-k)!/(2*n-k), with T(0, 0) = 2, read by rows.
- A157000 (program): Triangle T(n,k) = (n/k)*binomial(n-k-1, k-1) read by rows.
- A157001 (program): Fractions x/y, with 1<=x,y<=n, that reduce to (odd)/(even).
- A157002 (program): Transform of Catalan numbers whose Hankel transform gives the Somos-4 sequence.
- A157003 (program): Transform of Catalan numbers whose Hankel transform gives the Somos-4 sequence.
- A157004 (program): Transform of central binomial coefficients A000984 whose Hankel transform obeys a Somos-4 recurrence.
- A157005 (program): A Somos-4 variant.
- A157010 (program): a(n) = 1681*n^2 - 756*n + 85.
- A157014 (program): Expansion of x*(1-x)/(1 - 22*x + x^2).
- A157019 (program): a(n) = Sum_{d|n} binomial(n/d+d-2, d-1).
- A157020 (program): a(n) = Sum_{d|n} d*binomial(n/d+d-2,d-1).
- A157024 (program): a(0)=1, a(n) = (3n-1)*3n*(3n+1)/2 for n>0.
- A157027 (program): Denominator of Euler(n, 1/26).
- A157029 (program): A007318 * A157019.
- A157031 (program): Triangle A054521 * A157019, where A054521 = an infinite lower triangular matrix and A157019 = a vector [1, 2, 2, 4, 2, 8, 2, 10, 8, …].
- A157032 (program): Let d(i) be the i-th digit of the decimal expansion of phi=1.6180339887498948482045868…,so that d(0) = 1, d(1) = 6, d(2) = 1, etc. Then a(0) = 1, thereafter a(n) = d(d(n)).
- A157037 (program): Numbers with prime arithmetic derivative A003415.
- A157040 (program): 121n^2 - 2n.
- A157052 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 6.
- A157053 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 8.
- A157054 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 10.
- A157055 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 12.
- A157056 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 14.
- A157057 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 16.
- A157058 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 18.
- A157059 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 20.
- A157060 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 22.
- A157061 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 24.
- A157062 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 26.
- A157063 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 28.
- A157064 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 30.
- A157065 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 32.
- A157066 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 34.
- A157067 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 36.
- A157068 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 38.
- A157069 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 40.
- A157070 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 42.
- A157071 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 44.
- A157072 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 46.
- A157073 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 48.
- A157074 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 50.
- A157075 (program): Positive integers n for which the Diophantine equation x^2 + y^2 = n^2/2 has relatively prime solutions.
- A157077 (program): Triangle read by rows, coefficients of the Legendre polynomials P(n, x) times 2^n: T(n, k) = 2^n * [x^k] P(n, x), n >= 0, 0 <= k <= n.
- A157078 (program): a(n) = 32805000*n^2 - 55096200*n + 23133601.
- A157079 (program): a(n) = 32805000*n^2 - 10513800*n + 842401.
- A157080 (program): a(n) = 32805000*n^2 - 16200*n + 1.
- A157081 (program): a(n) = 32805000*n^2 + 16200*n + 1.
- A157084 (program): Consider all consecutive integer Pythagorean quintuples (X, X+1, X+2, Z-1, Z) ordered by increasing Z; sequence gives X values.
- A157085 (program): Consider all Consecutive Integer Pythagorean quintuples (X, X+1, X+2, Z-1, Z) ordered by increasing Z; sequence gives Z values.
- A157088 (program): Consider all consecutive integer Pythagorean septuples (X, X+1, X+2, X+3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives X values.
- A157089 (program): Consider all Consecutive Integer Pythagorean septuples (X, X+1, X+2, X+3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives Z values.
- A157092 (program): Consider all consecutive integer Pythagorean 9-tuples (X, X+1, X+2, X+3, X+4, Z-3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives X values.
- A157093 (program): Consider all Consecutive Integer Pythagorean 9-tuples (X,X+1,X+2,X+3,X+4,Z-3,Z-2,Z-1,Z) ordered by increasing Z; sequence gives Z values.
- A157094 (program): Denominator of Euler(n, 1/27).
- A157096 (program): Consider all consecutive integer Pythagorean 11-tuples (X, X+1, X+2, X+3, X+4, X+5, Z-4, Z-3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives X values.
- A157097 (program): Consider all Consecutive Integer Pythagorean 11-tuples (X, X+1, X+2, X+3, X+4, X+5, Z-4, Z-3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives Z values.
- A157100 (program): Transform of Catalan numbers whose Hankel transform satisfies the Somos-4 recurrence.
- A157101 (program): A Somos-4 variant.
- A157102 (program): Tuple-chromatic Van der Waerden numbers.
- A157103 (program): Array A(n, k) = Fibonacc(n+1, k), with A(n, 0) = A(n, n) = 1, read by antidiagonals.
- A157104 (program): Arithmetic derivative of cubefree numbers.
- A157105 (program): a(n) = 137842*n - 30996.
- A157106 (program): 5651522n^2 - 2541672n + 285769.
- A157108 (program): Triangle, read by rows, T(n, k) = binomial(n*binomial(n, k), k).
- A157110 (program): a(n) = 1681*n^2 - 2606*n + 1010.
- A157111 (program): a(n) = 137842*n - 106846.
- A157112 (program): a(n) = 5651522*n^2 - 8761372*n + 3395619.
- A157121 (program): Decimal expansion of 11+3*sqrt(2).
- A157122 (program): Decimal expansion of 11 - 3*sqrt(2).
- A157123 (program): Decimal expansion of (11 + 3*sqrt(2))/(11 - 3*sqrt(2)).
- A157124 (program): a(1)=1; a(n) = floor((n-1)*Sum_{k=1..n-1} 1/a(k)).
- A157125 (program): A transform of the Catalan numbers.
- A157126 (program): Expansion of (1-2x-3x^2+x^3-x^5)/(1+4x^3+x^6).
- A157127 (program): A transform of the Catalan numbers with a simple Hankel transform.
- A157128 (program): Expansion of (1 - x - x^2 + x^3 - x^5) / ((1 + x)^2*(1 - x + x^2)^2).
- A157129 (program): An analog of the Kolakoski sequence A000002, only now a(n) = (length of n-th run divided by 2) using 1 and 2 and starting with 1,1.
- A157130 (program): Partial sums of A128201.
- A157132 (program): Factorial of primes divided by prime numbers’ respective places in the sequence of primes.
- A157142 (program): Signed denominators of Leibniz series for Pi/4.
- A157194 (program): Fibonacci sequence beginning 41, 43.
- A157195 (program): a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of the proper divisors of n.
- A157196 (program): a(n)=(1/2)*(sum of elements of n-th run) using 1 and 2 starting with 1,1.
- A157201 (program): Numbers k such that 66*k + 1 is prime.
- A157202 (program): Numbers k such that 66*k + 5 is prime.
- A157206 (program): Numerator of Euler(n, 1/28).
- A157214 (program): Decimal expansion of 18 + 5*sqrt(2).
- A157215 (program): Decimal expansion of 18 - 5*sqrt(2).
- A157216 (program): Decimal expansion of (18 + 5*sqrt(2))/(18 - 5*sqrt(2)).
- A157219 (program): Triangle T(n, k) = binomial(n*f(n,k), f(n,k)), where f(n, k) = k if k <= floor(n/2) otherwise n-k, read by rows.
- A157223 (program): Number of primitive inequivalent oblique sublattices of centered rectangular lattice of index n.
- A157224 (program): Number of primitive inequivalent (up to Pi/2 rotation) nonsquare sublattices of square lattice of index n.
- A157226 (program): Number of primitive inequivalent sublattices of square lattice having mirrors parallel to the sides of the unit cell of the parent lattice of index n.
- A157227 (program): Number of primitive inequivalent (up to Pi/3 rotation) non-hexagonal sublattices of hexagonal (triangular) lattice of index n.
- A157228 (program): Number of primitive inequivalent inclined square sublattices of square lattice of index n.
- A157230 (program): Number of primitive inequivalent sublattices of square lattice having mirrors parallel to the diagonals of the unit cell of the parent lattice of index n.
- A157233 (program): Numerator of Euler(n, 5/28).
- A157234 (program): Numerator of Euler(n, 9/28).
- A157235 (program): Number of primitive inequivalent oblique sublattices of hexagonal (triangular) lattice of index n (equivalence and symmetry of sublattices are determined using only parent lattice symmetries).
- A157236 (program): Numerator of Euler(n, 11/28).
- A157239 (program): Numerator of Euler(n, 13/28).
- A157240 (program): a(n) = A128018(n) + 1.
- A157241 (program): Expansion of x / ((1-x)*(4*x^2-2*x+1)).
- A157249 (program): Generalized Wilson quotients (or Wilson quotients for composite moduli).
- A157252 (program): Denominator of Euler(n, 1/29).
- A157258 (program): Decimal expansion of 7 + 2*sqrt(2).
- A157259 (program): Decimal expansion of 7 - 2*sqrt(2).
- A157260 (program): Decimal expansion of (7 + 2*sqrt(2))/(7 - 2*sqrt(2)).
- A157262 (program): a(n) = 36*n^2 - 55*n + 21.
- A157263 (program): a(n) = 1728*n - 1320.
- A157264 (program): a(n) = 10368*n^2 - 15840*n + 6049.
- A157265 (program): a(n) = 36*n^2 - 17*n + 2.
- A157266 (program): a(n) = 1728*n - 408.
- A157267 (program): a(n) = 10368*n^2 - 4896*n + 577.
- A157279 (program): Product 1*2*…*r mod n, where r = integer part of sqrt(n).
- A157282 (program): Maximum cardinality of a weakly triple-free subset of {1, 2, …, n}.
- A157284 (program): Triangle T(n, k, m) = (m+1)^n*binomial(n,k)*f(n,m)*f(k,n-m)/n!, with T(n, 0, m) = 1, where f(n, k) = Product_{j=1..n} ( (1 - (k+1)^J)/(-k)^j ), f(n, 0) = n!, and m = 0, read by rows.
- A157286 (program): a(n) = 36*n^2 - n.
- A157287 (program): a(n) = 1728*n - 24.
- A157288 (program): a(n) = 10368*n^2 - 288*n + 1.
- A157298 (program): Decimal expansion of (251+66*sqrt(2))/233.
- A157300 (program): Decimal expansion of (1683 + 58*sqrt(2))/41^2.
- A157317 (program): G.f. A(x) = Product_{n>=1} 1/(1 - 2^(n^2)*x^n).
- A157319 (program): Possible total points for a single team in a game of American football, ignoring safeties (and time constraints).
- A157320 (program): Symmetrical Hahn weights on q-form factorials:m=1;q=2; q-form:t(n,m)=If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; Hahn weight:b(n,k,m)=If[n == 0, 1, (n!*t[m + 1, k]*t[m + 1, n - k])/(k!*(n - k)!*t[1, n])].
- A157324 (program): a(n) = 36*n^2 + n.
- A157325 (program): a(n) = 1728*n + 24.
- A157326 (program): a(n) = 10368*n^2 + 288*n + 1.
- A157328 (program): Expansion of 1/(1-2x*c(4x)) with c(x) g.f. of Catalan numbers (A000108).
- A157330 (program): a(n) = 64*n - 8.
- A157331 (program): a(n) = 128*n^2 - 32*n + 1.
- A157335 (program): Expansion of 1/( (1+x)*(1-7*x+x^2) ).
- A157336 (program): a(n) = 8*(8*n + 1).
- A157337 (program): a(n) = 128*n^2 + 32*n + 1.
- A157338 (program): First primes in successive prime centuries.
- A157349 (program): Decimal expansion of (297 + 68*sqrt(2))/281.
- A157351 (program): Row sums of triangle T(j,k) = (j^k) mod (j*k) for 1 <= k <= j (see A096133).
- A157358 (program): Triple-safe primes p: p, (p-1)/2, (p-3)/4, and (p-7)/8 are all prime.
- A157361 (program): Triangle read by rows, A051731 * (A114810 * 0^(n-k))
- A157362 (program): a(n) = 49*n^2 - 2*n.
- A157363 (program): 686n - 14.
- A157364 (program): a(n) = 4802*n^2 - 196*n + 1.
- A157365 (program): a(n) = 49*n^2 + 2*n.
- A157366 (program): a(n) = 686*n + 14.
- A157367 (program): a(n) = 4802*n^2 + 196*n + 1.
- A157368 (program): a(n) = 49*n^2 - 78*n + 31.
- A157369 (program): a(n) = 343*n - 273.
- A157370 (program): a(n) = 2401*n^2 - 3822*n + 1520.
- A157371 (program): a(n) = (n+1)*(9-9*n+5*n^2-n^3).
- A157373 (program): a(n) = 49*n^2 - 20*n + 2.
- A157374 (program): a(n) = 343*n - 70.
- A157375 (program): a(n) = 2401*n^2 - 980*n + 99.
- A157376 (program): a(n) = 6561*n^2 - 7732*n + 2278.
- A157377 (program): a(n) = 531441*n - 313146.
- A157378 (program): a(n) = 43046721*n^2 - 50729652*n + 14945957.
- A157391 (program): A partition product of Stirling_1 type [parameter k = 1] with biggest-part statistic (triangle read by rows).
- A157410 (program): Final primes in successive prime centuries.
- A157411 (program): a(n) = 30*n^4 - 120*n^3 + 120*n^2 - 19.
- A157416 (program): Length of maximal uncrossed cycle of knight moves on n X n board.
- A157417 (program): Primes of the form floor((4*n^2-8*n-9)/3).
- A157418 (program): a(n) is the number of ways to insert single pairs of parenthesis to completely separate n identical objects in a straight line such that at least one of the objects at the two ends is not enclosed.
- A157423 (program): Triangle read by rows, T(n,k) = 0 if (n-k+1) is prime, else 1.
- A157431 (program): a(n) = 4*n^2 + 73*n + 333.
- A157432 (program): 64n + 584.
- A157433 (program): 128n^2 + 2336n + 10657.
- A157434 (program): a(n) = 4*n^2 + 79*n + 390.
- A157435 (program): 64n + 632.
- A157436 (program): a(n) = 128*n^2 + 2528*n + 12481.
- A157437 (program): Primes congruent to 1, 5, 7, or 11 modulo 24.
- A157440 (program): a(n) = 121*n^2 - 204*n + 86.
- A157441 (program): a(n) = 1331*n - 1122.
- A157442 (program): a(n) = 14641*n^2 - 24684*n + 10405.
- A157443 (program): a(n) = 121*n^2 - 38*n + 3.
- A157444 (program): a(n) = 1331*n - 209.
- A157445 (program): a(n) = 14641*n^2 - 4598*n + 362.
- A157446 (program): a(n) = 16*n^2 - n.
- A157447 (program): a(n) = 512*n - 16.
- A157448 (program): a(n) = 2048*n^2 - 128*n + 1.
- A157449 (program): Difference between n and the sum of its divisors except 1 and itself.
- A157451 (program): Number generated by regarding the numbers in row n of A139038 as digits of a base n number.
- A157452 (program): Number generated by regarding the numbers in row n of A003983 as digits of a base n number.
- A157454 (program): Triangle read by rows: T(n, m) = min(2*m - 1, 2*(n - m) + 1).
- A157455 (program): Number generated by regarding the numbers in row n of A157454 as digits of a base n number.
- A157456 (program): Expansion of x*(1-x) / ( 1 - 16*x + x^2 ).
- A157457 (program): Read n-th row of triangle in A157458 and regard it as the expansion of a number in base n+1.
- A157458 (program): Triangle, read by rows, double tent function: T(n,k) = min(1 + 2*k, 1 + 2*(n-k), n).
- A157459 (program): Expansion of 72*x^2 / (1 - 323*x + 323*x^2 - x^3).
- A157460 (program): Expansion of 88*x^2 / (1-483*x+483*x^2-x^3).
- A157461 (program): Expansion of x*(x+1) / (x^2-26*x+1).
- A157462 (program): Denominator of Euler(n, 1/30).
- A157467 (program): Primes of the form p^2 + 2*p + 2 where p is prime.
- A157470 (program): Decimal expansion of (99+14*sqrt(2))/97.
- A157472 (program): Decimal expansion of (627 + 238*sqrt(2))/23^2.
- A157474 (program): a(n) = 16n^2 + n.
- A157475 (program): 512n + 16.
- A157476 (program): 2048n^2 + 128n + 1.
- A157491 (program): A050165*A130595 as infinite lower triangular matrices.
- A157492 (program): Apply partial sum operator twice to sequence of squares of the first n primes.
- A157493 (program): Apply partial sum operator thrice to sequence of squares of the first n primes.
- A157497 (program): Triangle read by rows, A156348 * A127648
- A157499 (program): Denominator of Euler(n, 1/31).
- A157502 (program): Even numbers without the squares.
- A157505 (program): a(n) = 1458*n + 18.
- A157506 (program): a(n) = 13122*n^2 + 324*n + 1.
- A157507 (program): a(n) = 81*n^2 - 2*n.
- A157508 (program): a(n) = 1458*n - 18.
- A157509 (program): a(n) = 13122*n^2 - 324*n + 1.
- A157510 (program): a(n) = 1000*n + 20.
- A157511 (program): a(n) = 5000*n^2 + 200*n + 1.
- A157512 (program): Partial sums of A157502.
- A157514 (program): a(n) = 25*n^2 - n.
- A157515 (program): a(n) = 1000*n - 20.
- A157516 (program): a(n) = 5000*n^2 - 200*n + 1.
- A157517 (program): a(n) = 7 + 12*n - 6*n^2.
- A157522 (program): Triangle T(n, k) = f(n, k) + f(n, n-k) - 1, where f(n, k) = k if k <= floor(n/4), floor(n/2) - k if floor(n/4) < k <= floor(n/2), k - floor(n/2) if floor(n/2) < k <= floor(3*n/4), otherwise n-k, read by rows.
- A157524 (program): a(n) = A140783(n+4)/9.
- A157528 (program): Triangle read by rows: T(n, k) = 2*k*(n - k) with T(n, 0) = T(n, n) = 1.
- A157531 (program): Triangle T(n, k) = binomial(2*n, n) + binomial(n, k)^2, read by rows.
- A157532 (program): a(1) = 2; for n > 1, a(n) = 3.
- A157603 (program): Triangle read by rows: T(n,k) = 1 for k <= n/2, T(n,k)=A055248 otherwise.
- A157606 (program): a(1)=1. a(n) = the largest integer coprime to a(n-1) and less than n^2.
- A157609 (program): 2662n - 22.
- A157610 (program): 29282n^2 - 484n + 1.
- A157613 (program): a(n) = 2662*n + 22.
- A157614 (program): a(n) = 29282*n^2 + 484*n + 1.
- A157615 (program): On an n X n board, a(n) is the maximal number of squares covered by a self-avoiding path made of alternated vertical and horizontal unitary steps.
- A157616 (program): On an n X n board, a(n) is the maximal number of squares covered by a self-avoiding path that starts from a corner and is made of alternated vertical and horizontal unitary steps.
- A157617 (program): On an n X n board, a(n) is the maximal number of squares covered by a self-avoiding cycle made of alternated vertical and horizontal unit length steps.
- A157618 (program): a(n) = 625*n^2 - 886*n + 314.
- A157619 (program): 31250n - 22150.
- A157620 (program): 781250n^2 - 1107500n + 392499.
- A157621 (program): a(n) = 625n^2 - 364n + 53.
- A157622 (program): 31250n - 9100.
- A157623 (program): 781250n^2 - 455000n + 66249.
- A157625 (program): Product of the composite numbers between n+1 and 2n, both inclusive.
- A157626 (program): a(n) = 100n^2 - 151n + 57.
- A157627 (program): 8000n - 6040.
- A157628 (program): 80000n^2 - 120800n + 45601.
- A157632 (program): Triangle T(n,m) read by rows: 1 in column m=0 and on the diagonal, else 3*n*m*(n-m).
- A157633 (program): Triangle T(n,m) read rows: 1 in column m=0 and on the diagonal, 2*m*(n-m)*(m^2-n*m+2*n^2) otherwise.
- A157635 (program): Triangle read by rows: T(n,m) = 1 if n*m*(n-m) = 0, and n*m*(n-m) otherwise.
- A157636 (program): Triangle read by rows: T(n, k) = 1 if k=0 or k=n, otherwise = n*k*(n-k)/2.
- A157639 (program): Least number of lattice points from which every point of a square n X n lattice is visible.
- A157645 (program): A157644(n+39)-A157644(n).
- A157647 (program): Decimal expansion of (33+8*sqrt(2))/31.
- A157648 (program): Decimal expansion of (1539+850*sqrt(2))/31^2.
- A157649 (program): Decimal expansion of (387 + 182*sqrt(2))/17^2.
- A157651 (program): a(n) = 100*n^2 - 49*n + 6.
- A157652 (program): a(n) = 40*(200*n - 49).
- A157653 (program): a(n) = 80000*n^2 - 39200*n + 4801.
- A157657 (program): a(1) = 1, a(n) = -mu(n) for n >= 2.
- A157658 (program): a(1) = 0, a(n) = -mu(n) for n >= 2.
- A157659 (program): a(n) = 100*n^2 - n.
- A157660 (program): a(n) = 8000*n - 40.
- A157661 (program): a(n) = 80000*n^2 - 800*n + 1.
- A157663 (program): a(n) = 8000*n + 40.
- A157664 (program): a(n) = 80000*n^2 + 800*n + 1.
- A157665 (program): a(n) = 729*n^2 - 1016*n + 354.
- A157666 (program): a(n) = 19683*n - 13716.
- A157667 (program): a(n) = 531441*n^2 - 740664*n + 258065.
- A157668 (program): a(n) = 729*n^2 - 442*n + 67.
- A157669 (program): a(n) = 19683*n - 5967.
- A157670 (program): a(n) = 531441*n^2 - 322218*n + 48842.
- A157671 (program): Numbers whose ternary representation begins with 2.
- A157672 (program): Number of unordered factorizations of n! into two distinct proper factors.
- A157674 (program): G.f.: A(x) = 1 + x/exp( Sum_{k>=1} (A((-1)^k*x) - 1)^k/k ).
- A157676 (program): Numbers n such that n + (product of digits of n) is prime.
- A157681 (program): Fibonacci sequence beginning 29, 31.
- A157684 (program): a(n)=#{1<=k<=n : [K(k),K(k+1)]=[1,2]} where K=A000002
- A157685 (program): a(n)=#{1<=k<=n : [K(k),K(k+1)]=[2,1]} where K=A000002
- A157686 (program): a(n) = A157684(n) - A157685(n).
- A157687 (program): a(n)=n-A054353(A156351(n)).
- A157694 (program): Triangle read by rows: the Pascal triangle A007318 with all elements replaced by 1 which do not equal the central binomial coefficients.
- A157695 (program): Composite numbers that are not multiples of 3.
- A157696 (program): Define k(n) to be the sequence of integers such that k(n)F(n)=F(2n)(Fibonacci sequence) (A000204); in turn define g(n) to be the sequence of integers such that g(n)k(n)=k(3n)(A110391); finally a(n) is the sequence of integers such that a(n)g(n)=g(5n).
- A157697 (program): Decimal expansion of sqrt(2/3).
- A157706 (program): The z^2 coefficients of the polynomials in the GF1 denominators of A156921.
- A157707 (program): The z^2 coefficients of the polynomials in the GF3 denominators of A156927 divided by 2
- A157713 (program): a(n)=(2*n+1)!*(2*n-2)!/((n-1)!*(n!)^2*6) ,n=1,2… .
- A157716 (program): One-eighth of triangular numbers (integers only).
- A157721 (program): a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of composite (nonprime) divisors of n.
- A157725 (program): a(n) = Fibonacci(n) + 2.
- A157726 (program): a(n) = Fibonacci(n) + 3.
- A157727 (program): a(n) = Fibonacci(n) + 4.
- A157728 (program): a(n) = Fibonacci(n) - 4.
- A157729 (program): a(n) = Fibonacci(n) + 5.
- A157730 (program): a(n) = 441*n^2 - 488*n + 135.
- A157731 (program): a(n) = 18522*n - 10248.
- A157732 (program): a(n) = 388962*n^2 - 430416*n + 119071.
- A157734 (program): a(n) = 441*n^2 - 394*n + 88.
- A157735 (program): 18522n - 8274.
- A157736 (program): a(n) = 388962*n^2 - 347508*n + 77617.
- A157737 (program): a(n) = 441*n^2 - 2*n.
- A157738 (program): 18522n - 42.
- A157739 (program): a(n) = 388962*n^2 - 1764*n + 1.
- A157740 (program): 18522n + 42.
- A157741 (program): a(n) = 388962*n^2 + 1764*n + 1.
- A157742 (program): A006094(n+3) mod 9.
- A157751 (program): Triangle of coefficients of polynomials F(n,x) in descending powers of x generated by F(n,x)=(x+1)*F(n-1,x)+F(n-1,-x), with initial F(0,x)=1.
- A157757 (program): a(n) = 2809*n^2 - 4618*n + 1898.
- A157758 (program): a(n) = 297754*n - 244754.
- A157759 (program): a(n) = 15780962*n^2 - 25943924*n + 10662963.
- A157760 (program): a(n) = 2809*n^2 - 1000*n + 89.
- A157761 (program): a(n) = 297754*n - 53000.
- A157762 (program): a(n) = 15780962*n^2 - 5618000*n + 500001.
- A157765 (program): Expansion of (2 - 2*x) / (1 - 10*x - 7*x^2).
- A157767 (program): Numerator of Euler(n, 1/32).
- A157768 (program): 27225n^2 - 39202n + 14112.
- A157769 (program): 8984250n - 6468330.
- A157770 (program): 1482401250n^2 - 2134548900n + 768398401.
- A157772 (program): Numbers n such that 100n + 13 is prime.
- A157779 (program): Numerator of Bernoulli(n, 1/2).
- A157780 (program): Denominator of Bernoulli(n, 1/2).
- A157782 (program): Denominator of Bernoulli(n, -1/2).
- A157786 (program): a(n) = 27225*n^2 - 15248*n + 2135.
- A157787 (program): 8984250n - 2515920.
- A157788 (program): 1482401250n^2 - 830253600n + 116250751.
- A157791 (program): Least number of lattice points on two adjacent sides from which every point of a square n X n lattice is visible.
- A157792 (program): Least number of lattice points on one side from which every point of a square n X n lattice is visible.
- A157795 (program): Largest subset of the discrete triangular grid { (a,b,c): a+b+c = n, a,b,c >= 0 } that does not contain any upward-pointing triangles (i.e., triples (a+r,b,c), (a,b+r,c), (a,b,c+r) with r positive).
- A157796 (program): a(n) = 27225*n^2 - 12098*n + 1344.
- A157797 (program): a(n) = 8984250*n - 1996170.
- A157798 (program): a(n) = 1482401250*n^2 - 658736100*n + 73180801.
- A157800 (program): Denominator of Bernoulli(n, 1/3).
- A157802 (program): a(n) = 27225*n^2 - 51302*n + 24168.
- A157803 (program): a(n) = 8984250*n - 8464830.
- A157804 (program): a(n) = 1482401250*n^2 - 2793393900*n + 1315947601.
- A157805 (program): Numerator of Euler(n,3).
- A157806 (program): Absolute value of the difference between numerator and denominator of fractions arranged by Cantor’s ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, …) with equivalent fractions removed.
- A157807 (program): Numerators of fractions arranged in Cantor’s ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, 5/2, …) with equivalent fractions removed.
- A157810 (program): Period 4: repeat [2, 1, 3, 2].
- A157813 (program): Denominators of fractions arranged in Cantor’s ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, 5/2, …) with equivalent fractions removed.
- A157814 (program): a(n) = 27225*n^2 - 2*n.
- A157815 (program): a(n) = 8984250*n - 330.
- A157816 (program): a(n) = 1482401250*n^2 - 108900*n + 1.
- A157818 (program): Denominator of Bernoulli(n, 1/4).
- A157820 (program): 27225n^2 + 2n.
- A157821 (program): 8984250n + 330.
- A157822 (program): 1482401250n^2+108900n+1.
- A157823 (program): a(n) = A156591(n) + A156591(n+1).
- A157824 (program): 3600n^2 - 6751n + 3165.
- A157825 (program): 1728000n - 1620240.
- A157826 (program): 103680000n^2 - 194428800n + 91152001.
- A157834 (program): Numbers n such that 3n-2 and 3n+2 are both prime.
- A157838 (program): 3600n^2 - 6049n + 2541.
- A157839 (program): 1728000n - 1451760.
- A157840 (program): 103680000n^2 - 174211200n + 73180801.
- A157842 (program): a(n) = 3600*n^2 - 5599*n + 2177.
- A157843 (program): 1728000n - 1343760.
- A157844 (program): 103680000n^2 - 161251200n + 62697601.
- A157845 (program): a(0) = 1, a(n) = sum of binary digits of all prior terms, expressed in binary.
- A157853 (program): 3600n^2 - 1601n + 178.
- A157854 (program): 1728000n - 384240.
- A157855 (program): 103680000n^2 - 46108800n + 5126401.
- A157857 (program): a(n) = 3600*n^2 - n.
- A157858 (program): a(n) = 1728000*n - 240.
- A157859 (program): a(n) = 103680000*n^2 - 28800*n + 1.
- A157861 (program): a(n) = 3600*n^2 + n.
- A157862 (program): a(n) = 1728000*n + 240.
- A157863 (program): a(n) = 103680000*n^2 + 28800*n + 1.
- A157865 (program): a(n) is the number of numbers of the form 4n+2 in A082542.
- A157867 (program): Denominator of Bernoulli(n, 1/5).
- A157870 (program): a(n) = (4n+1)*(4n+2) = (4n+2)!/(4n)!.
- A157872 (program): a(n) = 9*n^2 - 3.
- A157874 (program): Expansion of 104*x^2 / (-x^3+675*x^2-675*x+1).
- A157877 (program): Expansion of (1-x)*x/(x^2-30*x+1).
- A157878 (program): Expansion of x*(1+x)/(x^2-30*x+1).
- A157879 (program): Expansion of 120*x^2 / (-x^3+899*x^2-899*x+1).
- A157880 (program): Expansion of 136*x^2 / (-x^3+1155*x^2-1155*x+1).
- A157881 (program): Expansion of 152*x^2 / (-x^3+1443*x^2-1443*x+1).
- A157884 (program): For each positive integer m there exist at least one prime Q=Q(m) and at least one prime P=P(m) such that (2m-1)^2 < Q < (2m)^2 - (2m-1) <= P < (2m)^2. Sequence lists pairs P(m), Q(m) for m >= 1. If more than one prime for P or Q exists, we take the smallest.
- A157887 (program): The domatic number of the n-cube.
- A157888 (program): a(n) = 81*n^2 + 9.
- A157889 (program): a(n) = 18*n^2 + 1.
- A157892 (program): Values of k in A080075.
- A157893 (program): Values of m in A080075.
- A157909 (program): a(n) = 81*n^2 - 9.
- A157910 (program): a(n) = 18*n^2 - 1.
- A157911 (program): Nonprimes whose digits are all cubes.
- A157912 (program): 64*n^2 + 16.
- A157913 (program): a(n) = 64*n^2 - 16.
- A157914 (program): a(n) = 8*n^2 - 1.
- A157915 (program): a(n) = 625*n^2 + 25.
- A157916 (program): a(n) = 50*n^2 + 1.
- A157918 (program): a(n) = 625*n^2 - 25.
- A157919 (program): a(n) = 50*n^2 - 1.
- A157921 (program): a(n) = 72*n - 1.
- A157923 (program): a(n) = 49*n^2 - n.
- A157924 (program): a(n) = 98*n - 1.
- A157928 (program): a(n) = 0 if n < 2, = 1 otherwise.
- A157931 (program): Numbers that are both the sum and the product of two primes.
- A157932 (program): Numbers k such that (3^(35*k) + 5^(21*k) + 7^(15*k)) mod 105 is prime.
- A157947 (program): a(n) = 98n + 1.
- A157948 (program): a(n) = 64*n^2 - n.
- A157949 (program): a(n) = 128*n - 1.
- A157951 (program): a(n) = 128*n + 1.
- A157952 (program): a(n) = 162*n + 1.
- A157953 (program): a(n) = 81n^2 - n.
- A157954 (program): 162n - 1.
- A157955 (program): 200n - 1.
- A157956 (program): a(n) = 200*n + 1.
- A157958 (program): a(n) = 242*n + 1.
- A157960 (program): a(n) = 121*n^2 - n.
- A157961 (program): a(n) = 242*n - 1.
- A157966 (program): Number of 3’s in A157733(n).
- A157970 (program): Evil twin locations: first members of pairs of consecutive evil numbers.
- A157971 (program): Odious twin locations: first members of pairs of consecutive odious numbers.
- A157974 (program): Primes p such that 12*p + 11 is also prime.
- A157975 (program): Primes p such that 16*p + 15 is also prime.
- A157976 (program): Primes p such that 18*p + 17 is also prime.
- A157977 (program): Primes p such that 20*p + 19 is also prime.
- A157978 (program): Primes p such that 4*p - 3 is also a prime.
- A157983 (program): a(n)=3!*n!/(8!*19!)
- A157984 (program): a(n) = n!/(7 * 20!).
- A157988 (program): a(n)=16*n!/(253*43!).
- A157990 (program): a(n) = 288*n + 1.
- A157996 (program): Primes which are sum of 1 and two nonconsecutive primes p1 and p2, p2 - p1 > 2.
- A157997 (program): 288n - 1.
- A157998 (program): 169n^2 - n.
- A157999 (program): 338n - 1.
- A158000 (program): a(n) = 338*n + 1.
- A158001 (program): Period 6: repeat [9, 10, 9, 4, 4, 1].
- A158002 (program): a(n) = 392*n + 1.
- A158003 (program): a(n) = 196*n^2 - n.
- A158004 (program): a(n) = 392*n - 1.
- A158010 (program): a(n) = 256*n^2 - n.
- A158011 (program): a(n) = 512n - 1.
- A158012 (program): A000796(n)*A000796(n+1) mod 9.
- A158014 (program): Primes p such that (p-1)/8 is also prime.
- A158015 (program): Primes p such that 6*p-1 is also prime.
- A158016 (program): Primes p such that 8*p-1 is also prime.
- A158017 (program): Primes p such that 10*p-1 is also prime.
- A158018 (program): Primes p such that (p - 1)/12 is also prime.
- A158019 (program): Numbers such that (n-1)/2 and 10*n-1 are both prime.
- A158037 (program): A106044 sorted and duplicates removed.
- A158038 (program): Difference between n-th prime and next cube.
- A158040 (program): Determinant of power series of gamma matrix with determinant 2!.
- A158054 (program): a(1)=2, a(n+1) is the smallest prime > n*(sum of decimal digits of a(n)).
- A158055 (program): a(1)=2, a(n+1) is the smallest prime > n*first digit of a(n).
- A158056 (program): a(n) = 16*n^2 + 2*n.
- A158057 (program): First differences of A051870: 16*n + 1.
- A158058 (program): a(n) = 16*n^2 - 2*n.
- A158059 (program): a(1)=2, a(n+1) is the smallest prime >= n*sum of digits of a(n).
- A158060 (program): a(n) = 25*n + 1.
- A158062 (program): a(n) = 36*n^2 - 2*n.
- A158064 (program): a(n) = 36*n^2 + 2*n.
- A158065 (program): a(n) = 36*n + 1.
- A158066 (program): a(n) = 49*n + 1.
- A158067 (program): a(n) = 64*n^2 - 2*n.
- A158068 (program): Period 6: repeat [1, 2, 2, 1, 5, 5].
- A158070 (program): a(n) = 64*n^2 + 2*n.
- A158071 (program): a(n) = 64*n + 1.
- A158082 (program): Squares whose decimal expansion contains no digit greater than 4.
- A158083 (program): a(n) = Fibonacci(n+3) for n < 5 and 9*n - 15 otherwise.
- A158090 (program): Period 9: repeat [0, 6, 0, 6, 0, 0, 3, 3, 0].
- A158095 (program): G.f.: A(x) = exp( Sum_{n>=1} 2*sigma(n,n-1)*x^n/n ).
- A158096 (program): G.f.: A(x) = exp( Sum_{n>=1} x^n/n * 2^(n^2)/(1 + 2^(n^2)*x^n) ).
- A158099 (program): Euler transform of square powers of 2: [2,2^4,2^9,…,2^(n^2),…].
- A158111 (program): E.g.f.: sm^-1(x) = Sum_{n>=0} a(n)*x^(3n+1)/(3n+1)!; a(n) = coefficient of x^(3n+1)/(3n+1)! in the Maclaurin expansion of the inverse of the Dixon elliptic function sm(x,0).
- A158116 (program): Triangle T(n,k) = 6^(k*(n-k)), read by rows.
- A158117 (program): Triangle T(n, k) = 10^(k*(n-k)), read by rows.
- A158121 (program): Given n points in the complex plane, let M(n) the number of distinct Moebius transformations that take 3 distinct points to 3 distinct points. Note that the triples may have some or all of the points in common.
- A158123 (program): a(n) = 81*n + 1.
- A158127 (program): a(n) = 100*n^2 + 2*n.
- A158128 (program): 100n + 1.
- A158129 (program): 100n^2 - 2n.
- A158130 (program): 121n - 1.
- A158131 (program): a(n) = 121*n + 1.
- A158132 (program): 144n^2 + 2n.
- A158133 (program): 144n + 1.
- A158134 (program): Fourth quadrisection of A157261.
- A158135 (program): a(n) = 144*n^2 - 2*n.
- A158136 (program): a(n) = 144*n - 1.
- A158137 (program): Period 9: repeat [-2,4,-2,4,-2,-2,1,1,-2].
- A158138 (program): Number of nondecreasing integer sequences of length 4 with sum zero and sum of absolute values 2n.
- A158186 (program): a(n) = 10*n^2 - 7*n + 1.
- A158187 (program): a(n) = 10*n^2 + 1.
- A158190 (program): Nonprime numbers with final digit prime.
- A158196 (program): Expansion of (1-x^2*c(x)^4)/(1-3*x*c(x)^2), c(x) the g.f. of A000108.
- A158197 (program): Expansion of (1-x^2*c(x)^4)/(1-4*x*c(x)^2), c(x) the g.f. of A000108.
- A158198 (program): Triangle T(n, k) = Sum_{j=0..k-1} (-1)^j*binomial(k, j+1)*(k-j)^(n-k), read by rows.
- A158204 (program): Terms in A178335 not divisible by 10.
- A158210 (program): Number omega(n) of distinct primes dividing n multiplied by -1 when n is squarefree (thus Omega(n) = omega(n)).
- A158218 (program): 169n^2 - 2n.
- A158219 (program): 169n - 1.
- A158220 (program): a(n) = 169*n^2 + 2*n.
- A158221 (program): a(n) = 169n + 1.
- A158222 (program): a(n) = 196*n^2 + 2*n.
- A158223 (program): a(n) = 196*n + 1.
- A158224 (program): a(n) = 196*n^2 - 2*n.
- A158225 (program): 196n - 1.
- A158226 (program): 225n^2-2n.
- A158227 (program): 225n - 1.
- A158228 (program): 225n^2 + 2n.
- A158229 (program): 225n + 1.
- A158230 (program): 256n^2+2n.
- A158231 (program): a(n) = 256*n + 1.
- A158241 (program): Decimal expansion of theta = arctan((sqrt(10-2*sqrt(5))-2)/(sqrt(5)-1)).
- A158243 (program): Derangements with at least one 2-cycle.
- A158249 (program): a(n) = 256*n^2 - 2*n.
- A158250 (program): a(n) = 256*n - 1.
- A158251 (program): a(n)=S(S(n)) where S=A054353 gives the partial sums of Kolakoski sequence.
- A158252 (program): 289n^2 - 2n.
- A158253 (program): 289n - 1.
- A158254 (program): 289n^2 + 2n.
- A158255 (program): 289n + 1.
- A158265 (program): G.f.: A(x) = exp( Sum_{n>=1} 2*sigma(n,n+1)*x^n/n ).
- A158266 (program): G.f.: A(x) = exp( Sum_{n>=1} C(2n-1,n)^2*x^n/n ).
- A158270 (program): Single-digit numbers in A061049.
- A158271 (program): 324n^2 + 2n.
- A158272 (program): 324n + 1.
- A158273 (program): Indices of single-digit numbers in A061049.
- A158274 (program): Numerators of antiharmonic means of divisors of n.
- A158275 (program): Denominators of antiharmonic means of divisors of n.
- A158276 (program): Numbers k such that sigma_1(k) not divides sigma_2(k).
- A158277 (program): The lesser of twin prime pairs with each prime in a different century.
- A158280 (program): Octosection: A145511(8n+4) or A145501(8n+4).
- A158289 (program): Period 18 zigzag sequence: repeat [0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1].
- A158293 (program): Primes whose digit sum is a multiple of 10.
- A158298 (program): Denominators of averages of squares of the divisors of n.
- A158299 (program): Numerators of averages of squares of the divisors of n.
- A158302 (program): “1” followed by repeats of 2^k deleting all 4^k, k>0
- A158303 (program): Triangle read by rows, A007318 * ((A158300 * 0^(n-k)).
- A158304 (program): Numbers k such that k^2 contains no digit greater than 4.
- A158305 (program): 324n^2 - 2n.
- A158306 (program): 324n - 1.
- A158307 (program): 361n^2 - 2n.
- A158308 (program): 361n - 1.
- A158309 (program): 361n^2 + 2n.
- A158310 (program): 361n + 1.
- A158312 (program): 400n^2 + 2n.
- A158313 (program): a(n) = 400 * n + 1.
- A158315 (program): A158280(n)/7.
- A158316 (program): 400n^2 - 2n.
- A158317 (program): a(n) = 400*n - 1.
- A158318 (program): Primes p such that 5p-2 is prime.
- A158319 (program): 441n - 1.
- A158321 (program): a(n) = 441n^2 + 2n.
- A158322 (program): a(n) = 441*n + 1.
- A158324 (program): Successive powers of two, represented as binary coded decimal. (0x1, 0x2, 0x4, 0x8, 0x16, 0x32, etc.)
- A158325 (program): a(n) = 484n^2 + 2n.
- A158326 (program): 484n + 1.
- A158327 (program): a(n) = A145444(n)-A145511(n).
- A158329 (program): 484n^2 - 2n.
- A158330 (program): 484n - 1.
- A158333 (program): Position of number of digits increment in the sequence of powers of 3.
- A158338 (program): Composite numbers k such that k - number of divisors of k = prime.
- A158362 (program): a(n)=binomial((n+1)^3,n+2), n=1,2… .
- A158363 (program): a(n)=binomial((n+2)^3,n+1),n=0,1… .
- A158364 (program): 529n^2 - 2n.
- A158365 (program): 529n - 1.
- A158366 (program): Least k such that n! divides (n+k)!/(n+1)!.
- A158367 (program): 529n^2 + 2n.
- A158368 (program): 529n + 1.
- A158369 (program): 576n^2 + 2n.
- A158370 (program): 576n + 1.
- A158371 (program): 576n^2 - 2n.
- A158372 (program): 576n - 1.
- A158373 (program): 625n^2 - 2n.
- A158374 (program): 625n - 1.
- A158378 (program): a(1) = 0, a(n) = gcd(A051904(n), A051903(n)) for n >= 2.
- A158382 (program): a(n) = 625*n^2 + 2*n.
- A158383 (program): 625n + 1.
- A158385 (program): a(n) = 676*n^2 + 2*n.
- A158386 (program): 676n + 1.
- A158387 (program): a(n) = -1 if n is a square, 1 if n is not a square.
- A158388 (program): -1 followed by infinitely many 1’s.
- A158392 (program): 676n^2 - 2n.
- A158393 (program): a(n) = 676*n - 1.
- A158394 (program): 729n^2 - 2n.
- A158395 (program): 729n - 1.
- A158396 (program): 729n^2 + 2n.
- A158397 (program): 729n + 1.
- A158398 (program): 784n^2 - 2n.
- A158399 (program): 784n - 1.
- A158401 (program): a(n) = 841*n^2 - 2*n.
- A158402 (program): a(n) = 841*n - 1.
- A158403 (program): 841n^2 + 2n.
- A158404 (program): 841n + 1.
- A158405 (program): Triangle T(n,m) = 1+2*m of odd numbers read along rows, 0<=m<n.
- A158406 (program): a(n) = 900*n^2 + 2*n.
- A158407 (program): a(n) = 900*n + 1.
- A158408 (program): a(n) = 900*n^2 - 2*n.
- A158409 (program): a(n) = 900*n - 1.
- A158410 (program): a(n) = 961*n^2 - 2*n.
- A158411 (program): Maximum number of colors required to paint a map having n regions.
- A158412 (program): 961n - 1.
- A158413 (program): 961n^2 + 2n.
- A158414 (program): 961n + 1.
- A158416 (program): Expansion of (1+x-x^3)/(1-x^2)^2.
- A158420 (program): 1024n^2 - 2n.
- A158421 (program): a(n) = 1024*n - 1.
- A158440 (program): Triangle T(n,k) read by rows: row n contains n times n+1 followed by n 1’s.
- A158443 (program): 16n^2 - 4.
- A158444 (program): a(n) = 16*n^2 + 4.
- A158445 (program): 25n^2 + 5.
- A158446 (program): 25n^2 - 5.
- A158447 (program): a(n) = 10*n^2 - 1.
- A158454 (program): Riordan array (1/(1-x^2), x/(1+x)^2).
- A158455 (program): a(n) = 2^(n-1)*(n-1)!*(4*n+1).
- A158456 (program): Signature sequence for log(3)/log(2).
- A158458 (program): Numbers k such that k + bigomega(k) is prime.
- A158459 (program): Period 4: repeat [0, 3, 2, 1].
- A158461 (program): A102370(n) mod 3 .
- A158462 (program): a(n) = 36*n^2 - 6.
- A158463 (program): a(n) = 12*n^2 - 1.
- A158464 (program): Number of distinct squares in row n of Pascal’s triangle.
- A158478 (program): Number of colors needed to paint n sectors of a circle.
- A158479 (program): 36n^2 + 6.
- A158480 (program): a(n) = 12*n^2 + 1.
- A158481 (program): 49n^2 + 7.
- A158482 (program): a(n) = 14*n^2 + 1.
- A158483 (program): Triangle read by rows: T(n,k) = (4k+3)/(n+2k+2)*binomial(2n,n+2k+1).
- A158484 (program): 49n^2 - 7.
- A158485 (program): a(n) = 14*n^2 - 1.
- A158487 (program): a(n) = 64*n^2 - 8.
- A158488 (program): a(n) = 64*n^2 + 8.
- A158490 (program): 100n^2 - 10.
- A158491 (program): 20n^2 - 1.
- A158492 (program): a(n) = 100*n^2 + 10.
- A158493 (program): a(n) = 20*n^2 + 1.
- A158494 (program): Boundary area of the T-square fractal.
- A158495 (program): Expansion of ((1-4x)+sqrt(1-4x))/(2(1-2x)).
- A158496 (program): Expansion of (1-4x+x^2)/(1+x^2)^2.
- A158497 (program): Triangle T(n,k) formed by the coordination sequences and the number of leaves for trees.
- A158498 (program): a(n) = (1/2)*(n^3 - 6*n^2 + 13*n - 6).
- A158499 (program): Expansion of (1+sqrt(1-4x))/(2-4x).
- A158500 (program): Expansion of (1+sqrt(1+4x))*(1+2x)/(2*sqrt(1+4x)).
- A158501 (program): Hankel transform of A158500.
- A158510 (program): Generalized Fibonacci numbers Fib(n + 0.5) rounded to an integer.
- A158513 (program): a(n) = Hermite(n,5).
- A158515 (program): Number of colors needed to paint a wheel graph on n nodes.
- A158516 (program): a(n) = Hermite(n,6).
- A158522 (program): Dirichlet inverse of number of unitary divisors of n (A034444).
- A158523 (program): Moebius transform of negate primes in factorization of n.
- A158525 (program): Number of connected spanning subgraphs and number of forests of the wheel graph W_n.
- A158526 (program): n and (1 + 2*n + 2*n^2) are primes.
- A158528 (program): Sum of primes between consecutive positive cubes.
- A158530 (program): a(n) = Hermite(n,7).
- A158531 (program): a(n) = Hermite(n,8).
- A158532 (program): a(n) = Hermite(n,9).
- A158534 (program): a(n) = Hermite(n,10).
- A158535 (program): a(n) = Hermite(n,11).
- A158536 (program): 121n^2 + 11.
- A158537 (program): a(n) = 22*n^2 + 1.
- A158538 (program): a(n) = Hermite(n,12).
- A158539 (program): a(n) = 121*n^2 - 11.
- A158540 (program): a(n) = 22*n^2 - 1.
- A158542 (program): a(n) = Hermite(n,13).
- A158543 (program): a(n) = 144*n^2 - 12.
- A158544 (program): a(n) = 24*n^2 - 1.
- A158545 (program): a(n) = Hermite(n,14).
- A158546 (program): a(n) = 144*n^2 + 12.
- A158547 (program): a(n) = 24*n^2 + 1.
- A158548 (program): a(n) = 169*n^2 + 13.
- A158549 (program): a(n) = 26*n^2 + 1.
- A158550 (program): a(n) = 169*n^2 - 13.
- A158551 (program): a(n) = 26*n^2 - 1.
- A158552 (program): a(n) = A144433(n) - A106833(n).
- A158553 (program): a(n) = 196*n^2 - 14.
- A158554 (program): a(n) = 28*n^2 - 1.
- A158555 (program): a(n) = 196*n^2 + 14.
- A158556 (program): a(n) = 28*n^2 + 1.
- A158557 (program): a(n) = 225*n^2 + 15.
- A158558 (program): a(n) = 30n^2 + 1.
- A158559 (program): a(n) = 225*n^2 - 15.
- A158560 (program): a(n) = 30n^2 - 1.
- A158561 (program): a(n)=((2^n)*((2^n)+1) - (2^(n-1))*((2^(n-1))+1))/2, a(1)=3.
- A158562 (program): a(n) = 256*n^2 - 16.
- A158563 (program): a(n) = 32*n^2 - 1.
- A158569 (program): a(n) = Sum_{i=1..F(n)} F(i), n >= 1, where F(k) is A000045, Fibonacci numbers.
- A158570 (program): a(n) = A007814((2n-1)!! + 1).
- A158572 (program): a(n) = A007814((2n-1)!! - 1).
- A158573 (program): Numbers k such that 30*k + 7 is prime.
- A158574 (program): a(n) = 256*n^2 + 16.
- A158575 (program): a(n) = 32*n^2 + 1.
- A158580 (program): a(n) = Hermite(n, 15).
- A158581 (program): Numbers having in binary representation at least two ones and two zeros.
- A158582 (program): Numbers having in binary representation at least two zeros.
- A158585 (program): a(n) = 289*n^2 + 17.
- A158586 (program): a(n) = 34*n^2 + 1.
- A158587 (program): a(n) = 289*n^2 - 17.
- A158588 (program): a(n) = 34*n^2 - 1.
- A158589 (program): a(n) = 324*n^2 - 18.
- A158590 (program): a(n) = 324*n^2 + 18.
- A158591 (program): a(n) = 36*n^2 + 1.
- A158592 (program): a(n) = 361*n^2 + 19.
- A158593 (program): a(n) = 38*n^2 + 1.
- A158595 (program): a(n) = 361*n^2 - 19.
- A158596 (program): a(n) = 38*n^2 - 1.
- A158597 (program): a(n) = 400*n^2 - 20.
- A158598 (program): a(n) = 40*n^2 - 1.
- A158601 (program): a(n) = 400*n^2 + 20.
- A158602 (program): a(n) = 40*n^2 + 1.
- A158603 (program): a(n) = 441*n^2 + 21.
- A158604 (program): a(n) = 42*n^2 + 1.
- A158607 (program): Period 5: repeat 9,11,13,5,7.
- A158608 (program): a(n) = a(n-1) + 16*a(n-2), starting a(0)=1, a(1)=4.
- A158609 (program): Expansion of (1+8*x)/(1-x-81*x^2).
- A158610 (program): Expansion of (1+15*x)/(1-x-256*x^2).
- A158611 (program): 0, 1 and the primes.
- A158613 (program): Expansion of (1 - 2*x^3 - x^4 - x^5 + x^6 + x^7 - x^8)/(1 - x^3)^3.
- A158614 (program): Numbers n such that 30*n + 11 is prime.
- A158617 (program): a(n) = Hermite(n, 16).
- A158618 (program): Number of gates in Ladner-Fisher prefix circuit.
- A158619 (program): Twin prime pairs concatenated in binary representation.
- A158620 (program): Partial products of A068601.
- A158621 (program): Partial products of A001093.
- A158622 (program): Numerator of the reduced fraction A158620(n)/A158621(n).
- A158623 (program): Denominator of the reduced fraction A158620(n)/A158621(n).
- A158626 (program): a(n) = 42*n^2 - 1.
- A158627 (program): a(n) = 484*n^2-22.
- A158628 (program): a(n) = 44*n^2 - 1.
- A158629 (program): a(n) = 484*n^2 + 22.
- A158630 (program): a(n) = 44*n^2+1.
- A158631 (program): a(n) = 529*n^2 + 23.
- A158632 (program): a(n) = 46*n^2 + 1.
- A158633 (program): a(n) = 529*n^2 - 23.
- A158634 (program): a(n) = 46*n^2 - 1.
- A158635 (program): 6n - A008578(n).
- A158636 (program): a(n) = 576*n^2 - 24.
- A158637 (program): a(n) = 576*n^2 + 24.
- A158638 (program): a(n) = 48*n^2 + 1.
- A158639 (program): a(n) = 676*n^2 - 26.
- A158640 (program): 52*n^2 - 1.
- A158643 (program): a(n) = 676*n^2 + 26.
- A158644 (program): a(n) = 52*n^2 + 1.
- A158645 (program): a(n) = 729*n^2 + 27.
- A158646 (program): a(n) = 54*n^2 + 1.
- A158647 (program): A145501(16n+8).
- A158648 (program): Numbers n such that 30*n + 17 is prime.
- A158654 (program): Denominator of Bernoulli(n, 1/8).
- A158655 (program): a(n) = 729*n^2 - 27.
- A158656 (program): a(n) = 54*n^2 - 1.
- A158657 (program): a(n) = 784*n^2 - 28.
- A158658 (program): a(n) = 56*n^2 - 1.
- A158659 (program): a(n) = 784*n^2 + 28.
- A158660 (program): a(n) = 56*n^2 + 1.
- A158662 (program): Sum of primes <= n if 1 is counted as a prime.
- A158665 (program): a(n) = 841*n^2 + 29.
- A158666 (program): a(n) = 58*n^2 + 1.
- A158667 (program): 841*n^2 - 29.
- A158668 (program): a(n) = 58*n^2 - 1.
- A158669 (program): a(n) = 900*n^2 - 30.
- A158670 (program): a(n) = 60*n^2 - 1.
- A158672 (program): a(n) = 900*n^2 + 30.
- A158673 (program): a(n) = 60*n^2 + 1.
- A158674 (program): Period 18: repeat 3, 4, 0, 8, 6, 3, 3, 7, 0, 2, 6, 6, 3, 1, 0, 5, 6, 0.
- A158675 (program): a(n) = 961*n^2 + 31.
- A158676 (program): a(n) = 62*n^2 + 1.
- A158677 (program): Period 6: repeat [3, 4, 0, 5, 6, 3].
- A158678 (program): Period 18: repeat 0,0,0,3,0,0,0,3,0,-3,0,3,0,-3,0,0,0,-3.
- A158679 (program): a(n) = 961*n^2 - 31.
- A158680 (program): a(n) = 62*n^2 - 1.
- A158681 (program): Wiener indexes of the complete binary trees with n levels, root being at level 0.
- A158683 (program): a(n) = 1024*n^2 - 32.
- A158684 (program): a(n) = 64*n^2 - 1.
- A158685 (program): 32*(32*n^2+1).
- A158686 (program): 64n^2 + 1.
- A158687 (program): Riordan array (1/(1-x),x(1+x)^2/(1-x)).
- A158688 (program): a(n) = 1089*n^2 + 33.
- A158689 (program): a(n) = 66*n^2 + 1.
- A158692 (program): a(n) = 1089*n^2 - 33.
- A158693 (program): a(n) = 66*n^2 - 1.
- A158696 (program): a(n) = Hermite(n, 17).
- A158698 (program): Numbers not occurring in A073627.
- A158699 (program): Start with 0; then add one to each single digit.
- A158700 (program): a(n) = Hermite(n, 18).
- A158702 (program): a(n) = Hermite(n, 19).
- A158703 (program): a(n) = Hermite(n, 20).
- A158704 (program): Nonnegative integers with an even number of even powers of 2 in their base-2 representation.
- A158705 (program): Nonnegative integers with an odd number of even powers of 2 in their base-2 representation.
- A158708 (program): Primes p such that p + floor(p/2) is prime.
- A158709 (program): Primes p such that p + ceiling(p/2) is prime.
- A158721 (program): Primes p such that (p + 1)/3 + p is prime.
- A158724 (program): Numbers n such that prime(n)^2 + 1 is a semiprime.
- A158727 (program): a(n) = Hermite(n, 21).
- A158729 (program): a(n) = 1156*n^2 - 34.
- A158730 (program): a(n) = 68*n^2 - 1.
- A158731 (program): a(n) = 1156*n^2 + 34.
- A158732 (program): a(n) = 68*n^2 + 1.
- A158733 (program): a(n) = 1225*n^2 + 35.
- A158734 (program): a(n) = 70*n^2 + 1.
- A158735 (program): a(n) = 1225*n^2 - 35.
- A158736 (program): a(n) = 70*n^2 - 1.
- A158737 (program): a(n) = 1296*n^2 - 36.
- A158738 (program): a(n) = 72*n^2 - 1.
- A158739 (program): 1296*n^2 + 36.
- A158740 (program): a(n) = 72*n^2 + 1.
- A158741 (program): a(n) = 1369*n^2 + 37.
- A158742 (program): a(n) = 74*n^2 + 1.
- A158743 (program): a(n) = 1369*n^2 - 37.
- A158744 (program): a(n) = 74*n^2 - 1.
- A158745 (program): a(3n)=A130750(n). a(3n+1)=A130752(n). a(3n+2)=A130755(n).
- A158746 (program): Numbers n such that 30*n + 13 is prime.
- A158747 (program): Triangle read by rows: T(n,m)=prime( 1+prime(n+1)-prime(m+1) ).
- A158749 (program): a(n) = n * 9^n.
- A158751 (program): a(n) = Hermite(n, 22).
- A158752 (program): a(n) = Hermite(n, 23).
- A158753 (program): Triangle T(n, k) = A000032(2*(n-k) + 1), read by rows.
- A158764 (program): 38*(38*n^2-1).
- A158765 (program): a(n) = 76*n^2 - 1.
- A158766 (program): a(n) = 1444*n^2 + 38.
- A158767 (program): a(n) = 76*n^2 + 1.
- A158768 (program): a(n) = 1521*n^2 + 39.
- A158769 (program): a(n) = 78*n^2 + 1.
- A158770 (program): a(n) = 1521*n^2 - 39.
- A158771 (program): a(n) = 78*n^2 - 1.
- A158772 (program): a(n) = A138635(n+18)-A138635(n).
- A158773 (program): a(n) = 1600*n^2 - 40.
- A158774 (program): a(n) = 80*n^2 - 1.
- A158775 (program): a(n) = 1600*n^2 + 40.
- A158776 (program): a(n) = 80*n^2 + 1.
- A158780 (program): a(2n) = A131577(n). a(2n+1) = A011782(n).
- A158783 (program): a(n) = Hermite(n, 24).
- A158791 (program): Numbers n such that 30*n + 23 is prime.
- A158793 (program): Triangle read by rows: product of A130595 and A092392 considered as infinite lower triangular arrays.
- A158797 (program): a(n) = a(n-1) + 36*a(n-2), a(0)=1, a(1)=6.
- A158798 (program): a(n) = a(n-1) + 64*a(n-2), a(0)=1, a(1)=8.
- A158799 (program): a(0)=1, a(1)=2, a(n)=3 for n>=2.
- A158802 (program): a(n) = n * n! * b(n), where b(n) = ((n-1)*(n-3)*b(n-1) - b(n-2) + b(n-3))/(n*(n - 1)) and b(0) = b(1) = 1, b(2) = -1.
- A158803 (program): Numbers k such that k^2 == 2 (mod 41).
- A158806 (program): Numbers n such that 30*n + 19 is prime.
- A158808 (program): Denominator of Bernoulli(n, 1/9).
- A158811 (program): Numerator of Hermite(n, 1/3).
- A158815 (program): Triangle T(n,k) read by rows, matrix product of A046899(row-reversed) * A130595.
- A158821 (program): Triangle read by rows: row n (n>=0) ends with 1, and for n>=1 begins with n; other entries are zero.
- A158822 (program): Triangle read by rows, matrix triple product A000012 * A145677 * A000012.
- A158823 (program): Triangle read by rows: matrix product A004736 * A158821.
- A158824 (program): Triangle T(n,k) = A000292(n) if k = 1 otherwise (k-1)*(n-k+1)*(n-k+2)/2, read by rows.
- A158841 (program): Triangle read by rows, matrix product of A145677 * A004736.
- A158842 (program): 1 + n*(n+1)*(n-1)/2.
- A158845 (program): Numbers k such that prepending 1 to the k-th triangular number produces a prime.
- A158849 (program): a(10n+m) is the integer with n+m concatenations of the digit m in base 10, 0<=m<=9.
- A158850 (program): Numbers n such that 30*n + 29 is prime.
- A158851 (program): a(n) = lcm(1,2,3,…,n) mod (n+1).
- A158854 (program): Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial (1-x)^(1+floor(n/2))* (1+x)^floor((n-1)/2) in row n, column k.
- A158859 (program): a(n) is formed by 2n+1 concatenations of the digit 2r+1 where n=r (mod 5).
- A158860 (program): Triangle T(n,k)= ( 1 +T(n-1,k)*T(n,k-1) ) / T(n-1,k-1) initialized by T(n,0)=3n-2, T(n,k)=0 if k>=n, read by rows 0<=k<n.
- A158863 (program): Maximal excess of a 3-normalized Hadamard matrix of order 4n.
- A158869 (program): Number of ways of filling a 2 X 3 X 2n hole with 1 X 2 X 2 bricks.
- A158874 (program): a(n) = (n + 4)*(n + 3)*(n + 2)*(n + 1)*n / 5 = 24*A000389(n+4).
- A158875 (program): Row sums of A099884, the XOR difference triangle of the powers of 2.
- A158876 (program): Expansion of e.g.f.: exp( Sum_{n>=1} (n-1)! * x^n ).
- A158879 (program): a(n) = 4^n + n.
- A158881 (program): a(n) = (n*2^n + 1)^(n-1).
- A158882 (program): G.f. A(x) satisfies: [x^n] A(x)^n = [x^n] A(x)^(n-1) for n>1 with A(0)=A’(0)=1.
- A158886 (program): a(n) = (n+1)^n * n! * C(1/(n+1), n).
- A158887 (program): a(n) = (n+1)^n * n! * binomial(n-1 + 1/(n+1), n).
- A158893 (program): Triangle read by rows: T(n,1)=7n-6; T(n,m)= 1+n-m, 1<m<=n.
- A158894 (program): Sawtooth pattern of one, then two, then three, then four etc. consecutive odd numbers, starting each time at 3.
- A158897 (program): The elements of A059100 at indices of triangular numbers, padded with zeros.
- A158899 (program): These are numbers n such that the reciprocal, 1/n, is a repeating fraction whose period is n/2 - 1.
- A158901 (program): A051731 * (1, 1, 2, 3, 4, 5, …).
- A158903 (program): Numerator of Hermite(n, 2/3).
- A158906 (program): Triangle read by rows: the matrix product A158821 * A051731.
- A158907 (program): Row sums of triangle A158906.
- A158908 (program): First differences of A061238.
- A158909 (program): Riordan array (1/((1-x)(1-x^2)), x/(1-x)^2). Triangle read by rows, T(n,k) for 0 <= k <= n.
- A158910 (program): First Differences of A061240.
- A158911 (program): Numbers of the form 2^i*5^j - 1.
- A158916 (program): Inverse binomial transform of A153130.
- A158919 (program): Beatty sequence for the tribonacci constant tau (A058265): a(n) = floor(n*tau).
- A158920 (program): Binomial transform of A008805 (triangular numbers with repeats).
- A158926 (program): First differences of A158916.
- A158927 (program): a(n) = -3a(n-1) - 3a(n-2) - 2a(n-3), n > 3.
- A158934 (program): Decimal expansion of xi = (cos(Pi/5) - 1/2) / (sin(Pi/5) + 1/2).
- A158935 (program): a(n)= -3a(n-1)-3a(n-2)-2a(n-3), n>3. a(0)=4, a(1)=4, a(2)=-5, a(3)=4.
- A158937 (program): Numbers of the form x^2+3y^2 where x and y are positive integers (with repetitions).
- A158942 (program): Nonsquares coprime to 10.
- A158943 (program): INVERT transform of A027656: (1, 0, 2, 0, 3, 0, 4, 0, 5, …).
- A158944 (program): Triangle by columns: the natural numbers interleaved with zeros in every column: (1, 0, 2, 0, 3, 0, 4, …)
- A158946 (program): Triangle read by rows, A000012(signed) * A145677 * A000012
- A158948 (program): Triangle read by rows, left border = natural numbers repeated (1, 1, 2, 2, 3, 3, …); all other columns = (1, 0, 1, 0, 1, 0, …).
- A158949 (program): Inverse Moebius transform of A065958.
- A158953 (program): Trajectory of 12 under repeated application of the map n –> A102370(n) .
- A158954 (program): Numerator of Hermite(n, 1/4).
- A158955 (program): First differences of A061241.
- A158958 (program): Numerator of Hermite(n, 3/4).
- A158960 (program): Numerator of Hermite(n, 1/5).
- A158961 (program): Numerator of Hermite(n, 2/5).
- A158965 (program): Numerator of Hermite(n, 3/5).
- A158967 (program): Numerator of Hermite(n, 4/5).
- A158968 (program): Numerator of Hermite(n, 1/6).
- A158969 (program): Numerator of Hermite(n, 5/6).
- A158973 (program): a(n) = count of numbers k <= n such that all proper divisors of k are divisors of n.
- A158974 (program): a(n) is the number of numbers k <= n such that not all proper divisors of k are divisors of n.
- A158980 (program): Numerator of Hermite(n, 1/7).
- A158981 (program): Numerator of Hermite(n, 2/7).
- A158987 (program): Numerator of Hermite(n, 3/7).
- A158991 (program): Numerator of Hermite(n, 4/7).
- A159005 (program): Numerator of Hermite(n, 5/7).
- A159006 (program): Transformation of prime(n): flip digits in the binary representation, revert the sequence of digits, and convert back to decimal.
- A159007 (program): Numbers k such that k == 32 or 41 (mod 73).
- A159008 (program): Positive numbers k such that k^2 == 2 (mod 89).
- A159013 (program): Numerator of Hermite(n, 6/7).
- A159014 (program): Numerator of Hermite(n, 1/8).
- A159017 (program): Numerator of Hermite(n, 3/8).
- A159018 (program): a(0)=5; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159019 (program): Numerator of Hermite(n, 5/8).
- A159020 (program): a(0)=11; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159021 (program): a(0)=19; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159022 (program): a(0)=29; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159023 (program): a(0)=41; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159024 (program): a(0)=55; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159025 (program): a(0)=71; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159026 (program): a(0)=89; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159027 (program): a(0)=109; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
- A159028 (program): Numerator of Hermite(n, 7/8).
- A159030 (program): Numerator of Hermite(n, 1/9).
- A159035 (program): a(0)=1=a(1), a(2)=2, a(3)=5; thereafter a(n+3)=4*a(n+2)-4*a(n+1)+2*a(n) for n>=1.
- A159036 (program): a(0)=0, a(1)=1, a(2)=4, a(3)=13; thereafter a(n+3)=4*a(n+2)-4*a(n+1)+2*a(n) for n>=1.
- A159038 (program): a(n) = 8 * n!.
- A159039 (program): E.g.f. sec(x)/(1-x) = 1/( cos(x) * (1-x) ).
- A159040 (program): A triangle of polynomial coefficients: p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= (less than or equal to) Floor[n/2], (-1)^i*A109128[n, i], -(-1)^(n - i)* A109128[n, i]]], {i, 0, n}]/(1 - x).
- A159047 (program): Primes which are triangular numbers plus 3.
- A159048 (program): Primes of the form m*(m+1)/2 + 4.
- A159049 (program): Primes of the form (5+ a triangular number A000217).
- A159057 (program): a(n) = A102370(n) mod 10.
- A159058 (program): A102370(n) modulo 8 .
- A159060 (program): A102370(n) modulo 6 .
- A159061 (program): Nearest integer to the expected number of tosses of a fair coin required to obtain at least n heads and n tails.
- A159066 (program): A102370(n) modulo 7 .
- A159067 (program): A102370(n) modulo 9 .
- A159068 (program): a(n) = Sum_{k=1..n} binomial(n,k) * gcd(k,n).
- A159069 (program): a(n) = A159068(n)/n.
- A159070 (program): Count of numbers k in the range 1 < k <= n such that set of proper divisors of k is a subset of the set of proper divisors of n.
- A159071 (program): Primes which are the sum of 6 consecutive triangular numbers A000217.
- A159072 (program): Count of numbers k in the range 1<=k<= n such that set of proper divisors of k is not a subset of the set of the proper divisors of n.
- A159075 (program): a(1) = -1, otherwise a(n) = 0.
- A159076 (program): A008474(n) + 2.
- A159077 (program): a(n) = A008475(n) + 1.
- A159081 (program): Let d be the largest element of A008578 which divides n, then a(n) is the position of d in A008578.
- A159083 (program): Products of 7 consecutive integers.
- A159197 (program): Numerator of Hermite(n, 2/9).
- A159200 (program): Decimal expansion of Sum_{k >= 1} (1/(10^(4*k + 2) - 1)) - (1/(10^(2*k + 1) - 1)), negated.
- A159217 (program): 1/8 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 17
- A159219 (program): Number of n X n arrays of squares of integers with every 2X2 subblock summing to 18
- A159221 (program): 1/2 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 20
- A159222 (program): 1/4 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 21
- A159225 (program): 1/4 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 25
- A159227 (program): 1/4 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 27
- A159229 (program): 1/16 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 30
- A159230 (program): 1/8 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 31
- A159232 (program): Numerator of Hermite(n, 4/9).
- A159240 (program): Numerator of Hermite(n, 5/9).
- A159242 (program): Numerator of Hermite(n, 7/9).
- A159245 (program): Numerator of Hermite(n, 8/9).
- A159247 (program): Numerator of Hermite(n, 1/10).
- A159249 (program): Numerator of Hermite(n, 3/10).
- A159252 (program): Numerator of Hermite(n, 7/10).
- A159254 (program): Numbers n with property that n^2 ends with 49.
- A159256 (program): a(0)=131; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).
- A159258 (program): a(0)=155; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).
- A159263 (program): a(0)=181; for n > 0, a(n) = a(n-1) + floor(sqrt a(n-1)).
- A159274 (program): a(0)=209; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1)).
- A159277 (program): Ways to write the identity as a product of n 3-cycles in symmetric group S_4.
- A159279 (program): Numerator of Hermite(n, 9/10).
- A159280 (program): Numerator of Hermite(n, 1/11).
- A159281 (program): Numerator of Hermite(n, 2/11).
- A159284 (program): Expansion of x*(1+x)/(1-x^2-2*x^3).
- A159285 (program): Expansion of (1+3*x)/(1-x^2-2*x^3).
- A159286 (program): Expansion of (x-1)^2/(1-x^2-2*x^3).
- A159287 (program): Expansion of x^2/(1-x^2-2*x^3)
- A159288 (program): Expansion of (1 + x + x^2)/(1 - x^2 - 2*x^3).
- A159289 (program): a(n+1) = 5*a(n) - 2*a(n-1).
- A159290 (program): A generalized Jacobsthal sequence.
- A159293 (program): a(n) = smallest prime congruent to 1 mod A051426(n).
- A159297 (program): Number of 3D matrices with positive integer entries such that sum of all entries equals n
- A159307 (program): Numerator of Hermite(n, 3/11).
- A159322 (program): G.f.: A(x) = Sum_{n>=0} log(1+x + 2^n*x^2)^n/n!.
- A159324 (program): n! times the average number of comparisons required by an insertion sort of n (distinct) elements.
- A159325 (program): Median number of comparisons used by insertion sort on n (distinct) elements.
- A159326 (program): Numerator of Hermite(n, 4/11).
- A159327 (program): Numerator of Hermite(n, 5/11).
- A159328 (program): Transform of 1 by the T_{1,1} transformation (see link)
- A159329 (program): Transform of the finite sequence (1, 0, -1) by the T_{1,1} transformation (see link).
- A159330 (program): Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,1} transformation (see link).
- A159333 (program): Roman factorial of n.
- A159334 (program): Transform of A056594 by the T_{1,1} transformation (see link)
- A159335 (program): Triangle read by rows: numerator of n/binomial(n,m).
- A159336 (program): Transform of the finite sequence (1, 0, -1) by the T_{1,0} transformation (see link).
- A159337 (program): Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,0} transformation (see link).
- A159338 (program): Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{1,0} transformation (see link).
- A159339 (program): Transform of A056594 by the T_{1,0} transformation (see link).
- A159340 (program): Transform of the finite sequence (1, 0, -1) by the T_{0,1} transformation (see link).
- A159341 (program): Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,1} transformation (see link).
- A159343 (program): Transform of A056594 by the T_{0,1} transformation (see link).
- A159347 (program): Transform of the finite sequence (1, 0, -1) by the T_{0,0} transformation.
- A159348 (program): Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,0} transform (see link).
- A159350 (program): Transform of A056594 by the T_{0,0} transformation (see link).
- A159353 (program): a(n) = the smallest positive integer such that a(n) *(2^n -2) is a multiple of n.
- A159354 (program): Decimal expansion of 18 - 24*log(2).
- A159355 (program): Number of n X n arrays of squares of integers summing to 4.
- A159359 (program): Number of n X n arrays of squares of integers summing to 5.
- A159363 (program): Number of n X n arrays of squares of integers summing to 6.
- A159367 (program): Number of n X n arrays of squares of integers summing to 7
- A159449 (program): Numerator of Hermite(n, 6/11).
- A159450 (program): Numerator of Hermite(n, 7/11).
- A159454 (program): Numerator of Hermite(n, 8/11).
- A159460 (program): Numerator of Hermite(n, 9/11).
- A159461 (program): Numbers of previous and following composites of n-th prime.
- A159465 (program): Sums of odd numbers, omitting squares.
- A159467 (program): Decimal expansion of (129+16*sqrt(2))/127.
- A159469 (program): Maximum remainder when (k + 1)^n + (k - 1)^n is divided by k^2 for variable n and k > 2.
- A159470 (program): Numerator of Hermite(n, 10/11).
- A159472 (program): Numerator of Hermite(n, 1/12).
- A159475 (program): a(1) = 1; for n >= 1, a(n) is the smallest number m > n such that gcd(n,m) > 1.
- A159476 (program): Expansion of e.g.f.: A(x) = exp( Sum_{n>=1} (n-1)!*x^n/n ).
- A159477 (program): a(n) = smallest prime >= n, if 1 is counted as a prime.
- A159480 (program): Numerator of Hermite(n, 5/12).
- A159481 (program): Number of evil numbers <= n, see A001969.
- A159482 (program): Greatest odd prime q < 2*n such that p < q and p prime and p = 2*n - q or 0 if no such prime exists.
- A159485 (program): Numerator of Hermite(n, 7/12).
- A159486 (program): Numerator of Hermite(n, 11/12).
- A159488 (program): Numerator of Hermite(n, 1/13).
- A159490 (program): Denominator of Bernoulli(n, 1/12).
- A159492 (program): Numerator of Hermite(n, 2/13).
- A159494 (program): Numerator of Hermite(n, 3/13).
- A159496 (program): Numerator of Hermite(n, 4/13).
- A159497 (program): Numerator of Hermite(n, 5/13).
- A159498 (program): Numerator of Hermite(n, 6/13).
- A159500 (program): Numerator of Hermite(n, 7/13).
- A159501 (program): Numerator of Hermite(n, 8/13).
- A159502 (program): Numerator of Hermite(n, 9/13).
- A159504 (program): Numerator of Hermite(n, 10/13).
- A159505 (program): Numerator of Hermite(n, 11/13).
- A159506 (program): Numerator of Hermite(n, 12/13).
- A159507 (program): Numerator of Hermite(n, 1/14).
- A159508 (program): Numerator of Hermite(n, 3/14).
- A159509 (program): Numerator of Hermite(n, 5/14).
- A159510 (program): Numerator of Hermite(n, 9/14).
- A159511 (program): Numerator of Hermite(n, 11/14).
- A159512 (program): Numerator of Hermite(n, 13/14).
- A159513 (program): Numerator of Hermite(n, 1/15).
- A159514 (program): Numerator of Hermite(n, 2/15).
- A159515 (program): Numerator of Hermite(n, 4/15).
- A159516 (program): Numerator of Hermite(n, 7/15).
- A159517 (program): Numerator of Hermite(n, 8/15).
- A159518 (program): Numerator of Hermite(n, 11/15).
- A159519 (program): Numerator of Hermite(n, 13/15).
- A159520 (program): Numerator of Hermite(n, 14/15).
- A159521 (program): Numerator of Hermite(n, 1/16).
- A159522 (program): Numerator of Hermite(n, 3/16).
- A159523 (program): Numerator of Hermite(n, 5/16).
- A159524 (program): Numerator of Hermite(n, 7/16).
- A159525 (program): Numerator of Hermite(n, 9/16).
- A159526 (program): Numerator of Hermite(n, 11/16).
- A159527 (program): Numerator of Hermite(n, 13/16).
- A159528 (program): Numerator of Hermite(n, 15/16).
- A159529 (program): Numerator of Hermite(n, 1/17).
- A159530 (program): Numerator of Hermite(n, 2/17).
- A159531 (program): Numerator of Hermite(n, 3/17).
- A159532 (program): Numerator of Hermite(n, 4/17).
- A159533 (program): Numerator of Hermite(n, 5/17).
- A159534 (program): Numerator of Hermite(n, 6/17).
- A159535 (program): Numerator of Hermite(n, 7/17).
- A159536 (program): Numerator of Hermite(n, 8/17).
- A159537 (program): Numerator of Hermite(n, 9/17).
- A159538 (program): Numerator of Hermite(n, 10/17).
- A159539 (program): Numerator of Hermite(n, 11/17).
- A159540 (program): Numerator of Hermite(n, 12/17).
- A159541 (program): Numerator of Hermite(n, 13/17).
- A159542 (program): Numerator of Hermite(n, 14/17).
- A159543 (program): Numerator of Hermite(n, 15/17).
- A159544 (program): Numerator of Hermite(n, 16/17).
- A159545 (program): Numerator of Hermite(n, 1/18).
- A159546 (program): Numerator of Hermite(n, 5/18).
- A159549 (program): Decimal expansion of (201+20*sqrt(2))/199.
- A159551 (program): a(n) = 101*n + 10.
- A159552 (program): Numerator of Hermite(n, 7/18).
- A159553 (program): a(n) = Sum_{k=0..n} binomial(n,k) * gcd(n,k).
- A159554 (program): a(n) = A159553(n)/n.
- A159561 (program): Numerator of Hermite(n, 11/18).
- A159562 (program): Numerator of Hermite(n, 13/18).
- A159563 (program): Numerator of Hermite(n, 17/18).
- A159564 (program): Numerator of Hermite(n, 1/19).
- A159566 (program): Decimal expansion of (243+22*sqrt(2))/241.
- A159575 (program): Decimal expansion of (339+26*sqrt(2))/337.
- A159582 (program): Expansion of (1+6*x+x^2-2*x^3)/((x^2+2*x-1)*(x^2-2*x-1)), bisection is NSW numbers.
- A159583 (program): Values of A110391(5n)/A110391(n).
- A159590 (program): Decimal expansion of (451+30*sqrt(2))/449.
- A159602 (program): G.f.: A(x) = Sum_{n>=0} log(1 + x/(1-2^n*x))^n/n!.
- A159605 (program): E.g.f: Sum_{n>=1} a(n)*x^(2n-1)/(2n-1)! = Series_Reversion of e.g.f. S(x) of A159601.
- A159612 (program): INVERT transform of (1, 3, 1, 3, 1, …).
- A159615 (program): The slowest increasing sequence beginning with a(1)=2 such that a(n) and n are both odious or both not odious.
- A159616 (program): Expansion of (1-x)/(1-5*x-2*x^2+8*x^3).
- A159617 (program): G.f.: (1-x)/(1-8*x-8*x^2+8*x^3).
- A159618 (program): Numerator of Hermite(n, 2/19).
- A159619 (program): Slowest increasing sequence beginning with 4 such that n and a(n) are either both evil or both odious.
- A159620 (program): Numerator of Hermite(n, 3/19).
- A159621 (program): Numerator of Hermite(n, 4/19).
- A159622 (program): Numerator of Hermite(n, 5/19).
- A159623 (program): Triangle read by rows: T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 1.
- A159624 (program): a(n)=A159619(2n)-A159615(2n)
- A159627 (program): Decimal expansion of (579 + 34*sqrt(2))/577.
- A159631 (program): Dimension of space of modular forms of weight 1/2, level 4*n and trivial character.
- A159634 (program): Coefficient for dimensions of spaces of modular & cusp forms of weight k/2, level 4*n and trivial character, where k>=5 is odd.
- A159637 (program): Start with [0], repeatedly apply the map 0 -> [01/10], 1 -> [10/01] .
- A159638 (program): Start with [1] and repeatedly apply the map 0 -> [01/10], 1 -> [10/01].
- A159640 (program): a(1) = a(2) = 1; for n > 2, a(n) = (a(1), a(2), a(3), …) dot (P(1), P(2), P(3), …); P = A000129.
- A159642 (program): Decimal expansion of (649 + 36*sqrt(2))/647.
- A159644 (program): Numerator of Hermite(n, 6/19).
- A159645 (program): Numerator of Hermite(n, 7/19).
- A159646 (program): Numerator of Hermite(n, 8/19).
- A159647 (program): Numerator of Hermite(n, 9/19).
- A159648 (program): Numerator of Hermite(n, 10/19).
- A159649 (program): Numerator of Hermite(n, 11/19).
- A159650 (program): Numerator of Hermite(n, 12/19).
- A159651 (program): Numerator of Hermite(n, 13/19).
- A159652 (program): Numerator of Hermite(n, 14/19).
- A159653 (program): Numerator of Hermite(n, 15/19).
- A159654 (program): Numerator of Hermite(n, 16/19).
- A159655 (program): Numerator of Hermite(n, 17/19).
- A159656 (program): Numerator of Hermite(n, 18/19).
- A159657 (program): Numerator of Hermite(n, 1/20).
- A159658 (program): Numerator of Hermite(n, 3/20).
- A159659 (program): Numerator of Hermite(n, 7/20).
- A159660 (program): Numerator of Hermite(n, 9/20).
- A159661 (program): The general form of the recurrences are the a(j, b(j) and n(j) solutions of the 2 equations problem: 11*n(j) + 1 = a(j)*a(j) and 13*n(j) + 1 = b(j)*b(j) with positive integer elements. the solutions of the 2 equations problem: 11*n(j) + 1 = a(j)*a(j); 13*n(j) + 1 = b(j)*b(j); with integer numbers.
- A159663 (program): Numerator of Hermite(n, 11/20).
- A159664 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 11*n(j) + 1 = a(j)*a(j) and 13*n(j) + 1 = b(j)*b(j), with positive integer numbers.
- A159665 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 11*n(j) + 1 = a(j)*a(j) and 13*n(j) + 1 = b(j)*b(j); with positive integer numbers.
- A159668 (program): Expansion of (1 - x)/(1 - 28*x + x^2).
- A159669 (program): Expansion of x*(1 + x)/(1 - 28*x + x^2).
- A159670 (program): Numerator of Hermite(n, 13/20).
- A159673 (program): Expansion of 56*x^2/(1 - 783*x + 783*x^2 - x^3).
- A159674 (program): Expansion of (1 - x)/(1 - 32*x + x^2).
- A159675 (program): Expansion of x*(1 + x)/(1 - 32*x + x^2).
- A159676 (program): Numerator of Hermite(n, 17/20).
- A159677 (program): Expansion of 64*x^2/(1 - 1023*x + 1023*x^2 - x^3).
- A159678 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2-equation problem 7*n(j) + 1 = a(j)*a(j) and 9*n(j) + 1 = b(j)*b(j) with positive integer numbers.
- A159679 (program): a(n) are solutions of the 2 equations: 7*a(n) +1 = c(n)^2 and 9*a(n) +1 = b(n)^2.
- A159680 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 9*n(j) + 1 = a(j)*a(j) and 11*n(j) + 1 = b(j)*b(j) with positive integer numbers.
- A159681 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 5*n(j)+1=a(j)*a(j) and 7*n(j)+1=b(j)*b(j) with positive integer numbers.
- A159682 (program): Numerator of Hermite(n, 19/20).
- A159683 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 3*n(j) + 1 = a(j)*a(j) and 5*n(j) + 1 = b(j)*b(j) with positive integer numbers.
- A159684 (program): Sturmian word: limit S(infinity) where S(0) = 0, S(1) = 0,1 and for n>=1, S(n+1) = S(n)S(n)S(n-1).
- A159689 (program): Fixed point of the morphism 0 -> 0,1,0; 1 -> 1,1; starting from a(0)=0.
- A159691 (program): Decimal expansion of (883 + 42*sqrt(2))/881.
- A159693 (program): Partial sums of A000463.
- A159694 (program): a(n) = 2*a(n-1) + 2^(n-1), for n > 0, with a(0)=6.
- A159695 (program): a(0)=7, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
- A159696 (program): a(0)=8, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
- A159697 (program): a(0)=9, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
- A159699 (program): Replace 2^k in binary expansion of n with A045623(k+1).
- A159702 (program): Decimal expansion of (969 + 44*sqrt(2))/967.
- A159705 (program): Numerator of Hermite(n, 1/21).
- A159706 (program): Numerator of Hermite(n, 2/21).
- A159707 (program): Numerator of Hermite(n, 4/21).
- A159709 (program): Numerator of Hermite(n, 5/21).
- A159710 (program): Number of permutations of 1..n arranged in a circle with exactly 2 local maxima.
- A159711 (program): Number of permutations of 1..n arranged in a circle with exactly 3 local maxima.
- A159715 (program): Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
- A159721 (program): Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
- A159727 (program): Number of permutations of 4 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
- A159733 (program): Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
- A159736 (program): Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
- A159738 (program): Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
- A159739 (program): Number of permutations of 8 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
- A159740 (program): Number of permutations of 9 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
- A159741 (program): a(n) = 8*(2^n - 1).
- A159742 (program): If an array is made of columns of -nacci sequences (Fibonacci, tribonacci, etc.), all starting with 1,1,2,…, the NW-to-SE diagonals can be extended by computation. This sequence is diagonal 6. See A159741 for details.
- A159745 (program): Numerator of Hermite(n, 8/21).
- A159751 (program): Decimal expansion of (51 + 14*sqrt(2))/47.
- A159752 (program): Decimal expansion of (3267 + 1702*sqrt(2))/47^2.
- A159753 (program): Numerator of Hermite(n, 10/21).
- A159754 (program): Numbers n with property that n^2 ends with 81.
- A159755 (program): Triangle of C. A. Laisant for k<=0 (see A062111 and A152920).
- A159756 (program): Triangle A159755 reversed .
- A159759 (program): Decimal expansion of (83+18*sqrt(2))/79.
- A159761 (program): Numerator of Hermite(n, 11/21).
- A159762 (program): Numerator of Hermite(n, 13/21).
- A159763 (program): Numerator of Hermite(n, 16/21).
- A159764 (program): Riordan array (1/(1+4x+x^2), x/(1+4x+x^2)).
- A159769 (program): Number of n-leaf binary trees that do not contain (((()())())(()(()()))) as a subtree.
- A159771 (program): Number of n-leaf binary trees that do not contain (()((()())((()())()))) as a subtree.
- A159772 (program): Number of n-leaf binary trees that do not contain (()((((()())())())())) as a subtree.
- A159776 (program): Numerator of Hermite(n, 17/21).
- A159778 (program): Decimal expansion of (171+26*sqrt(2))/167.
- A159780 (program): Inner product of the binary representation of n and its reverse.
- A159784 (program): Numerator of Hermite(n, 19/21).
- A159785 (program): a(n) = A152980(n)*3.
- A159790 (program): Toothpick number A139250(n) minus triangular number A000217(n).
- A159791 (program): Bisection of toothpick sequence A139250.
- A159792 (program): Bisection of toothpick sequence A139250.
- A159793 (program): a(n) = A153006(n)*2.
- A159794 (program): a(n) = A153006(n)*3.
- A159795 (program): a(n) = 4*A153006(n).
- A159797 (program): Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n-1.
- A159798 (program): Triangle read by rows in which row n lists n terms, starting with 1, such that the difference between successive terms is equal to n-3.
- A159801 (program): Partial sums of A153001.
- A159802 (program): Number of primes q with (2m)^2+1 <= q < (2m+1)^2-2m.
- A159803 (program): Number of primes p with (2m+1)^2 - 2m <= p < (2m+1)^2.
- A159804 (program): Number of primes q with (2n-1)^2+1 <= q < (2n)^2-(2n-1).
- A159805 (program): Number of primes p with (2m)^2-(2m-1) <= p < (2m)^2
- A159806 (program): Numerator of Hermite(n, 1/22).
- A159807 (program): Numerator of Hermite(n, 3/22).
- A159808 (program): Numerator of Hermite(n, 5/22).
- A159810 (program): Decimal expansion of (227+30*sqrt(2))/223.
- A159814 (program): Expansion of eta(z)^2*eta(4*z)^6/eta(2*z).
- A159826 (program): Numerator of Hermite(n, 7/22).
- A159828 (program): a(n) is smallest number m > 0 such that m^2 + n^2 + 1 is prime.
- A159830 (program): Exponential Riordan array [exp(exp(x)-1-2x),x]
- A159831 (program): Numerator of Hermite(n, 9/22).
- A159832 (program): Numerator of Hermite(n, 13/22).
- A159833 (program): a(n) = n^2*(n^2 + 15)/4.
- A159834 (program): Coefficient array of Hermite_H(n, (x-1)/sqrt(2))/(sqrt(2))^n.
- A159840 (program): Numerator of Hermite(n, 15/22).
- A159841 (program): Triangle T(n,k) = binomial(3*n+1, 2*n+k+1), read by rows.
- A159845 (program): Decimal expansion of (363 + 38*sqrt(2))/359.
- A159850 (program): Numerator of Hermite(n, 17/22).
- A159851 (program): Numerator of Hermite(n, 19/22).
- A159852 (program): n^2 mod 60.
- A159853 (program): Riordan array ((1-2*x+2*x^2)/(1-x), x/(1-x)).
- A159854 (program): Riordan array (1-x,x/(1-x)).
- A159855 (program): Riordan array ((1-2*x-x^2)/(1-x), x/(1-x)).
- A159856 (program): Triangle read by rows: T(n,0) = n+1, T(n,k) = 2*T(n-1,k) - T(n-1,k-1), T(n,k) = 0 if k > n and if k < 0.
- A159857 (program): Numerator of Hermite(n, 21/22).
- A159858 (program): Numerator of Hermite(n, 1/23).
- A159859 (program): Numerator of Hermite(n, 2/23).
- A159864 (program): Difference array of Fibonacci numbers A000045 read by antidiagonals.
- A159865 (program): Numerator of Hermite(n, 3/23).
- A159868 (program): Numerator of Hermite(n, 4/23).
- A159869 (program): Numerator of Hermite(n, 5/23).
- A159870 (program): Numerator of Hermite(n, 6/23).
- A159871 (program): Numerator of Hermite(n, 7/23).
- A159872 (program): Numerator of Hermite(n, 8/23).
- A159873 (program): Numerator of Hermite(n, 9/23).
- A159874 (program): Numerator of Hermite(n, 10/23).
- A159875 (program): Numerator of Hermite(n, 11/23).
- A159876 (program): Inverse Mobius transform of the rabbit sequence, A051731 * A005614
- A159877 (program): Numerator of Hermite(n, 12/23).
- A159880 (program): Infinite string related to Ehrlich’s swap method for generating permutations.
- A159882 (program): Numerator of Hermite(n, 13/23).
- A159883 (program): Numerator of Hermite(n, 14/23).
- A159884 (program): Numerator of Hermite(n, 15/23).
- A159888 (program): Numbers congruent to {-5,29,39,41,43,45,55,57,59,93,103,105,107,109,119,121} mod 256 .
- A159889 (program): Numerator of Hermite(n, 16/23).
- A159891 (program): Decimal expansion of (443+42*sqrt(2))/439.
- A159894 (program): Decimal expansion of (731+54*sqrt(2))/727.
- A159897 (program): Decimal expansion of (843+58*sqrt(2))/839.
- A159904 (program): Numerator of Hermite(n, 17/23).
- A159912 (program): Partial sums of A159913(k) = 2^bitcount(2k+1)-1 = A038573(2k+1), bitcount=A000120.
- A159913 (program): a(n) = 2^(A000120(n) + 1) - 1, where A000120(n) = number of nonzero bits in n.
- A159914 (program): Half the number of (n-3)-element subsets of {1,…,n} whose elements sum up to an odd value.
- A159915 (program): a(n) = floor((n+1)/4)*floor(n/2).
- A159916 (program): Triangle T(m,n) = number of subsets of {1,…,m} with n elements having an odd sum, 1 <= n <= m.
- A159917 (program): Fixed point of the morphism 0 -> 01, 1 -> 2, 2 -> 01, starting from a(0) = 0.
- A159918 (program): Number of ones in binary representation of n^2.
- A159919 (program): A square array of numbers, read by antidiagonals, called Sundaram’s sieve.
- A159920 (program): Sums of the antidiagonals of Sundaram’s sieve (A159919).
- A159921 (program): Numerator of Hermite(n, 18/23).
- A159925 (program): Row sums of triangle A159924.
- A159926 (program): The sum of all terms in row 1 through m of triangle A159924.
- A159928 (program): a(n) is the sum of the terms of row n of triangle A159927.
- A159929 (program): INVERT transform of phi(n), A000010.
- A159930 (program): Triangle read by rows: a(1,1)=1. a(m,n) = a(m-1,n) + (sum of all terms in row m-1), for n<m. a(m,m) = sum of all terms in row m-1.
- A159933 (program): INVERTi transform of d(n), A000005.
- A159937 (program): Triangle read by rows, A054525 * A127478, as infinite lower triangular matrices.
- A159938 (program): The number of homogeneous trisubstituted linear alkanes.
- A159940 (program): The number of trisubstitution products with composition C_n H_(2n-1) X_2 Y.
- A159941 (program): Number of trisubstituted linear alkanes of composition C_n H_(2n-1) XYZ.
- A159943 (program): Numerator of Hermite(n, 19/23).
- A159946 (program): Numerator of Hermite(n, 20/23).
- A159947 (program): Numerator of Hermite(n, 21/23).
- A159948 (program): Numerator of Hermite(n, 22/23).
- A159949 (program): Numerator of Hermite(n, 1/24).
- A159952 (program): Skinny numbers (A061909) containing no 3’s.
- A159954 (program): Numerator of Hermite(n, 5/24).
- A159955 (program): Period 9: repeat [0, 1, 2, 1, 2, 0, 2, 0, 1].
- A159956 (program): Period 16 : 0,1,2,3,1,2,3,0,2,3,0,1,3,0,1,2 .
- A159957 (program): Period 25 : 0,1,2,3,4,1,2,3,4,0,2,3,4,0,1,3,4,0,1,2,4,0,1,2,3 .
- A159958 (program): Lodumo_3 of A053838 .
- A159960 (program): Number of permutations of the set 1,2,…, 2n such that at least one pair of adjacent numbers in the permutation differ by n.
- A159961 (program): Cuban composites: composite numbers equal to the difference of two consecutive cubes.
- A159964 (program): a(n) = 2^n*(1-n).
- A159965 (program): Riordan array (1/sqrt(1-4x), (1-2x-(1-3x)c(x))/(x*sqrt(1-4x))), c(x) the g.f. of A000108.
- A159966 (program): Lodumo_4 of A102370 (sloping binary numbers).
- A159967 (program): Numerator of Hermite(n, 7/24).
- A159968 (program): Numerator of Hermite(n, 11/24).
- A159969 (program): Numerator of Hermite(n, 13/24).
- A159971 (program): Riordan array (2c(-x)-1, xc(-x)^3), c(x) the g.f. of A000108.
- A159972 (program): Row sums of number triangle A159971.
- A159973 (program): Non-refactorable numbers: number of divisors of n does not divide n.
- A159974 (program): Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, …) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, …) as the main diagonal and the rest zeros.
- A159981 (program): Catalan numbers read modulo 4.
- A159984 (program): Catalan numbers read modulo 5 .
- A159986 (program): Catalan numbers read modulo 7.
- A159987 (program): Catalan numbers read modulo 8.
- A159988 (program): Catalan numbers read modulo 11 .
- A159989 (program): Catalan numbers read modulo 12.
- A159991 (program): Powers of 60.
- A159996 (program): Numerator of Hermite(n, 17/24).
- A159997 (program): Numerator of Hermite(n, 19/24).
- A159998 (program): Numerator of Hermite(n, 23/24).
- A160003 (program): Numerator of Hermite(n, 1/25).
- A160004 (program): Numerator of Hermite(n, 2/25).
- A160005 (program): Numerator of Hermite(n, 3/25).
- A160007 (program): Deficient numbers more than 1 unit away from their predecessors.
- A160008 (program): Numerator of Hermite(n, 4/25).
- A160010 (program): Numerator of Hermite(n, 6/25).
- A160011 (program): Numerator of Hermite(n, 7/25).
- A160012 (program): Numerator of Hermite(n, 8/25).
- A160013 (program): Numerator of Hermite(n, 9/25).
- A160016 (program): Lodumo_2 transform of A159833.
- A160017 (program): Lodumo_2 of Thue-Morse sequence A010060.
- A160035 (program): Clausen-normalized numerators of the Bernoulli numbers of order 2.
- A160037 (program): Numerator of Hermite(n, 11/25).
- A160038 (program): Numerator of Hermite(n, 12/25).
- A160039 (program): Numerators of n!*(1 + 1/2 + 1/3 +…+ 1/(n+1))
- A160042 (program): Decimal expansion of (89+36*sqrt(2))/73.
- A160043 (program): Decimal expansion of (5907+1802*sqrt(2))/73^2.
- A160046 (program): Numerator of the Harary number for the cycle graph C_n.
- A160047 (program): Denominator of the Harary number for the cycle graph C_n.
- A160048 (program): Numerator of the Harary number for the path graph P_n.
- A160049 (program): Denominator of the Harary number for the path graph P_n.
- A160050 (program): Numerator of the Harary number for the star graph s_n.
- A160056 (program): Decimal expansion of (107+42*sqrt(2))/89.
- A160057 (program): Decimal expansion of (8979+2990*sqrt(2))/89^2.
- A160059 (program): Numerator of Hermite(n, 13/25).
- A160060 (program): Numerator of Hermite(n, 14/25).
- A160061 (program): Numerator of Hermite(n, 16/25).
- A160062 (program): Numerator of Hermite(n, 17/25).
- A160063 (program): Numerator of Hermite(n, 18/25).
- A160064 (program): Numerator of Hermite(n, 19/25).
- A160065 (program): Numerator of Hermite(n, 21/25).
- A160066 (program): Numerator of Hermite(n, 22/25).
- A160067 (program): Numerator of Hermite(n, 23/25).
- A160068 (program): Numerator of Hermite(n, 24/25).
- A160069 (program): Numerator of Hermite(n, 1/26).
- A160070 (program): Numerator of Hermite(n, 3/26).
- A160071 (program): Numerator of Hermite(n, 5/26).
- A160072 (program): Numerator of Hermite(n, 7/26).
- A160073 (program): Numerator of Hermite(n, 9/26).
- A160074 (program): Numerator of Hermite(n, 11/26).
- A160075 (program): Numerator of Hermite(n, 15/26).
- A160076 (program): Numerator of Hermite(n, 17/26).
- A160077 (program): Numerator of Hermite(n, 19/26).
- A160080 (program): Lodumo_4 of Fibonacci numbers .
- A160082 (program): Numerator of Hermite(n, 21/26).
- A160083 (program): Numerator of Hermite(n, 23/26).
- A160084 (program): Numerator of Hermite(n, 25/26).
- A160087 (program): Numerator of Hermite(n, 1/27).
- A160088 (program): Numerator of Hermite(n, 2/27).
- A160091 (program): Decimal expansion of (587+102*sqrt(2))/569.
- A160093 (program): Number of digits in n, excluding any trailing zeros.
- A160094 (program): 1 + the number of trailing zeros in n (A122840).
- A160096 (program): Partial sums of A010815 starting with offset 1, and signed (+ + - - + + …).
- A160099 (program): Decimal expansion of (843 + 418*sqrt(2))/601.
- A160103 (program): Numerator of Hermite(n, 4/27).
- A160104 (program): Numerator of Hermite(n, 5/27).
- A160107 (program): Numerator of Hermite(n, 7/27).
- A160117 (program): Number of “ON” cells after n-th stage in simple 2-dimensional cellular automaton (see Comments for precise definition).
- A160118 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton (see Comments for precise definition).
- A160119 (program): A three-dimensional version of the cellular automaton A160118, using cubes.
- A160128 (program): a(n) = number of grid points that are covered after (2^n)th stage of A139250.
- A160130 (program): 2 x 2 inner (dot) products taken on corresponding digits in Pi and e.
- A160131 (program): Numerator of Hermite(n, 8/27).
- A160132 (program): Numerator of Hermite(n, 10/27).
- A160134 (program): Nonprimitive e-perfect numbers.
- A160138 (program): a(n) = number of solutions to the system: x + y + z + w = n, -2x - y + z + 2w = 5 with nonnegative x, y, z, w.
- A160139 (program): Numerator of Hermite(n, 11/27).
- A160140 (program): Numerator of Hermite(n, 13/27).
- A160141 (program): Numerator of Hermite(n, 14/27).
- A160142 (program): Numerator of Hermite(n, 16/27).
- A160143 (program): a(n) = Numerator((-1)^n*Euler(2*n)*(2*n+1)/(4^(2*n+1)-2^(2*n+1))), where Euler(n) = A122045(n).
- A160144 (program): Numerator of (2*n+1)/(2^(2*n+1)-1).
- A160146 (program): Numerator of Hermite(n, 17/27).
- A160147 (program): Numerator of Hermite(n, 19/27).
- A160148 (program): Numerator of Hermite(n, 20/27).
- A160150 (program): Numerator of Hermite(n, 22/27).
- A160151 (program): Numerator of Hermite(n, 23/27).
- A160152 (program): Numerator of Hermite(n, 25/27).
- A160153 (program): Numerator of Hermite(n, 26/27).
- A160154 (program): 10^n-9n for n>=1
- A160155 (program): Decimal expansion of the one real root of x^5-x-1.
- A160156 (program): Partial sums of A007583.
- A160158 (program): Toothpick sequence starting from a segment of length 4 formed by two toothpicks.
- A160159 (program): First differences of A160158.
- A160162 (program): a(n) = A160158(n)/2.
- A160163 (program): First differences of A160162.
- A160164 (program): Number of toothpicks after n-th stage in the I-toothpick structure of A139250.
- A160172 (program): T-toothpick sequence (see Comments lines for definition).
- A160173 (program): Number of T-toothpicks added at n-th stage to the T-toothpick structure of A160172.
- A160174 (program): a(n) = (2*n - 1)*(24*n^2 - 42*n + 19).
- A160175 (program): Expansion of 1/(1 - 2*x - 2*x^2 - 2*x^3 - 2*x^4).
- A160177 (program): Decimal expansion of (633+100*sqrt(2))/617.
- A160180 (program): Largest proper divisor of the n-th composite number.
- A160181 (program): Number of partitions of sets containing from 0 to n elements into blocks of at least 2 elements.
- A160184 (program): Numerator of Hermite(n, 1/28).
- A160186 (program): Lodumo_5 of Lucas numbers.
- A160189 (program): Prime terms subtracted from Fibonacci terms (ignoring first two terms of Fibonacci sequence).
- A160190 (program): Prime terms multiplied by Fibonacci terms (omitting first two terms of Fibonacci sequence)
- A160192 (program): Numerator of Hermite(n, 3/28).
- A160193 (program): Numerator of Hermite(n, 5/28).
- A160194 (program): Numerator of Hermite(n, 9/28).
- A160195 (program): Numerator of Hermite(n, 11/28).
- A160196 (program): Numerator of Hermite(n, 13/28).
- A160197 (program): Numerator of Hermite(n, 15/28).
- A160201 (program): Decimal expansion of (1003+462*sqrt(2))/761.
- A160204 (program): Decimal expansion of (873+232*sqrt(2))/809.
- A160207 (program): Decimal expansion of (907+210*sqrt(2))/857.
- A160210 (program): Decimal expansion of (1179+506*sqrt(2))/937.
- A160213 (program): Decimal expansion of (969+124*sqrt(2))/953.
- A160215 (program): Primes congruent to 2^k+1 (mod 2^(k+1)), where k is any even integer >=0.
- A160216 (program): Primes congruent to 2^k+1 (mod 2^(k+1)), where k is any odd integer >=1.
- A160217 (program): Minimal increasing sequence with a(1)=3 and the property that a(n) and n are both in or both not in A003159.
- A160219 (program): Numerator of Hermite(n, 17/28).
- A160220 (program): Numerator of Hermite(n, 19/28).
- A160221 (program): Numerator of Hermite(n, 23/28).
- A160222 (program): Numerator of Hermite(n, 25/28).
- A160223 (program): Numerator of Hermite(n, 27/28).
- A160224 (program): Numerator of Hermite(n, 1/29).
- A160225 (program): Numerator of Hermite(n, 2/29).
- A160226 (program): Numerator of Hermite(n, 3/29).
- A160230 (program): a(n) = A004760(n+1)-A160217(n), n>=1.
- A160231 (program): Numerator of Hermite(n, 4/29).
- A160232 (program): Array read by antidiagonals: row n has g.f. ((1-x)/(1-2x))^n.
- A160236 (program): Numerator of Hermite(n, 5/29).
- A160237 (program): Numerator of Hermite(n, 6/29).
- A160239 (program): Number of “ON” cells in a 2-dimensional cellular automaton (“Fredkin’s Replicator”) evolving according to the rule that a cell is ON in a given generation if and only if there was an odd number of ON cells among the eight nearest neighbors in the preceding generation, starting with one ON cell.
- A160242 (program): Triangle A(n,m) read by rows: a quarter of the Fourier coefficient [cos(m*t)] of the shifted Boubaker polynomial B_n(2*cos t)-2*cos(n*t).
- A160243 (program): a(n) = Lucas(n+1) + prime(n).
- A160244 (program): A104449(n+1)+prime(n), sum of a Lucas and the prime sequence.
- A160246 (program): Numerator of Hermite(n, 7/29).
- A160248 (program): Table read by antidiagonals of “less regular” truncated tetrahedron numbers built of face-centered-cubic sphere packing.
- A160250 (program): a(n) = 64*n^3 - 168*n^2 + 148*n - 43.
- A160251 (program): Numerator of Hermite(n, 8/29).
- A160252 (program): Numerator of Hermite(n, 9/29).
- A160253 (program): Numerator of Hermite(n, 10/29).
- A160255 (program): The sum of all the entries in an n X n Cayley table for multiplication in Z_n.
- A160259 (program): Numerator of Hermite(n, 11/29).
- A160260 (program): Numerator of Hermite(n, 12/29).
- A160261 (program): Numerator of Hermite(n, 13/29).
- A160263 (program): Numerator of Hermite(n, 14/29).
- A160269 (program): Numerator of Hermite(n, 15/29).
- A160270 (program): Numerator of Hermite(n, 16/29).
- A160272 (program): Angle between the two hands of a 12 hour analog clock n*12 minutes after noon/midnight, measured in units of minutes.
- A160273 (program): Successive differences (divided by 3) of the average of twin prime pairs divided by 2 (A040040).
- A160278 (program): Angle in degrees between the two hands of a 12-hour analog clock at 12*n minutes after noon/midnight.
- A160279 (program): Numerator of Hermite(n, 17/29).
- A160280 (program): Numerator of Hermite(n, 18/29).
- A160281 (program): Numerator of Hermite(n, 19/29).
- A160282 (program): Numerator of Hermite(n, 20/29).
- A160283 (program): Numerator of Hermite(n, 21/29).
- A160284 (program): Numerator of Hermite(n, 22/29).
- A160285 (program): Numerator of Hermite(n, 23/29).
- A160286 (program): Numerator of Hermite(n, 24/29).
- A160287 (program): Numerator of Hermite(n, 25/29).
- A160288 (program): Numerator of Hermite(n, 26/29).
- A160289 (program): Numerator of Hermite(n, 27/29).
- A160290 (program): Numerator of Hermite(n, 28/29).
- A160291 (program): Numerator of Hermite(n, 1/30).
- A160292 (program): Numerator of Hermite(n, 7/30).
- A160293 (program): Numerator of Hermite(n, 11/30).
- A160294 (program): Numerator of Hermite(n, 13/30).
- A160295 (program): Numerator of Hermite(n, 17/30).
- A160296 (program): Numerator of Hermite(n, 19/30).
- A160297 (program): Numerator of Hermite(n, 23/30).
- A160298 (program): Numerator of Hermite(n, 29/30).
- A160299 (program): Numerator of Hermite(n, 1/31).
- A160300 (program): Numerator of Hermite(n, 2/31).
- A160301 (program): Numerator of Hermite(n, 3/31).
- A160302 (program): Numerator of Hermite(n, 4/31).
- A160303 (program): Numerator of Hermite(n, 5/31).
- A160304 (program): Numerator of Hermite(n, 6/31).
- A160305 (program): Numerator of Hermite(n, 7/31).
- A160306 (program): Numerator of Hermite(n, 8/31).
- A160307 (program): Numerator of Hermite(n, 9/31).
- A160308 (program): Numerator of Hermite(n, 10/31).
- A160309 (program): Numerator of Hermite(n, 11/31).
- A160310 (program): Numerator of Hermite(n, 12/31).
- A160311 (program): Numerator of Hermite(n, 13/31).
- A160312 (program): Numerator of Hermite(n, 14/31).
- A160313 (program): Numerator of Hermite(n, 15/31).
- A160314 (program): Numerator of Hermite(n, 16/31).
- A160315 (program): Numerator of Hermite(n, 17/31).
- A160316 (program): Numerator of Hermite(n, 18/31).
- A160317 (program): Numerator of Hermite(n, 19/31).
- A160324 (program): Number of ways to express n as the sum of a square, a pentagonal number and a hexagonal number.
- A160325 (program): Number of ways to express n=0,1,2,… as the sum of a triangular number, an even square and a pentagonal number.
- A160326 (program): Number of ways to express n=0,1,2,… as the sum of two squares and a pentagonal number.
- A160327 (program): Decimal expansion of (e-1)/(e+1).
- A160328 (program): Numerator of Hermite(n, 20/31).
- A160329 (program): Numerator of Hermite(n, 21/31).
- A160330 (program): Numerator of Hermite(n, 22/31).
- A160332 (program): Decimal expansion of the one real root of x^3-8x-10.
- A160333 (program): Number of pairs of rabbits in month n in the dying rabbits problem, if they become mature after 4 months and give birth to exactly 7 pairs, one per month.
- A160334 (program): Numerator of Hermite(n, 23/31).
- A160335 (program): Numerator of Hermite(n, 24/31).
- A160336 (program): Numerator of Hermite(n, 25/31).
- A160338 (program): Height (maximum absolute value of coefficients) of the n-th cyclotomic polynomial.
- A160344 (program): Numerator of Hermite(n, 26/31).
- A160345 (program): Numerator of Hermite(n, 27/31).
- A160346 (program): Numerator of Hermite(n, 28/31).
- A160347 (program): Numerator of Hermite(n, 29/31).
- A160349 (program): Numerator of Hermite(n, 30/31).
- A160361 (program): Numerator of Hermite(n, 1/32).
- A160362 (program): Numerator of Hermite(n, 3/32).
- A160363 (program): Numerator of Hermite(n, 5/32).
- A160372 (program): The 4-tuple (2, ((2*n+1)^2-1)/2, (2*n+3)^2-1)/2, a(n)}, where a(n)=4(3+20n+42n^2+32n^3+8n^4), has Diophantus’ property that the product of any two distinct terms plus one is a square.
- A160374 (program): Numerator of Hermite(n, 7/32).
- A160376 (program): Numerator of Hermite(n, 9/32).
- A160377 (program): Phi-torial of n (A001783) modulo n.
- A160378 (program): a(n) = n^3 - n*(n+1)/2.
- A160380 (program): a(0) = 0; for n >= 1, a(n) = number of 0’s in base-4 representation of n.
- A160381 (program): Number of 1’s in base-4 representation of n.
- A160382 (program): Number of 2’s in base-4 representation of n.
- A160383 (program): Number of 3’s in base-4 representation of n.
- A160384 (program): Number of nonzero digits in the base-3 representation of n.
- A160385 (program): Number of nonzero digits in base-4 representation of n.
- A160386 (program): Decimal expansion of Sum_{n>=0}(-1)^n/3^(2^n).
- A160388 (program): Decimal expansion of (e + 1)/3.
- A160389 (program): Decimal expansion of 2*cos(Pi/7).
- A160390 (program): Decimal expansion of sqrt(3) - 1.
- A160391 (program): Numerator of Hermite(n, 11/32).
- A160393 (program): Square root of A003462, rounded up.
- A160396 (program): Numerator of Hermite(n, 13/32).
- A160397 (program): Numerator of Hermite(n, 15/32).
- A160398 (program): Numerator of Hermite(n, 17/32).
- A160399 (program): a(n) = Sum_{k=1..n} binomial(n,k) * d(k), where d(k) = the number of positive divisors of k.
- A160400 (program): a(n) is the smallest positive integer such that a(n)*n = j^k, for some j (j>=1) and k (k>=2).
- A160401 (program): Table read by antidiagonals: a(m,n) = the smallest composite multiple of both m and n.
- A160406 (program): Toothpick sequence starting at the vertex of an infinite 90-degree wedge.
- A160407 (program): First differences of toothpick numbers A160406.
- A160408 (program): Toothpick pyramid (see Comments lines for definition).
- A160409 (program): First differences of toothpick numbers A160408.
- A160410 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton (see Comments for precise definition).
- A160411 (program): Number of cells turned “ON” at n-th stage of A160117.
- A160412 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton (see Comments for precise definition).
- A160413 (program): a(n) = A160411(n+1)/4.
- A160414 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton (same as A160410, but a(1) = 1, not 4).
- A160415 (program): First differences of A160118.
- A160417 (program): a(n) = A160415(n+1)/4.
- A160418 (program): a(n) = A160407(n+2)/2.
- A160424 (program): Partial sums of A139250.
- A160428 (program): Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160410, using cubes.
- A160429 (program): First differences of A160428.
- A160431 (program): Numerator of Hermite(n, 19/32).
- A160435 (program): Numerator of Hermite(n, 21/32).
- A160436 (program): Numerator of Hermite(n, 23/32).
- A160437 (program): Numerator of Hermite(n, 25/32).
- A160441 (program): Numerator of Hermite(n, 27/32).
- A160442 (program): Numerator of Hermite(n, 29/32).
- A160443 (program): Numerator of Hermite(n, 31/32).
- A160444 (program): G.f.: x^2*(-1-x+x^2)/(-1+2*x^2+2*x^4).
- A160445 (program): Numerator of Hermite(n, 20/21).
- A160451 (program): (4/3)u(u^3+6*u^2+8u-3) where u=Floor[{3n+5)/2].
- A160455 (program): Number of triangles that can be built from rods with lengths 1,2,…,n by using and concatenating all rods.
- A160457 (program): a(n) = n^2 - 2*n + 2.
- A160458 (program): Coefficients in the expansion of C^2/B^10, in Watson’s notation of page 106.
- A160459 (program): Omit first term of A160458 and divide by 5.
- A160467 (program): a(n) = 1 if n is odd; otherwise, a(n) = 2^(k-1) where 2^k is the largest power of 2 that divides n.
- A160469 (program): The left hand column of the triangle A160468.
- A160473 (program): The p(n) sequence that is associated with the Eta triangle A160464.
- A160481 (program): Row sums of the Beta triangle A160480.
- A160483 (program): Second right hand column of the Beta triangle A160480
- A160491 (program): First differences of A062481.
- A160501 (program): (n+1)^prime(n+1) + n^prime(n).
- A160505 (program): a(1)=1, a(n) = p*a(n-1), where p is the smallest prime satisfying gcd(n,p)=1.
- A160511 (program): Number of weighings needed to find lighter coins among n coins.
- A160517 (program): A walk of 10-divisible “less regular” figurate cuboctahedra, from sequence A160249.
- A160522 (program): The n-th odd composite number minus the n-th even composite number.
- A160529 (program): a(1) = 1; for n>1, a(n) = a(n-1) + d1 + d2 where d1 = 4 if n is even. d1 = 1 if n is odd, d2 = 15 if n mod 4 = 0, d2 = 0 if n mod 4 != 0.
- A160530 (program): Positive integers that contain only odd-length runs of 0’s and 1’s in their binary expansion.
- A160532 (program): Those positive integers n that contain runs of 0’s and 1’s that are each a power of 2 in length when n is represented in binary.
- A160536 (program): a(n) = Fibonacci(n) + n^2.
- A160538 (program): a(n) = 4*(n^4-n^3).
- A160541 (program): Number of odd-then-even runs to reach 1 under the modified `3x+1’ map: n -> n/2 if n is even, n -> (3n+1)/2 if n is odd.
- A160542 (program): Not divisible by 11
- A160543 (program): Not divisible by 17
- A160544 (program): Not divisible by 19.
- A160545 (program): Numbers coprime to 21.
- A160546 (program): Not divisible by 29.
- A160547 (program): Not divisible by 31.
- A160550 (program): a(n) = A001065(n) mod A000005(n).
- A160551 (program): Number of unordered ways of making change for n dollars using coins of denominations 1, 5, 10, and 25.
- A160552 (program): a(0)=0, a(1)=1; a(2^i+j) = 2*a(j) + a(j+1) for 0 <= j < 2^i.
- A160554 (program): Numerator of Laguerre(n, -12).
- A160555 (program): Denominator of Laguerre(n, -12).
- A160565 (program): Diagonal sums of number triangle [k<=n]*C(n,2n-2k)2^(n-k)A000108(n-k).
- A160566 (program): Numerator of Laguerre(n, -11).
- A160567 (program): a(n)=4*(a(n-1)a(n-3)-a(n-2)^2)/a(n-4), a(1)=a(2)=a(3)=1, a(4)=-4.
- A160568 (program): Diagonal sums of number triangle [k<=n]*C(n,2n-2k)3^(n-k)A000108(n-k).
- A160569 (program): a(n)=9*(a(n-1)a(n-3)-a(n-2)^2)/a(n-4), a(1)=a(2)=a(3)=1, a(4)=-9.
- A160572 (program): Elements of A160444, pairs of consecutive entries swapped.
- A160573 (program): G.f.: Product_{ k >= 0} (1 + x^(2^k-1) + x^(2^k)).
- A160575 (program): Decimal expansion of (363+130*sqrt(2))/313.
- A160578 (program): Decimal expansion of (473+168*sqrt(2))/409.
- A160581 (program): Decimal expansion of (601+276*sqrt(2))/457.
- A160584 (program): Decimal expansion of (537 +92*sqrt(2))/521.
- A160586 (program): Denominator of Laguerre(n, -11).
- A160587 (program): Numerator of Laguerre(n, -10).
- A160588 (program): Interleaving of A053645 and A000027.
- A160589 (program): Denominator of Laguerre(n, -10).
- A160590 (program): Next-to-least significant digit of 2^n.
- A160591 (program): Indices of primes congruent to 5 modulo 12.
- A160592 (program): Indices of primes congruent to 7 modulo 12.
- A160593 (program): Indices of primes congruent to 11 modulo 12.
- A160594 (program): Indices of primes congruent to 1 modulo 12.
- A160595 (program): Numerator of resilience R(n) = phi(n)/(n-1), with a(1) = 1 by convention.
- A160596 (program): Denominator of resilience R(n) = phi(n)/(n-1).
- A160597 (program): Denominator of coresilience C(n) = (n - phi(n))/(n-1).
- A160598 (program): Numerator of coresilience C(n) = (n - phi(n))/(n-1).
- A160601 (program): Numerator of Laguerre(n, -9).
- A160602 (program): Denominator of Laguerre(n, -9).
- A160603 (program): Numerator of Laguerre(n, -8).
- A160604 (program): Denominator of Laguerre(n, -8).
- A160605 (program): Numerator of Laguerre(n, -7).
- A160606 (program): Denominator of Laguerre(n, -7).
- A160607 (program): Numerator of Laguerre(n, -6).
- A160608 (program): Denominator of Laguerre(n, -6).
- A160609 (program): Numerator of Laguerre(n, -5).
- A160610 (program): Denominator of Laguerre(n, -5).
- A160611 (program): Numerator of Laguerre(n, -4).
- A160612 (program): Denominator of Laguerre(n, -4).
- A160613 (program): Numerator of Laguerre(n, -3).
- A160614 (program): Denominator of Laguerre(n, -3).
- A160615 (program): Numerator of Laguerre(n, -2).
- A160616 (program): Denominator of Laguerre(n, -2).
- A160617 (program): Numerator of Laguerre(n, -1).
- A160618 (program): Denominator of Laguerre(n, -1).
- A160619 (program): a(n) = Sum_{d|n} phi(n/d)*2^(d+1), with a(0) = 0.
- A160621 (program): Numerator of Laguerre(n, 1).
- A160622 (program): Denominator of Laguerre(n, 1).
- A160623 (program): Numerator of Laguerre(n, 2).
- A160624 (program): Denominator of Laguerre(n, 2).
- A160625 (program): Numerator of Laguerre(n, 3).
- A160626 (program): Denominator of Laguerre(n, 3).
- A160627 (program): Numerator of Laguerre(n, 4).
- A160628 (program): Denominator of Laguerre(n, 4).
- A160629 (program): Numerator of Laguerre(n, 5).
- A160630 (program): Denominator of Laguerre(n, 5).
- A160631 (program): Numerator of Laguerre(n, 6).
- A160632 (program): Denominator of Laguerre(n, 6).
- A160633 (program): Numerator of Laguerre(n, 7).
- A160634 (program): Denominator of Laguerre(n, 7).
- A160635 (program): Numerator of Laguerre(n, 8).
- A160637 (program): Hankel transform of A114464(n+1).
- A160638 (program): Bit-reversed 8-bit binary numbers.
- A160639 (program): Denominator of Laguerre(n, 8).
- A160640 (program): Numerator of Laguerre(n, 9).
- A160641 (program): Denominator of Laguerre(n, 9).
- A160644 (program): First of two sequences bisecting the second differences of the partition numbers (see A053445).
- A160649 (program): a(1)=2. a(n) = a(n-1) + A001222(a(n-1)); where A001222(m) is the sum of prime-factorization exponents of m (or, A001222(m) is the number of primes dividing m, with multiplicity).
- A160650 (program): a(n) = A001222(A160649(n)) = A160649(n+1) - A160649(n); where A001222(m) is the sum of prime-factorization exponents of m (or, A001222(m) is the number of primes dividing m, counted with multiplicity).
- A160651 (program): a(n) is the number of triangular nonnegative integers that are each equal to n(n+1)/2 - m(m+1)/2, for some m’s where 0 <= m <= n.
- A160653 (program): Numerator of Laguerre(n, 10).
- A160654 (program): Denominator of Laguerre(n, 10).
- A160655 (program): Numerator of Laguerre(n, 11).
- A160656 (program): The odd prime numbers together with 0: p - (-1)^p - 1 where p = n-th prime.
- A160664 (program): a(n) = a(n-1) + A000203(n), a(0)=1.
- A160666 (program): Numbers whose distance to the closest prime number is a prime number.
- A160667 (program): Denominator of Laguerre(n, 11).
- A160668 (program): Distance between prime(n) and the next higher power of 10.
- A160670 (program): Primes in A160668 in order of appearance.
- A160671 (program): Numerator of Laguerre(n, 12).
- A160672 (program): Denominator of Laguerre(n, 12).
- A160674 (program): A bisection of A063522.
- A160675 (program): Duplication root: the maximal number of distinct squarefree words that a word of length n can be reduced to by iterated application of string-rewriting rules uu->u.
- A160682 (program): The list of the A values in the common solutions to 13*k+1 = A^2 and 17*k+1 = B^2.
- A160692 (program): Iteration of (k terms=k, followed by 2^k-k terms=0), beginning with k=0.
- A160695 (program): Integers m such that 3*m+1 and 7*m+1 are both perfect squares.
- A160696 (program): Largest k such that k^2 divides prime(n)+1.
- A160697 (program): Record values in A160696.
- A160699 (program): A bisection of A063522.
- A160703 (program): Generalized Somos-4 Hankel determinant recurrence sequence.
- A160704 (program): Jacobsthal sequence A001045 convolved with A139251 (first differences of toothpick numbers).
- A160706 (program): Hankel transform of A052702(n+1).
- A160713 (program): 3 times numbers of Gould’s sequence: a(n) = A001316(n)*3.
- A160718 (program): a(n) = A160406(n+2)/2.
- A160719 (program): a(n) = A160406(n+2)/2 - 1.
- A160720 (program): Number of “ON” cells at n-th stage in 2-dimensional cellular automaton (see Comments for precise definition).
- A160721 (program): First differences of A160720.
- A160722 (program): Number of “ON” cells at n-th stage in a certain 2-dimensional cellular automaton based on Sierpinski triangles (see Comments for precise definition).
- A160723 (program): First differences of A160722.
- A160727 (program): a(n) = A161415(n+1)/4.
- A160728 (program): Toothpick cube: a(n) = A160408(n)*6.
- A160729 (program): First differences of A160728.
- A160734 (program): a(n) = (A160158(n+2)-4)/4.
- A160735 (program): First differences of A160734.
- A160736 (program): Toothpick sequence starting from a right angle formed by 2 toothpicks: a(n)=A160406(n)*2.
- A160737 (program): 4*P_5(n), 4 times the Legendre Polynomial of order 5 at n.
- A160738 (program): Toothpick sequence starting from a T formed by 3 toothpicks: a(n)=A160406(n)*3.
- A160739 (program): 16*P_6(n), 16 times the Legendre Polynomial of order 6 at n.
- A160740 (program): Toothpick sequence starting from a cross formed by 4 toothpicks.
- A160741 (program): Numerator of P_6(2n), the Legendre polynomial of order 6 at 2n.
- A160742 (program): a(n) = A151566(n)*2.
- A160743 (program): 8*P_7(n), 8 times the Legendre Polynomial of order 7 at n.
- A160744 (program): a(n) = A151566(n)*3.
- A160745 (program): First differences of A160744.
- A160746 (program): a(n) = A151566(n)*4.
- A160747 (program): Expansion of (1+10*x+20*x^2+10*x^3+x^4)/(1-x)^5.
- A160749 (program): a(n) = (11*n^2 + 19*n + 10)/2.
- A160755 (program): Number of correct digits of the MRB constant derived from the sequence of partial sums up to m=10^n terms as defined by S[n]= Sum[(-1)^k*(k^(1/k)-1),{k,m}].
- A160760 (program): Triangle read by rows, binomial transform of an infinite lower triangular Toeplitz matrix with A078008 in every column.
- A160762 (program): Convolved with the toothpick sequence A139250 = (2*n - 1): (1, 3, 5, 7, …).
- A160765 (program): Expansion of (1+13*x+32*x^2+13*x^3+x^4)/(1-x)^5.
- A160767 (program): Expansion of (1+12*x+28*x^2+12*x^3+x^4)/(1-x)^5.
- A160772 (program): Number of nodes (or order) of a graph model obtained using an automata scheme on sets of order prime(n) >= 5 and in which all not halt states are linked by arcs (edges).
- A160785 (program): Even squarefree numbers plus 1.
- A160790 (program): Vertex number of a rectangular spiral. The first differences (A160791) are the edge lengths of the spiral. The distances between two nearest edges, that are parallel to the initial edge, are the natural numbers.
- A160791 (program): First differences of A160790.
- A160792 (program): Vertex number of a rectangular spiral related to prime numbers. The distances between nearest edges of the spiral that are parallel to the initial edge are the prime numbers, while the distances between nearest edges perpendicular to the initial edge are all one.
- A160793 (program): Natural numbers and the sum of first n primes interleaved.
- A160796 (program): Total number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton which is the “corner” structure corresponding to A160118.
- A160797 (program): First differences of A160796.
- A160798 (program): a(n) = A160797(n+2)/3.
- A160799 (program): Partial sums of A160410.
- A160804 (program): Consider a permutation K = (k(1),k(2),…k(A000005(n))) of the positive divisors of n. Consider the partial sums S= sum{j=1 to m} k(j), 1<=m<=A000005(n). Then, a(n) = the minimum number, for any permutation K, of partial sums S that are coprime to n.
- A160805 (program): a(n) = (2*n^3 + 9*n^2 + n + 24) / 6.
- A160807 (program): a(n) = A160799(n)/4.
- A160810 (program): Numbers k such that the number of partitions of k into prime divisors of k exceeds the number of distinct transpositions of prime factors of k.
- A160811 (program): Numbers not dividing 24.
- A160812 (program): a(n) = A161205(n)-A000005(n).
- A160813 (program): a(n) = n-th squarefree number plus n-th cubefree number.
- A160823 (program): A transform of the large Schroeder numbers.
- A160827 (program): a(n) = 3*n^4 + 12*n^3 + 30*n^2 + 36*n + 17.
- A160828 (program): a(n) = 4*n^4 + 24*n^3 + 84*n^2 + 144*n + 98.
- A160830 (program): Integer part of the product of two consecutive primes divided by their sum.
- A160832 (program): Expansion of eta(q)*eta(q^2)*eta(q^4), where eta(q) = Product((1-q^m), m=1..oo).
- A160842 (program): Number of lines through at least 2 points of a 2 X n grid of points.
- A160843 (program): Number of lines through at least 2 points of a 3 X n grid of points.
- A160864 (program): 64*P_9(n), 64 times the Legendre polynomial of order 9 at n.
- A160865 (program): 128*P_11(n), 128 times the Legendre polynomial of order 11 at n.
- A160866 (program): 512*P_11(n), 512 times the Legendre polynomial of order 13 at n.
- A160867 (program): 1024*P_15(n), 1024 times the Legendre polynomial of order 15 at n.
- A160868 (program): 16384*P_17(n), 16384 times the Legendre polynomial of order 17 at n.
- A160869 (program): a(n) = sigma(6^(n-1)).
- A160873 (program): Number of isomorphism classes of connected (D_4)-fold coverings of a connected graph with circuit rank n.
- A160889 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4.
- A160890 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 3.
- A160891 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 5.
- A160892 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 4.
- A160893 (program): a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n).
- A160894 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 5.
- A160895 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7.
- A160896 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 6.
- A160897 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8.
- A160898 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 7.
- A160900 (program): a(n) = the smallest positive multiple of n that has exactly a prime number of (non-leading) 0’s in its binary representation.
- A160902 (program): Square array read by antidiagonals: a(m,n) = the smallest prime >= m*n.
- A160903 (program): Square array read by antidiagonals: a(m,n) = the largest noncomposite <= m*n.
- A160904 (program): Row sums of A159881.
- A160906 (program): Row sums of A159841.
- A160908 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 9.
- A160909 (program): Row sums of triangle defined in A096539.
- A160910 (program): Decimal expansion of c = sum over twin primes (p, p+2) of (1/p^2 + 1/(p+2)^2).
- A160912 (program): [1, 3, 5, 7, …] convolved with [1, 4, 0, 0, 0, …].
- A160913 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 8.
- A160914 (program): Extended s-block elements for Janet table.
- A160924 (program): a(n)= n + reversal(n+1)
- A160925 (program): a(n)= n - reversal(n+1)
- A160926 (program): a(n)= n * reversal(n+1)
- A160927 (program): a(n) = n + reversal(n-1).
- A160928 (program): a(n) = n - reversal(n-1)
- A160929 (program): a(n)= n * reversal(n-1)
- A160930 (program): a(n)= n + reversal(n-1) + reversal(n+1)
- A160931 (program): a(n)= n + digital sum(n+1)
- A160933 (program): a(n)= n - reversal(n-1) - reversal(n+1)
- A160936 (program): a(n)= n * reversal(n-1) * reversal(n+1).
- A160938 (program): a(n)= n * digital sum(n+1)
- A160939 (program): a(n) = n + digital sum (n-1).
- A160941 (program): a(n)= n - digital sum(n-1)
- A160942 (program): a(n)= n * digital sum(n-1)
- A160943 (program): a(n) = n + digital sum(n-1) + digital sum(n+1).
- A160944 (program): a(n)= n * digital sum(n-1) * digital sum(n+1)
- A160947 (program): Numbers k that are multiples of the digital sum of k+1.
- A160948 (program): Numbers n that are multiples of the digital sum of n-1.
- A160949 (program): a(n) = n - digital sum(n+1)
- A160950 (program): Primes p such that 2p + 105 is prime.
- A160953 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 10.
- A160956 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 9.
- A160957 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 11.
- A160958 (program): a(n) = (9^n - (-7)^n)/(9 - (-7)).
- A160959 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 10.
- A160964 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 11.
- A160967 (program): Numbers of the form (4^k - 1)/3 or 2^k.
- A160970 (program): Indices of square numbers that are also 18-gonal numbers.
- A160973 (program): a(n) is the number of positive integers of the form (n-3k)/(2k+1), 1 <= k <= (n-1)/5.
- A160993 (program): The number of ordered ways to achieve a score of n in American football.
- A160997 (program): Antidiagonal sums of the Wythoff array A035513
- A161003 (program): A list of the composite numbers divided by their largest prime factors.
- A161007 (program): a(n+1) = 2*a(n) + 16*a(n-1), a(0)=0, a(1)=1.
- A161011 (program): Decimal expansion of tan(1/2).
- A161021 (program): Collatz (or 3x+1) trajectory starting at 703.
- A161051 (program): Number of partitions of 2n into powers of two where every part appears at least twice.
- A161116 (program): a(n) is the number of nontrivial positive divisors of 2n+3.
- A161120 (program): Number of cycles with entries of opposite parities in all fixed-point-free involutions of {1,2,…,2n}.
- A161122 (program): Number of cycles with entries of the same parity in all fixed-point-free involutions of {1,2,…,2n}.
- A161124 (program): Number of inversions in all fixed-point-free involutions of {1,2,…,2n}.
- A161125 (program): Number of descents in all involutions of {1,2,…,n}.
- A161128 (program): a(n) = n!*(1/1 + 1/2 + … + 1/n) - (1! + 2! + … + n!).
- A161129 (program): Triangle read by rows: T(n,k) is the number of non-derangements of {1,2,…,n} for which the difference between the largest and smallest fixed points is k (n>=1; 0 <= k <= n-1).
- A161130 (program): Sum of the differences between the largest and the smallest fixed points over all non-derangement permutations of {1,2,…,n}.
- A161131 (program): Number of permutations of {1,2,…,n} that have no odd fixed points.
- A161132 (program): Number of permutations of {1,2,…,n} that have no even fixed points.
- A161149 (program): a(n) = (2*n)!*(2*n+1)!/n! = n!*A000909(n), n=0,1…
- A161150 (program): a(n) = (largest odd divisor of n)*(largest power of 2 dividing (n+1)).
- A161151 (program): a(n) = (largest odd divisor of (n+1))*(largest power of 2 dividing n).
- A161152 (program): Positive integers n such that {the number of (non-leading) 0’s in the binary representation of n} is coprime to n.
- A161153 (program): Positive integers that are coprime to their number of digits in binary representation.
- A161154 (program): Positive integers n such that both {the number of (non-leading) 0’s in the binary representation of n} is coprime to n and {the number of 1’s in the binary representation of n} is coprime to n.
- A161158 (program): a(n) = A003696(n+1)/A001353(n+1).
- A161159 (program): a(n) = A003739(n)/(5*A001906(n)*A006238(n)).
- A161163 (program): Indices of the isolated primes in the prime sequence, if indices are odd.
- A161165 (program): The n-th twin prime plus the n-th isolated prime.
- A161168 (program): a(n) = 2^n + 4^n.
- A161175 (program): Triangle read by rows, modified Thue-Morse sequence (A010060 with offset 1): change 0 to 2, else 1.
- A161176 (program): a(n) = 4n^2 - 10n + 107.
- A161178 (program): Sum of the double factorials of the digits of n.
- A161179 (program): A double interspersion, R(n,k), by antidiagonals.
- A161182 (program): Successive differences between positions of squares in list of nonprimes.
- A161187 (program): Let S = A089237\{0} = union of primes and nonzero squares; sequence gives indices of squares.
- A161188 (program): Let S = A089237\{0} = union of primes and nonzero squares; sequence gives indices of primes.
- A161199 (program): Numerators in expansion of (1-x)^(-5/2).
- A161200 (program): Numerators in expansion of (1-x)^(3/2).
- A161201 (program): Numerators in expansion of (1-x)^(-7/2)
- A161202 (program): Numerators in expansion of (1-x)^(5/2)
- A161203 (program): n-th square plus n-th squarefree number.
- A161204 (program): a(0)=2. a(n+1) = 2*a(n) + period 4: repeat -5,1,3,1.
- A161205 (program): Triangle read by rows in which row n lists 2n-1 followed by 2n numbers 2n.
- A161219 (program): a(n) = (1/n) * Sum_{d|n} phi(n/d)*2^(d+1).
- A161220 (program): The n-th member of a twin prime pair minus 2*n.
- A161221 (program): Consider necklaces with n beads, each black or white, where the n segments of cord between the beads are each colored red or green; a(n) is the number of different necklaces under the action of the dihedral group D_{2n}.
- A161225 (program): a(n) = number of distinct integers that can be constructed by removing one or more 0’s from the binary representation of n, and concatenating while leaving the remaining digits in their same order.
- A161226 (program): a(0)=0. a(n) = the smallest integer of the form k^j, j>=2, such that a(n) >= a(n-1) + n.
- A161321 (program): Decimal expansion of (sqrt(35)-5)/10.
- A161325 (program): Partial sums of A160414.
- A161339 (program): Partial sums of A161205.
- A161342 (program): Number of “ON” cubic cells at n-th stage in simple 3-dimensional cellular automaton: a(n) = A160428(n)/8.
- A161343 (program): a(n) = 7^A000120(n).
- A161344 (program): Numbers k with A033676(k)=2, where A033676 is the largest divisor <= sqrt(k).
- A161345 (program): Numbers k whose largest divisor <= sqrt(k) is 3.
- A161346 (program): a(n) = A161345(n)/3.
- A161351 (program): a(n) = n + sum_of_digits(n) + product_of_digits(n).
- A161365 (program): a(n) = 3/2 + 5*n - 5*(-1)^n/2.
- A161367 (program): Primes such that p(n)-p(n-1)+1 is not prime
- A161370 (program): a(n) = 2*A010844(n) + 1.
- A161380 (program): Triangle read by rows: T(n,k) = 2*k*T(n-1,n-1) + 1 (n >= 0, 0 <= k <= n), with T(0,0) = 1.
- A161381 (program): Triangle read by rows: T(n,k) = n!*2^k/(n-k)! (n >= 0, 0 <= k <= n).
- A161382 (program): (0,1)-sequence where n-th run has length n^2.
- A161385 (program): (1,2)-sequence where n-th run has length n^2.
- A161400 (program): Positive integers that are palindromes (of even length) in binary, each made by concatenating two identical binary palindromes.
- A161411 (program): First differences of A160410.
- A161415 (program): First differences of A160414.
- A161416 (program): Partial sums of A056737.
- A161418 (program): Number of triangles in the Y-toothpick structure after n rounds.
- A161422 (program): a(n) = A161418(n)/6.
- A161424 (program): Numbers k whose largest divisor <= sqrt(k) equals 4.
- A161425 (program): a(n) = A161424(n)/2.
- A161426 (program): Y-toothpick sequence starting at the outside corner of an infinite triangle-shaped polygon as the sieve of A160120 after 2^k rounds.
- A161427 (program): First differences of A161426.
- A161428 (program): a(n) = A161424(n)/4.
- A161434 (program): Number of 6-compositions.
- A161435 (program): Number of reduced words of length n in the Weyl group A_3 (or D_3).
- A161436 (program): Number of reduced words of length n in the Weyl group A_4.
- A161440 (program): Numbers m such that A160700(m) = 0.
- A161441 (program): Numbers n such that A160700(n) = 1.
- A161442 (program): Numbers n such that A160700(n) = 2.
- A161443 (program): Numbers m such that A160700(m) = 3.
- A161444 (program): Numbers n such that A160700(n) = 4.
- A161445 (program): Numbers n such that A160700(n) = 5.
- A161446 (program): Numbers n such that A160700(n) = 6.
- A161447 (program): Numbers n such that A160700(n) = 7.
- A161448 (program): Numbers n such that A160700(n) = 8.
- A161449 (program): Numbers n such that A160700(n) = 9.
- A161450 (program): Numbers n such that A160700(n) = 10.
- A161451 (program): Numbers n such that A160700(n) = 11.
- A161452 (program): Numbers m such that A160700(m) = 12.
- A161453 (program): Numbers n such that A160700(n) = 13.
- A161454 (program): Numbers n such that A160700(n) = 14.
- A161455 (program): Numbers n such that A160700(n) = 15.
- A161462 (program): Final digit of the sum of all the integers from n to 2*n-1.
- A161463 (program): Sum of all primes from n-th prime to (2*n-1)-th prime.
- A161464 (program): Sum of all digits of primes from n-th prime to (2*n-1)-th prime.
- A161474 (program): Triple factorials n!!!: a(n) = n*a(n-3).
- A161480 (program): Decimal expansion of (129 +44*sqrt(2))/113.
- A161484 (program): Decimal expansion of (187 + 78*sqrt(2))/151.
- A161488 (program): Decimal expansion of (209+60*sqrt(2))/191.
- A161495 (program): Expansion of x*(3*x-1)*(x-3)/(1-15*x+32*x^2-15*x^3+x^4).
- A161498 (program): Expansion of x*(1-x)*(1+x)/(1-13*x+36*x^2-13*x^3+x^4).
- A161504 (program): Primes congruent to {1, 2, 10, 11, 19, 20} mod 21.
- A161511 (program): Number of 1…0 pairs in the binary representation of 2n.
- A161513 (program): Number of reduced words of length n in the Weyl group A_20.
- A161517 (program): Sum of remainders of c mod k where k = 1, 2, 3, …, c and c is the n-th composite number.
- A161518 (program): Number of reduced words of length n in the Weyl group A_21.
- A161521 (program): Number of reduced words of length n in the Weyl group A_22.
- A161522 (program): prime(n)*( prime(n)-n ).
- A161523 (program): Number of reduced words of length n in the Weyl group A_23.
- A161524 (program): Number of reduced words of length n in the Weyl group A_24.
- A161525 (program): Number of reduced words of length n in the Weyl group A_25.
- A161526 (program): Number of reduced words of length n in the Weyl group A_26.
- A161527 (program): Numerators of cumulative sums of rational sequence A038110(k)/A038111(k).
- A161528 (program): Expansion of the q-series Sum_{n >= 0} (-1)^nq^(n(n+1)/2)(1-q)(1-q^2)…(1-q^n)/((1-q^(n+1))(1-q^(n+2))…(1-q^(2n+1))).
- A161530 (program): Number of reduced words of length n in the Weyl group A_27.
- A161532 (program): a(n) = 2n^2 + 8n + 1.
- A161537 (program): a(n) = n-th composite + n.
- A161538 (program): Numbers n such that composite (n) + n is a prime, where composite (n) denotes the n-th composite number.
- A161539 (program): Numbers n such that composite (n) + n is a composite, where composite (n) denotes the n-th composite number.
- A161540 (program): Primes which are the sum of a smaller n and its composite(n) subscript. A002808 + a(n) (= prime)
- A161541 (program): Composite which are the sum of a smaller n and its composite(n) subscript A002808 + a(n) (= composite)
- A161542 (program): m-th composite composite(m) is included iff composite(m) + m is prime.
- A161543 (program): The m-th composite number composite(m) is a term iff composite(m) + m is composite.
- A161549 (program): a(n) = 2n^2 + 14n + 1.
- A161550 (program): Largest prime <= n^2+n.
- A161552 (program): E.g.f. satisfies: A(x,y) = exp(x*y*exp(x*A(x,y))).
- A161556 (program): Exponential Riordan array [1 + (sqrt(Pi)/2)*x*exp(x^2/4)*erf(x/2), x].
- A161560 (program): a(n) = floor(A000069(n)/2-1/2).
- A161561 (program): The smallest number larger than n with digital sum equal to n.
- A161565 (program): E.g.f. satisfies: A(x) = exp(x*exp(2*x*A(x))).
- A161569 (program): Sum of first n nonprimes minus their indices.
- A161570 (program): Sum of all numbers from n up to A018252(n).
- A161571 (program): Number of reduced words of length n in the Weyl group A_28.
- A161572 (program): Number of reduced words of length n in the Weyl group A_29.
- A161573 (program): Number of reduced words of length n in the Weyl group A_30.
- A161579 (program): Positions n such that A010060(n) = A010060(n+3).
- A161580 (program): Positions n such that A010060(n) + A010060(n+3) = 1.
- A161581 (program): a(n) = (3n)!/(n!(n+1)!(n+2)!).
- A161582 (program): The list of the k values in the common solutions to the 2 equations 5*k+1=A^2, 9*k+1=B^2.
- A161583 (program): The list of the k values in the common solutions to the 2 equations 15*k+1=A^2, 19*k+1=B^2.
- A161584 (program): The list of the k values in the common solutions to the 2 equations 13*k+1=A^2, 17*k+1=B^2.
- A161585 (program): The list of the k values in the common solutions to the 2 equations 7*k+1=A^2, 11*k+1=B^2.
- A161586 (program): The list of the k values in the common solutions to the 2 equations 9*k+1=A^2, 13*k+1=B^2.
- A161587 (program): a(n) = 13n^2 + 10n + 1.
- A161588 (program): The list of the k values in the common solutions to the 2 equations 11*k+1=A^2, 15*k+1=B^2.
- A161591 (program): The list of the B values in the common solutions to the 2 equations 13*k + 1 = A^2, 17*k + 1 = B^2.
- A161595 (program): The list of the A values in the common solutions to the 2 equations 15*k+1=A^2, 19*k+1=B^2.
- A161599 (program): The list of the B values in the common solutions to the 2 equations 15*k + 1 = A^2, 19*k + 1 = B^2.
- A161601 (program): Positive integers k that are less than the value of the reversal of k’s representation in binary.
- A161602 (program): Positive integers k that are greater than the value of the reversal of k’s binary representation.
- A161603 (program): Odd elements of sequence A161602.
- A161604 (program): A positive integer k is included if the value of (the reversal of k’s representation in binary) divides k.
- A161606 (program): a(n) = gcd(A008472(n), A001222(n)).
- A161607 (program): Positive integers k that are coprime to the value of the reversal of k’s representation in binary.
- A161617 (program): 8*n^2+20*n+1.
- A161621 (program): Numerator of (b(n+1) - b(n))/(b(n+2) - b(n)), where b(n) = A038107(n) is the number of primes up to n^2.
- A161622 (program): Denominators of the ratios (in lowest terms) of numbers of primes in one square interval to that of the interval and its successor.
- A161624 (program): Sum of all numbers from n to n-th prime.
- A161625 (program): Sum of all numbers from 1 up to the final digit of prime(n).
- A161626 (program): Sum of all numbers from 2*n-1 up to prime(n).
- A161627 (program): Positions n such that A010060(n)=A010060(n+4).
- A161628 (program): E.g.f.: A(x,y) = LambertW(x*y*exp(x))/(x*y*exp(x)), as a triangle of coefficients T(n,k) = [x^n*y^k/n! ] A(x,y), read by rows.
- A161629 (program): E.g.f. satisfies: A(x) = exp( x*Catalan(x*A(x)) ), where Catalan(x) = (1-sqrt(1-4*x))/(2*x) is the g.f. of A000108.
- A161630 (program): E.g.f. satisfies: A(x) = exp( x/(1 - x*A(x)) ).
- A161631 (program): E.g.f. satisfies: A(x) = 1 + x*exp(x*A(x)).
- A161632 (program): E.g.f. satisfies: A(x) = (1 + x*exp(x*A(x)))^2.
- A161633 (program): E.g.f. satisfies: A(x) = 1/(1 - x*exp(x*A(x))).
- A161634 (program): G.f. satisfies: A(x) = 1/(1 - x*(1 + x*A(x))^2).
- A161635 (program): E.g.f. satisfies: A(x) = exp( x/(1 - x*A(x))^2 ).
- A161636 (program): Number of reduced words of length n in the Weyl group A_31.
- A161639 (program): Positions n such that A010060(n) = A010060(n+8).
- A161640 (program): Number of reduced words of length n in the Weyl group A_32.
- A161641 (program): Positions n such that A010060(n) + A010060(n+4) = 1.
- A161642 (program): Triangle (by rows): T(n,k) = A007318(n,k) / A003989(n+1,k+1).
- A161646 (program): Number of reduced words of length n in the Weyl group A_33.
- A161647 (program): Number of reduced words of length n in the Weyl group A_34.
- A161648 (program): Number of reduced words of length n in the Weyl group A_35.
- A161649 (program): Number of reduced words of length n in the Weyl group A_36.
- A161650 (program): Number of reduced words of length n in the Weyl group A_37.
- A161651 (program): Number of reduced words of length n in the Weyl group A_38.
- A161652 (program): Number of reduced words of length n in the Weyl group A_39.
- A161653 (program): Number of reduced words of length n in the Weyl group A_40.
- A161654 (program): a(n) = the largest multiple of {the number of divisors of n} that is <= n.
- A161655 (program): a(n) = the smallest multiple of {the number of divisors of n} that is >= n.
- A161656 (program): The largest multiple of {the sum of the distinct prime divisors of n} that is <=n.
- A161657 (program): a(n) = the smallest multiple of {the sum of the distinct prime divisors of n} that is >= n.
- A161658 (program): a(n) = the largest multiple of {the sum of the prime-factorization exponents of n} that is <= n.
- A161659 (program): a(n) = the smallest multiple of {the sum of the prime-factorization exponents of n} that is >= n.
- A161662 (program): Number of reduced words of length n in the Weyl group A_41.
- A161663 (program): Number of reduced words of length n in the Weyl group A_42.
- A161664 (program): a(n) = Sum_{i=1..n} (i - d(i)), where d(n) is the number of divisors of n (A000005).
- A161668 (program): Number of reduced words of length n in the Weyl group A_43.
- A161671 (program): a(n) = prime(n) - A141468(n).
- A161673 (program): Positions n such that A010060(n) + A010060(n+8) = 1.
- A161674 (program): Positions n such that A010060(n) + A010060(n+2) = 1.
- A161679 (program): Number of reduced words of length n in the Weyl group A_44.
- A161680 (program): a(n) = binomial(n,2): number of size-2 subsets of {0,1,…,n} that contain no consecutive integers.
- A161690 (program): Number of reduced words of length n in the Weyl group A_45.
- A161691 (program): Number of reduced words of length n in the Weyl group A_46.
- A161692 (program): Number of reduced words of length n in the Weyl group A_47.
- A161693 (program): Number of reduced words of length n in the Weyl group A_48.
- A161694 (program): Number of reduced words of length n in the Weyl group A_49.
- A161695 (program): Number of reduced words of length n in the Weyl group A_50.
- A161696 (program): Number of reduced words of length n in the Weyl group B_3.
- A161701 (program): a(n) = (n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120.
- A161702 (program): a(n) = (-n^3 + 9n^2 - 5n + 3)/3.
- A161703 (program): a(n) = (4*n^3 - 12*n^2 + 14*n + 3)/3.
- A161704 (program): a(n) = (3*n^5 - 35*n^4 + 145*n^3 - 235*n^2 + 152*n + 30)/30.
- A161705 (program): a(n) = 18*n + 1.
- A161707 (program): a(n) = (4*n^3 - 9*n^2 + 11*n + 3)/3.
- A161708 (program): a(n) = -n^3 + 7*n^2 - 5*n + 1.
- A161709 (program): a(n) = 22*n + 1.
- A161711 (program): a(n) = (-4*n^3 + 27*n^2 - 20*n + 3)/3.
- A161712 (program): a(n) = (4*n^3 - 6*n^2 + 8*n + 3)/3.
- A161713 (program): a(n) = (-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40.
- A161714 (program): a(n) = 28*n + 1.
- A161718 (program): Expansion of (1+3*x^2)/(1+x)^2.
- A161720 (program): a(n) = (prime(n) - 7)/2.
- A161722 (program): Generalized Bernoulli numbers B_n(X,0), X a Dirichlet character modulus 8.
- A161726 (program): a(n) = n^2 - 917*n + 9479.
- A161727 (program): a(n) = ((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).
- A161728 (program): a(n) = ((3+sqrt(3))*(4+sqrt(3))^n-(3-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).
- A161729 (program): a(n) = ((4+sqrt(3))*(8+2*sqrt(3))^n-(4-sqrt(3))*(8-2*sqrt(3))^n)/(2*sqrt(3)).
- A161731 (program): Expansion of (1-3*x)/(1-8*x+14*x^2).
- A161734 (program): a(n) = ((2+sqrt(2))*(5+sqrt(2))^n+(2-sqrt(2))*(5-sqrt(2))^n)/4.
- A161736 (program): Denominators of the column sums of the BG2 matrix.
- A161737 (program): Numerators of the column sums of the BG2 matrix.
- A161738 (program): Sequence related to the column sums of the BG2 matrix
- A161744 (program): The subfactorial with index prime(n).
- A161745 (program): The subfactorial with index Fibonacci(n).
- A161750 (program): Numbers n such that the decimal digits of 123456789*n are all distinct.
- A161753 (program): Squares of nonprime numbers A141468.
- A161756 (program): The sum of all numbers from n up to A002808(n)-3.
- A161757 (program): a(n) = (prime(n))^2 - (nonprime(n))^2.
- A161758 (program): a(n)=n-p+1 where p is the maximal prime less than n-2.
- A161762 (program): Sum of all numbers from Fibonacci(n-1) to Fibonacci(n).
- A161763 (program): Product of the two primes with indices equal to the members of the n-th twin prime pair.
- A161764 (program): a(n) is the largest multiple of {the number of 1’s in the binary representation of n} that is <= n.
- A161765 (program): a(n) is the smallest multiple of {the number of 1’s in the binary representation of n} that is >= n.
- A161769 (program): A positive integer n is included if the greatest common divisor of (the sum of the distinct primes dividing n) and (the sum of the exponents in the prime-factorization of n) is > 1.
- A161770 (program): n 1’s followed by three 0’s.
- A161777 (program): n-th nonprime*(n-th nonprime-1)/2
- A161784 (program): Product of primes on successive square intervals.
- A161788 (program): a(n) is the largest integer of the form 2^k - 1 that divides n.
- A161789 (program): a(n) is the largest integer k such that 2^k - 1 divides n.
- A161790 (program): The positive integer n is included if 1 is the largest integer of the form {2^k - 1} to divide n.
- A161797 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^3).
- A161798 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^3)^2.
- A161799 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^2)^3.
- A161809 (program): G.f.: A(x) = exp( Sum_{n>=1} 3*A038500(n) * x^n/n ), where A038500 is the highest power of 3 dividing n.
- A161811 (program): Difference between nonprime(n+2) and nonprime(n).
- A161816 (program): Denominator of fraction in Redheffer type matrix.
- A161823 (program): Among any n lines on the plane, there exists a pair at an angle not more than a(n)degrees.
- A161824 (program): Numbers such that A010060(n) = A010060(n+6).
- A161825 (program): a(n) is the GCD of n and {the number made by reversing the order of the digits of n written in binary}.
- A161826 (program): Number of maximal vertex-independent sets in the hypergraph with nodes V = {1, 2, …, n} and “edges” consisting of the triples (X,Y,Z) with X<Y<Z and X+Y=Z.
- A161827 (program): Complement of A006446.
- A161828 (program): Number of rhombuses in the Y-toothpick structure of A160120 after n rounds.
- A161830 (program): Y-toothpick triangle (see Comments lines for definition).
- A161831 (program): First differences of A161830.
- A161832 (program): a(n) = (A161830(n+1)-1)/2.
- A161833 (program): First differences of A161832.
- A161834 (program): a(n) = A161828(n)/3.
- A161835 (program): Numbers k whose largest divisor <= sqrt(k) is 5.
- A161836 (program): Number of concave-convex hexagons in the Y-toothpick structure of A160120 after n rounds.
- A161838 (program): a(n) = A161836(n)/3.
- A161839 (program): a(n) = A161835(n)/5.
- A161840 (program): Number of noncentral divisors of n.
- A161841 (program): Number of factors, with repetition, in all distinct pairs (a <= b) such that a*b = n.
- A161842 (program): Partial sums of A161841.
- A161843 (program): a(n) = n-th composite plus n-th nonprime.
- A161844 (program): Product of the n-th composite by the n-th nonprime.
- A161845 (program): a(n) = A002808(n)^A141468(n).
- A161847 (program): Denominator of the ratio (prime((n+1)^2) - prime(n^2))/prime(n).
- A161849 (program): a(n) = A052369(n) mod A056608(n).
- A161850 (program): Subsequence of A161986 consisting of all terms that are prime.
- A161852 (program): Solutions to the simultaneous equations m(n)+1=a(n)^2 and 7*m(n)+1=b(n)^2.
- A161859 (program): Number of reduced words of length n in the Weyl group B_13.
- A161862 (program): Number of reduced words of length n in the Weyl group B_14.
- A161865 (program): Numerators of ratio of nonprimes in a square interval to that of nonprimes in that interval and its successor.
- A161867 (program): Denominators of ratio of nonprimes in a square interval to that of nonprimes in that interval and its successor.
- A161870 (program): Convolution square of A000219.
- A161877 (program): Number of reduced words of length n in the Weyl group B_17.
- A161878 (program): Number of reduced words of length n in the Weyl group B_18.
- A161879 (program): Number of reduced words of length n in the Weyl group B_19.
- A161880 (program): Number of reduced words of length n in the Weyl group B_20.
- A161882 (program): Smallest k such that n^2 = a_1^2+…+a_k^2 and all a_i are positive integers less than n.
- A161886 (program): Number of nonzero elements in the n X n Redheffer matrix.
- A161891 (program): Primes p with the property that every non-solvable transitive permutation group of degree p is alternating or symmetric.
- A161899 (program): Number of reduced words of length n in the Weyl group B_21.
- A161900 (program): Number of reduced words of length n in the Weyl group B_22.
- A161903 (program): Convert n into a sequence of binary digits, apply one step of the rule 110 cellular automaton, and interpret the results as a binary integer.
- A161907 (program): Primes of the form n^3+n+91.
- A161909 (program): Inverse binomial transform of A181586.
- A161910 (program): Y-toothpick sequence starting at the corner of an infinite hexagon from which protrudes a half toothpick with an angle = Pi/6.
- A161911 (program): a(n) is the n-th difference between consecutive primes minus the number of divisors of n.
- A161912 (program): a(n) = A040976(n+1) - A006218(n).
- A161913 (program): Numbers k such that A001223(k) <> A000005(k).
- A161916 (program): The smallest k such that A010060(n+k)=A010060(n).
- A161918 (program): Numbers n such that the sum of the divisors minus the sum of the prime factors (counted with multiplicity) is equal to n+1.
- A161920 (program): a(n) = A161511(A004760(n)).
- A161921 (program): The bisection A053445(2n+1).
- A161930 (program): Number of reduced words of length n in the Weyl group B_23.
- A161931 (program): Number of reduced words of length n in the Weyl group B_24.
- A161932 (program): Number of reduced words of length n in the Weyl group B_25.
- A161933 (program): Number of reduced words of length n in the Weyl group B_26.
- A161935 (program): 28-gonal numbers: a(n) = n*(13*n - 12).
- A161936 (program): The number of direct isometries that are derangements of the (n-1)-dimensional facets of an n-cube.
- A161937 (program): The number of indirect isometries that are derangements of the (n-1)-dimensional facets of an n-cube.
- A161938 (program): a(n) = ((3+sqrt(2))*(2+sqrt(2))^n + (3-sqrt(2))*(2-sqrt(2))^n)/2.
- A161939 (program): a(n) = ((3+sqrt(2))*(4+sqrt(2))^n + (3-sqrt(2))*(4-sqrt(2))^n)/2.
- A161940 (program): a(n) = ((3+sqrt(2))*(5+sqrt(2))^n + (3-sqrt(2))*(5-sqrt(2))^n)/2.
- A161941 (program): a(n) = ((4+sqrt(2))*(2+sqrt(2))^n + (4-sqrt(2))*(2-sqrt(2))^n)/4.
- A161942 (program): Odd part of sum of divisors of n.
- A161944 (program): a(n) = ((4+sqrt(2))*(3+sqrt(2))^n + (4-sqrt(2))*(3-sqrt(2))^n)/4.
- A161945 (program): Numbers n with property that three consecutive odd numbers {n,n+2,n+4} are all composite.
- A161946 (program): Odd part of sum of unitary divisors of n.
- A161947 (program): a(n) = ((4+sqrt(2))*(5+sqrt(2))^n + (4-sqrt(2))*(5-sqrt(2))^n)/4.
- A161954 (program): Number of reduced words of length n in the Weyl group B_27.
- A161956 (program): Number of reduced words of length n in the Weyl group B_28.
- A161964 (program): Prime(n) raised to the nonprime(n)-th power.
- A161969 (program): Expansion of f(q)^8 in powers of q where f() is a Ramanujan theta function.
- A161972 (program): Number of reduced words of length n in the Weyl group B_29.
- A161976 (program): Number of reduced words of length n in the Weyl group B_30.
- A161977 (program): Number of reduced words of length n in the Weyl group B_31.
- A161983 (program): Irregular triangle read by rows: the group of 2n + 1 integers starting at A014105(n).
- A161984 (program): Table read by rows: the number n followed by the odd numbers from n(n-1)+1 to (n-1)(n+2)+1.
- A161986 (program): a(n) = k+r where k is composite(n) and r is (largest prime divisor of k) mod (smallest prime divisor of k).
- A161987 (program): Number of reduced words of length n in the Weyl group B_32.
- A161988 (program): Number of reduced words of length n in the Weyl group B_33.
- A161989 (program): Numbers having more than 2 or fewer than 2 ones in their binary representation.
- A161991 (program): Number of reduced words of length n in the Weyl group B_34.
- A161992 (program): Numbers which squared are a sum of 3 distinct nonzero squares.
- A161996 (program): A (negated) characteristic function of twin composite odd numbers.
- A161999 (program): For n even a(n) = a(n-1) + 10*a(n-2), for n odd a(n) = a(n-3) + 10 a(n-2); with a(1) = 0, a(2) = 1.
- A162004 (program): Primes of the form n+(n+3)^3, n>=0.
- A162022 (program): Smallest prime factor of n-th odd composite integers A071904.
- A162023 (program): Exactly 10 consecutive odd integers starting with n are composite.
- A162024 (program): Number of n X n binary arrays with rows and columns, considered as binary numbers, in nondecreasing order, and all but the outermost row or column zero.
- A162142 (program): Numbers that are the cube of a product of two distinct primes (p^3*q^3).
- A162143 (program): a(n) = A007304(n)^2.
- A162144 (program): Products of cubes of 3 distinct primes.
- A162147 (program): a(n) = n*(n+1)*(5*n + 4)/6.
- A162148 (program): a(n) = n*(n+1)*(5*n+7)/6.
- A162149 (program): Number of reduced words of length n in the Weyl group B_35.
- A162150 (program): Number of reduced words of length n in the Weyl group B_36.
- A162153 (program): Differences between the sum of consecutive composites and the prime that precedes them.
- A162154 (program): Odd-indexed terms are the number of consecutive prime numbers until a composite, even-indexed terms are the number of consecutive composite numbers until a prime.
- A162165 (program): Number of reduced words of length n in the Weyl group B_37.
- A162166 (program): Number of reduced words of length n in the Weyl group B_38.
- A162168 (program): Number of reduced words of length n in the Weyl group B_39.
- A162169 (program): Exponential series expansion of (cos(x) - sin(x))*cosh(t*x) + sinh(t*x).
- A162171 (program): Third column of A162170.
- A162176 (program): Number of reduced words of length n in the Weyl group B_40.
- A162177 (program): a(n) is the number of composite numbers that are smaller than A008578(n).
- A162178 (program): Number of reduced words of length n in the Weyl group B_41.
- A162179 (program): Number of reduced words of length n in the Weyl group B_42.
- A162181 (program): Number of reduced words of length n in the Weyl group B_43.
- A162182 (program): Number of reduced words of length n in the Weyl group B_44.
- A162183 (program): Number of reduced words of length n in the Weyl group B_45.
- A162186 (program): Number of reduced words of length n in the Weyl group B_46.
- A162188 (program): Numbers k such that A001223(k) > A000005(k).
- A162189 (program): Numbers k such that A001223(k) < A000005(k).
- A162191 (program): Number of reduced words of length n in the Weyl group B_47.
- A162193 (program): Number of reduced words of length n in the Weyl group B_48.
- A162194 (program): Sum of divisors of nonprime number A018252(n).
- A162195 (program): Sum of proper divisors of n-th nonprime number A018252(n).
- A162196 (program): Sum of proper divisors minus the number of proper divisors of nonprime number A018252(n).
- A162200 (program): Number on the positive y axis of the n-th horizontal component in the graph of the “mountain path” function for prime numbers.
- A162201 (program): First differences of A162200.
- A162204 (program): Number of reduced words of length n in the Weyl group B_49.
- A162205 (program): Number of reduced words of length n in the Weyl group B_50.
- A162213 (program): a(n) = the smallest positive multiple of n with exactly n digits when written in binary.
- A162214 (program): a(n) = the largest positive multiple of n with exactly n digits when written in binary.
- A162245 (program): Triangle T(n,m) = 6*m*n + 3*m + 3*n + 1 read by rows.
- A162246 (program): Swinging polynomials, coefficients read by rows.
- A162251 (program): Sum of digits of product of previous terms, with a(1) = 2.
- A162254 (program): a(n) = (2*n^3 + 5*n^2 + n)/2.
- A162255 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 2.
- A162256 (program): a(n) = (2*n^3 + 5*n^2 - 3*n)/2.
- A162257 (program): a(n) = (2*n^3 + 5*n^2 - 11*n)/2.
- A162258 (program): a(n) = (2*n^3 + 5*n^2 - 9*n)/2.
- A162259 (program): a(n) = (2*n^3 + 5*n^2 - 17*n)/2.
- A162260 (program): a(n) = (n^3 + 4*n^2 - n)/2.
- A162261 (program): a(n) = (2*n^3 + 5*n^2 - 7*n)/2.
- A162262 (program): a(n) = (2*n^3 + 5*n^2 - 13*n)/2.
- A162263 (program): a(n) = (2*n^3 + 5*n^2 + 11*n)/2.
- A162264 (program): a(n) = (2*n^3 + 5*n^2 + 7*n)/2.
- A162265 (program): a(n) = (2*n^3 + 5*n^2 - 5*n)/2.
- A162266 (program): a(n) = (2*n^3 + 5*n^2 + 21*n)/2.
- A162267 (program): a(n) = (2*n^3 + 5*n^2 + 5*n)/2.
- A162268 (program): a(n) = ((5+sqrt(2))*(1+sqrt(2))^n + (5-sqrt(2))*(1-sqrt(2))^n)/2.
- A162269 (program): a(n) = ((5+sqrt(2))*(2+sqrt(2))^n + (5-sqrt(2))*(2-sqrt(2))^n)/2.
- A162270 (program): a(n) = ((5+sqrt(2))*(3+sqrt(2))^n + (5-sqrt(2))*(3-sqrt(2))^n)/2.
- A162271 (program): a(n) = ((5+sqrt(2))*(4+sqrt(2))^n + (5-sqrt(2))*(4-sqrt(2))^n)/2.
- A162272 (program): a(n) = ((1+sqrt(3))*(5+sqrt(3))^n + (1-sqrt(3))*(5-sqrt(3))^n)/2.
- A162273 (program): a(n) = ((2+sqrt(3))*(3+sqrt(3))^n + (2-sqrt(3))*(3-sqrt(3))^n)/2.
- A162274 (program): a(n) = ((2+sqrt(3))*(4+sqrt(3))^n + (2-sqrt(3))*(4-sqrt(3))^n)/2.
- A162275 (program): a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 2, a(1) = 13.
- A162285 (program): Periodic length 8 sequence [1, -1, -1, 1, -1, 1, 1, -1, …].
- A162289 (program): a(n) = 1 if n is relatively prime to 30 else 0.
- A162291 (program): Primes of the form n^3-n^2-1.
- A162292 (program): Primes of the form k^3-k^2+1, k>0.
- A162293 (program): Numbers k such that k^2*(k-1)-1 is prime.
- A162294 (program): Numbers k such that k^3-k^2-k-1 is prime.
- A162295 (program): Primes of the form k^3-k^2-k-1.
- A162296 (program): Sum of divisors of n that have a square factor.
- A162307 (program): Primes of the form k*(k+2)/3 - 2, k > 0.
- A162308 (program): Number of twin primes A001097 smaller than the non-twin prime A007510(n).
- A162309 (program): a(n) is the number of isolated primes up to the smaller component of the n-th twin prime pair.
- A162310 (program): The count of lesser-twin-primes smaller than the n-th isolated prime.
- A162312 (program): Triangular array, inverse of 2*P - I, where P is Pascal’s triangle and I is the identity matrix.
- A162313 (program): Triangular array P*(2*I - P^2)^-1, where P is Pascal’s triangle A007318 and I is the identity matrix.
- A162314 (program): Row sums of A162313.
- A162315 (program): Triangular array 2*P - P^-1, where P is Pascal’s triangle A007318.
- A162316 (program): a(n) = 5n^2 + 20n + 1.
- A162317 (program): A positive integer k is included if |d(k+1) - d(k)| is a prime, where d(k) is the number of divisors of k.
- A162318 (program): A positive integer n is included if |d(n+1)-d(n)| = 2, where d(n) is the number of divisors of n.
- A162319 (program): Array read by antidiagonals: a(n,m) = the number of digits of m is when written in base n. The top row is the number of digits for each m in base 1.
- A162320 (program): Array read by antidiagonals: a(n,m) = the number of digits of m when written in base n. The top row is the number of digits for each m in base 2.
- A162322 (program): Take sequence A000005 (where A000005(n) = the number of divisors of n). To get {a(k)}, replace each run of multiple occurrences of the same integer in sequence A000005 with just one occurrence of that integer, such that a(n) never equals a(n+1).
- A162325 (program): a(n) = the largest divisor of n such that this and every smaller divisor of n are all coprime to each other.
- A162326 (program): Let a(0) = a(1) = 1, and n*a(n) = 2*(-7+5*n)*a(n-1) + 9*(2-n)*a(n-2) for n >= 2.
- A162329 (program): Sum of all parts of the partitions of n, minus sigma(n).
- A162330 (program): Blocks of 4 numbers of the form 2k, 2k-1, 2k, 2k+1, k=1,2,3,4,…
- A162336 (program): Primes p of the form p = r+(r+1)/2 (where r is a prime number).
- A162337 (program): Primes p such that floor(p/3) is prime.
- A162338 (program): Primes q such that q = floor(p/3) for some prime p.
- A162339 (program): Numbers A161912 such that a(n)<>a(n+1).
- A162340 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton whose virtual skeleton is a polyedge as the graph of the “mountain path” function for prime numbers.
- A162341 (program): a(n) = number of grid points P(x,y) that are covered by a polyedge as the graph of the “mountain path” function for prime numbers, where x=n and y=0..oo.
- A162342 (program): Partial sums of A162200.
- A162345 (program): Length of n-th edge in the graph of the zig-zag function for prime numbers.
- A162349 (program): First differences of A160412.
- A162351 (program): Values x of pairs (x,y) that generate the graph of the “mountain path” function for prime numbers.
- A162356 (program): a(n) = 8*a(n-1)-14*a(n-2) for n>1; a(0) = 2; a(1) = 9.
- A162361 (program): Central prime factor of A014612(n).
- A162364 (program): Number of reduced words of length n in the Weyl group D_22.
- A162365 (program): Number of reduced words of length n in the Weyl group D_23.
- A162366 (program): Number of reduced words of length n in the Weyl group D_24.
- A162367 (program): Number of reduced words of length n in the Weyl group D_25.
- A162368 (program): Number of reduced words of length n in the Weyl group D_26.
- A162369 (program): Number of reduced words of length n in the Weyl group D_27.
- A162370 (program): Number of reduced words of length n in the Weyl group D_28.
- A162376 (program): Number of reduced words of length n in the Weyl group D_29.
- A162377 (program): Number of reduced words of length n in the Weyl group D_30.
- A162378 (program): Number of reduced words of length n in the Weyl group D_31.
- A162379 (program): Number of reduced words of length n in the Weyl group D_32.
- A162380 (program): Number of reduced words of length n in the Weyl group D_33.
- A162381 (program): Number of reduced words of length n in the Weyl group D_34.
- A162382 (program): Triangle, read by rows, defined by: T(n,k) = 1/((k+1)n-1) binomial((k+1)n-1,n) for n,k>0.
- A162384 (program): Number of reduced words of length n in the Weyl group D_35.
- A162388 (program): Number of reduced words of length n in the Weyl group D_36.
- A162389 (program): Number of reduced words of length n in the Weyl group D_37.
- A162392 (program): Number of reduced words of length n in the Weyl group D_38.
- A162395 (program): a(n) = -(-1)^n * n^2.
- A162396 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 2.
- A162397 (program): a(n) = n * Kronecker(-3, n).
- A162399 (program): Number of reduced words of length n in the Weyl group D_39.
- A162402 (program): Number of reduced words of length n in the Weyl group D_40.
- A162410 (program): Numbers n such that 10*n + 3 and 10*n + 7 are prime.
- A162411 (program): Number of reduced words of length n in the Weyl group D_42.
- A162412 (program): Number of reduced words of length n in the Weyl group D_43.
- A162413 (program): Number of reduced words of length n in the Weyl group D_44.
- A162415 (program): L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} x^(2^n-1) ).
- A162417 (program): Find max {primes such that p < n^2, n = 2,3,…}, then the gap g(n) between that prime and its successor. This sequence is the sequence of differences {2n - g(n)}.
- A162418 (program): Number of reduced words of length n in the Weyl group D_45.
- A162419 (program): a(n) = sigma(n)*|A002129(n)| where sigma(n) = A000203(n).
- A162420 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*|A002129(n)|*x^n/n ).
- A162421 (program): Numbers whose prime factors all have the same number of digits.
- A162422 (program): Numbers with at least 2 different numbers of digits among their prime factors.
- A162425 (program): Row 2 of table A162424.
- A162431 (program): Row 2 of table A162430.
- A162432 (program): Row 3 of table A162430.
- A162433 (program): Row 4 of table A162430.
- A162436 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 3.
- A162437 (program): a(1)=1, a(2)=2. Take terms a(n-1) and a(n-2), then convert to binary. Concatenate them, with either binary a(n-1) on the left and a(n-2) on the right, or with a(n-1) on the right and a(n-2) on the left such that the value of the resulting binary number is minimized. a(n) = the decimal equivalent of the resulting binary number.
- A162438 (program): a(1)=1, a(2)=2. Take terms a(n-1) and a(n-2), then convert to binary. Concatenate them, with either binary a(n-1) on the left and a(n-2) on the right, or with a(n-1) on the right and a(n-2) on the left such that the value of the resulting binary number is maximized. a(n) = the decimal equivalent of the resulting binary number.
- A162439 (program): Write down the binary representation of n. Partition the string which is this binary representation by placing a ‘+’ just left of every 1. Add the resulting base 2 numbers. a(n) = decimal equivalent of this sum.
- A162440 (program): The pg(n) sequence that is associated with the Eta triangle A160464.
- A162441 (program): Numerators of the column sums of the EG1 matrix coefficients
- A162442 (program): Denominators of the column sums of the EG1 matrix coefficients
- A162445 (program): A sequence related to the Beta function
- A162452 (program): Number of reduced words of length n in the Weyl group D_46.
- A162456 (program): Number of reduced words of length n in the Weyl group D_47.
- A162459 (program): A002321*A000079.
- A162460 (program): First differences of A161762.
- A162461 (program): Number of reduced words of length n in the Weyl group D_48.
- A162462 (program): Sum of all numbers from n to sigma(n).
- A162466 (program): a(n) = 12*a(n-2) for n > 2; a(1) = 1, a(2) = 8.
- A162469 (program): Number of reduced words of length n in the Weyl group D_49.
- A162473 (program): Write n in binary n times and concatenate (see example). a(n) is the decimal equivalent.
- A162475 (program): Expansion of c(x/(1-x)^4), c(x) the g.f. of A000108.
- A162476 (program): Expansion of (1/(1-x))*c(x/(1-x)^4), c(x) the g.f. of A000108.
- A162477 (program): Expansion of (1/(1-x)^2)*c(x/(1-x)^4), c(x) the g.f. of A000108.
- A162478 (program): Expansion of 1/sqrt(1-4x/(1-x)^4).
- A162479 (program): Expansion of 1/((1-x)*sqrt(1-4x/(1-x)^4)).
- A162480 (program): Expansion of 1/((1-x)^2*sqrt(1-4x/(1-x)^4)).
- A162481 (program): Expansion of (1/(1-x)^3)*c(x/(1-x)^3), c(x) the g.f. of A000108.
- A162483 (program): a(n) is the number of perfect matchings of an edge-labeled 2 X (2n+1) Mobius grid graph.
- A162484 (program): a(1) = 2, a(2) = 8; a(n) = 2 a(n - 1) + a(n - 2) - 4*(n mod 2).
- A162485 (program): a(1)=4, a(2)=6; for n > 2, a(n) = 2*a(n-1) + a(n-2) - 4*((n-1) mod 2).
- A162492 (program): Number of reduced words of length n in the Weyl group D_50.
- A162495 (program): Number of reduced words of length n in the icosahedral reflection group [3,5] of order 120.
- A162500 (program): Expansion of the polynomial (1-x^3) * (1-x^6) * (1-x^9) / (1-x)^3.
- A162508 (program): A binomial sum of powers related to the Bernoulli numbers, triangular array, read by rows.
- A162509 (program): Row sums of the absolute values of a triangular array related to the Bernoulli numbers.
- A162510 (program): Dirichlet inverse of A076479.
- A162511 (program): Multiplicative function with a(p^e) = (-1)^(e-1).
- A162512 (program): Dirichlet inverse of A162511.
- A162514 (program): Triangle of coefficients of polynomials defined by the Binet form P(n,x) = U^n + L^n, where U = (x + d)/2, L = (x - d)/2, d = (4 + x^2)^(1/2). Decreasing powers of x.
- A162515 (program): Triangle of coefficients of polynomials defined by Binet form: P(n,x) = (U^n - L^n)/d, where U = (x + d)/2, L = (x - d)/2, d = sqrt(x^2 + 4).
- A162520 (program): Pairs (i,j) of positive integers where j<10.
- A162526 (program): Numbers k whose largest divisor <= sqrt(k) equals 6.
- A162527 (program): Numbers k whose largest divisor <= sqrt(k) equals 7.
- A162528 (program): Numbers k whose largest divisor <= sqrt(k) equals 8.
- A162529 (program): Numbers k whose largest divisor <= sqrt(k) equals 9.
- A162530 (program): Numbers k whose largest divisor <= sqrt(k) equals 10.
- A162531 (program): Numbers k whose largest divisor <= sqrt(k) is 11.
- A162532 (program): Numbers k such that their largest divisor <= sqrt(k) equals 12.
- A162533 (program): a(n) = Sum_{k=0..n} binomial(n,2k)*A002426(k).
- A162535 (program): A positive integer k is included if every length of the runs of 0’s and 1’s in the binary representation of k is coprime to k.
- A162540 (program): a(n) = (2*n+1)*(2*n+3)*(2*n+5)/3.
- A162547 (program): Somos-4 variant: if n!=4k+1, then a(n) = (4*a(n-1)*a(n-3) - 4*a(n-2)^2) / a(n-4), otherwise a(n) = 0, with a(-2) = a(-1) = a(0) = 1.
- A162550 (program): 2n repeated C_n times, where C_n = A000108(n) is a Catalan number.
- A162551 (program): a(n) = 2 * C(2*n,n-1).
- A162552 (program): L.g.f.: log( Sum_{n>=1} x^(n^2) ), the log of the characteristic function of the squares.
- A162557 (program): a(n) = ((3+sqrt(3))*(4+sqrt(3))^n+(3-sqrt(3))*(4-sqrt(3))^n)/6.
- A162558 (program): a(n) = ((3+sqrt(3))*(5+sqrt(3))^n + (3-sqrt(3))*(5-sqrt(3))^n)/6.
- A162559 (program): a(n) = ((4+sqrt(3))*(1+sqrt(3))^n + (4-sqrt(3))*(1-sqrt(3))^n)/2.
- A162560 (program): a(n) = (4+sqrt(3))*(3+sqrt(3))^n + (4-sqrt(3))*(3-sqrt(3))^n.
- A162561 (program): a(n) = ((4+sqrt(3))*(5+sqrt(3))^nv+v(4-sqrt(3))*(5-sqrt(3))^n)/2.
- A162562 (program): a(n) = ((5+sqrt(3))*(1+sqrt(3))^n + (5-sqrt(3))*(1-sqrt(3))^n)/2.
- A162563 (program): a(n) = ((5+sqrt(3))*(2+sqrt(3))^n + (5-sqrt(3))*(2-sqrt(3))^n)/2.
- A162581 (program): G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^2 * x^n/n ), where A006519(n) = highest power of 2 dividing n.
- A162589 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^n*A006519(n) * x^n/n ), where A006519(n) = highest power of 2 dividing n.
- A162590 (program): Polynomials with e.g.f. exp(x*t)/csch(t), triangle of coefficients read by rows.
- A162593 (program): Differences of squares: T(n,n) = n^2, T(n,k) = T(n,k+1) - T(n-1,k), 0 <= k < n, triangle read by rows.
- A162594 (program): Differences of cubes: T(n,n) = n^3, T(n,k) = T(n,k+1) - T(n-1,k), 0 <= k < n, triangle read by rows.
- A162607 (program): a(n) = n*(n^2 - 4*n + 5)/2.
- A162608 (program): Triangle read by rows in which row n lists n+1 terms, starting with n!, such that the difference between successive terms is also equal to n!.
- A162609 (program): Triangle read by rows in which row n lists n terms, starting with 1, with gaps = n-2 between successive terms.
- A162610 (program): Triangle read by rows in which row n lists n terms, starting with 2n-1, with gaps = n-1 between successive terms.
- A162611 (program): Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^2 - 1.
- A162612 (program): Triangle read by rows in which row n lists n terms, starting with n^2+n-1, with gaps = n^2-1 between successive terms.
- A162613 (program): Triangle read by rows in which row n lists n terms, starting with n, with gaps = n^2-1 between successive terms.
- A162614 (program): Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^3 - 1.
- A162615 (program): Triangle read by rows in which row n lists n terms, starting with n, such that the difference between successive terms is equal to n^3 - 1 = A068601(n).
- A162616 (program): Triangle read by rows in which row n lists n terms, starting with n^3 + n - 1, such that the difference between successive terms is equal to n^3 - 1 = A068601(n).
- A162618 (program): Triangle read by rows in which row n lists n consecutive natural numbers A000027, starting with A008578(n-1) - n + 1.
- A162619 (program): Triangle read by rows in which row n lists n consecutive natural numbers A000027, starting with A014689(n) = A000040(n)-n.
- A162620 (program): Triangle read by rows in which row n lists n consecutive natural numbers A000027, starting with A000040(n)-n+1.
- A162622 (program): Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^4 - 1.
- A162623 (program): Triangle read by rows in which row n lists n terms, starting with n, such that the difference between successive terms is equal to n^4 - 1 = A123865(n).
- A162624 (program): Triangle read by rows in which row n lists n terms, starting with n^4 + n - 1, such that the difference between successive terms is equal to n^4 - 1 = A123865(n).
- A162626 (program): If 0 <= n <= 3 then a(n) = n(n+1)(n+2)/3, if n >= 4 then a(n) = n(n^2+5)/3.
- A162630 (program): Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.
- A162641 (program): Number of even exponents in canonical prime factorization of n.
- A162642 (program): Number of odd exponents in the canonical prime factorization of n.
- A162643 (program): Numbers whose number of divisors is not a power of 2.
- A162644 (program): Numbers m such that A162511(m) = +1.
- A162645 (program): Numbers m such that A162511(m) = -1.
- A162648 (program): Locations of patterns 1001 or 0110 in the Thue-Morse sequence A010060.
- A162652 (program): Primes p such that there are positive integers m and n and a prime q such that p = m^2+m-q = n^2+n+q.
- A162660 (program): Triangle read by rows, the coefficients of the complementary Swiss-Knife polynomials.
- A162664 (program): a(n) = sigma(n) + tau(n)^2.
- A162666 (program): a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A162667 (program): a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A162668 (program): a(n) = n*(n+1)*(n+2)*(n+3)/3.
- A162669 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5.
- A162670 (program): Expansion of x/(1 - x - 100*x^2).
- A162671 (program): Generalized Fibonacci numbers
- A162672 (program): Lunar product 19*n.
- A162673 (program): Number of different fixed (possibly) disconnected trominoes bounded (not necessarily tightly) by an n*n square
- A162674 (program): Number of different fixed (possibly) disconnected tetrominoes bounded (not necessarily tightly) by an n X n square.
- A162677 (program): Number of different fixed (possibly) disconnected polyominoes (of any area) bounded (not necessarily tightly) by an n*n square.
- A162691 (program): Strictly positive numbers n such that 24*n/(24+n) is an integer.
- A162693 (program): Strictly positive numbers n such that 30*n/(30+n) are integers.
- A162694 (program): Strictly positive numbers n such that 36*n/(36+n) are integers.
- A162695 (program): E.g.f. satisfies: A(x) = exp( x*A(x) * exp(x*A(x)) ).
- A162698 (program): Numbers n such that the incidence matrix of the grid n X n has -1 as eigenvalue.
- A162699 (program): Odd numbers not divisible by 7.
- A162720 (program): A014499 represented in binary.
- A162723 (program): a(n) = 9 a (n-1)-26 a(n-2) +24 a(n-3) (n >= 3) with a(0) =a(1)=1, a(2)=2.
- A162725 (program): a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) (n >= 3) with a(0) = a(1) = 1, a(2) = 2.
- A162728 (program): G.f.: x/(1-x) = Sum_{n>=1} a(n)*log(1+x^n)/n.
- A162729 (program): a(n) = 5^n*(5^n-1)/2.
- A162731 (program): a(n) is the n-th triprime (A014612) minus its central prime factor.
- A162734 (program): An alternating sum of all numbers from the n-th up to the (n+1)st isolated prime.
- A162735 (program): An alternating sum of all numbers from prime(n) to prime(n+1).
- A162738 (program): a(n) is the smallest positive multiple of {the n-th composite} that is greater than the n-th prime.
- A162740 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
- A162741 (program): Fibonacci-Pascal triangle; same as Pascal triangle, but beginning another Pascal triangle to the right of each row starting at row 2.
- A162746 (program): Row sums of Fibonacci-Pascal triangle A162745.
- A162747 (program): A factorial-Pascal matrix.
- A162748 (program): Row sums of factorial-Pascal matrix A162747.
- A162750 (program): The a(n)-th (odd) binary palindrome is A162749(n).
- A162751 (program): Write down in binary the n-th positive (odd) integer that is a palindrome in base 2. Take only the leftmost half of the digits (including the middle digit if there are an odd number of digits). a(n) is the decimal equivalent of the result.
- A162752 (program): a(1)=2^2. a(n) = the smallest p^q, p and q primes, that is > a(n-1), and where the base (p) of a(n) is the exponent (q) of a(n-1).
- A162753 (program): a(0)=a(1)=2; a(n) is the smallest prime such that a(n-1)^a(n) > a(n-2)^a(n-1).
- A162757 (program): a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
- A162758 (program): a(n) = 14*a(n-1)-46*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
- A162759 (program): a(n) = 16*a(n-1)-61*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
- A162761 (program): Minimal total number of floors an elevator must move to transport n people initially waiting at floors i = 1, …, n to their destination floors n-i+1 (= n, …, 1), when the elevator can hold at most one person at a time and starts at floor 1, and no passenger may get off the elevator before reaching his/her destination.
- A162762 (program): Minimal number of floors an elevator must move to transport n passengers initially waiting at floors i = 1, …, n to their destinations, floor n+1-i (= n, …, 1), if the elevator can transport at most C = 2 persons at a time and starts at floor 1, and no one may get off the elevator before reaching their destination.
- A162764 (program): Minimal total number of floors that an elevator must move to get n persons waiting, respectively, on floors i = 1, 2, …, n, to their destination floors n-i+1 (= n, n-1, …, 1), if the elevator can hold up to C = 4 persons at a time and starts at floor 1, and no passenger may get off the elevator before reaching his destination.
- A162766 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 4, a(2) = 3.
- A162769 (program): a(n) = ((1+sqrt(5))*(4+sqrt(5))^n + (1-sqrt(5))*(4-sqrt(5))^n)/2.
- A162770 (program): a(n) = ((2+sqrt(5))*(1+sqrt(5))^n + (2-sqrt(5))*(1-sqrt(5))^n)/2.
- A162771 (program): a(n) = ((2+sqrt(5))*(3+sqrt(5))^n + (2-sqrt(5))*(3-sqrt(5))^n)/2.
- A162772 (program): a(n) = ((2+sqrt(5))*(4+sqrt(5))^n + (2-sqrt(5))*(4-sqrt(5))^n)/2.
- A162773 (program): a(n) = ((2+sqrt(5))*(5+sqrt(5))^n + (2-sqrt(5))*(5-sqrt(5))^n)/2.
- A162775 (program): a(n) = A141042(n+1)/2.
- A162776 (program): a(n) = A161828(n)*2/3.
- A162777 (program): a(n) = A153003(n) - A153006(n).
- A162779 (program): Rows of A162777 when written as a triangle converge to this sequence.
- A162784 (program): a(n) = (A048883(n)+1)/2.
- A162786 (program): a(n) = A162526(n)/6.
- A162787 (program): a(n) = A162527(n)/7.
- A162788 (program): a(n) = A162528(n)/8.
- A162789 (program): a(n) = A162529(n)/9.
- A162790 (program): a(n) = A162530(n)/10.
- A162792 (program): a(n) = A162532(n)/12.
- A162793 (program): Number of toothpicks added to the toothpick structure A139250 at the n-th odd round.
- A162794 (program): Number of toothpicks added to the toothpick structure A139250 at the n-th even round.
- A162795 (program): Total number of toothpicks in the toothpick structure A139250 that are parallel to the initial toothpick, after n odd rounds.
- A162796 (program): Number of toothpicks in the toothpick structure A139250 that are orthogonal to the initial toothpick after n even rounds.
- A162797 (program): a(n) = difference between the number of toothpicks of A139250 that are orthogonal to the initial toothpick and the number of toothpicks that are parallel to the initial toothpick, after n even rounds.
- A162800 (program): a(n) = n-th grid point that is covered by the zig-zag function for prime numbers such that the grid point is a vertex in the graph of the function.
- A162801 (program): Bisection of A162800.
- A162802 (program): Bisection of A162800.
- A162813 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 5, a(2) = 3.
- A162814 (program): a(n) = 6*a(n-1)-6*a(n-2) for n > 1; a(0) = 5, a(1) = 18.
- A162815 (program): a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 5, a(1) = 23.
- A162816 (program): a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
- A162817 (program): Positive numbers n such that 40*n/(40+n) are integers.
- A162818 (program): Strictly positive numbers n such that (42*n)/(42+n) is an integer.
- A162819 (program): Positive numbers n such that 48*n/(48+n) are integers.
- A162820 (program): Positive numbers n such that 60*n/(60+n) are integers.
- A162826 (program): Positive numbers n such that 2*60*n/(60+n) are integers.
- A162845 (program): Sum of digits of binomial(3n,n).
- A162852 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 3, a(2) = -1.
- A162857 (program): Primes of form 4p-1, p a prime.
- A162860 (program): Numbers k such that k^2+4*k+1 is prime.
- A162867 (program): a(n) is the sum of all possible pairs of the first n primes.
- A162880 (program): Numbers k such that tau(sigma(k)) is not equal to sigma(tau(k)).
- A162886 (program): Even numbers in an alternating 1-based sum up to some odd nonprime.
- A162888 (program): An alternating sum of the first n nonprimes.
- A162897 (program): a(1)=a(2)=2. a(n) = the smallest integer >= 2 such that a(n-1)^a(n) > a(n-2)^a(n-1).
- A162898 (program): a(n) = A162897(n)^A162897(n+1).
- A162899 (program): Partial sums of [A052938(n)^2].
- A162902 (program): An increasing sequence of alternatingly squarefree and nonsquarefree numbers.
- A162903 (program): a(n) = A162531(n)/11.
- A162904 (program): Primes 2 less than a tetrahedral number.
- A162905 (program): Primes of form p^2-6, p also a prime.
- A162906 (program): a(n) = n - A081707(n).
- A162907 (program): Sum of all numbers from tau(n) to sigma(n).
- A162909 (program): Numerators of Bird tree fractions.
- A162910 (program): Denominators of Bird tree fractions.
- A162911 (program): Numerators of drib tree fractions, where drib is the bit-reversal permutation tree of the Bird tree.
- A162912 (program): Denominators of drib tree fractions, where drib is the bit-reversal permutation tree of the Bird tree.
- A162917 (program): Numbers n which are not in A161983.
- A162918 (program): Natural numbers n such that there are s and w satisfying 0 < s < w and 2*s + 5*w = n.
- A162920 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
- A162921 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
- A162932 (program): a(n) = A053445(n-2) - A053445(n-4).
- A162934 (program): Shift sequence A162932 twice then subtract from the original sequence.
- A162938 (program): A 2-based alternate sum over the numbers from 0 to the n-th nonprime.
- A162939 (program): A 1-based alternate sum over the numbers from 0 to prime(n).
- A162940 (program): a(n) = binomial(n+1,2)*6^2.
- A162942 (program): a(n) = binomial(n + 1, 2)*7^2.
- A162943 (program): a(n) = 2^(1-A002321(n)).
- A162944 (program): A162943(A010766).
- A162947 (program): Numbers k such that the product of all divisors of k equals k^3.
- A162956 (program): a(0) = 0, a(1) = 1; a(2^i + j) = 3a(j) + a(j + 1) for 0 <= j < 2^i.
- A162959 (program): The pairs (x,y) such that (x^2 + y^2)/(x*y + 1) is a perfect square, i.e., 4.
- A162962 (program): a(n) = 5*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
- A162963 (program): a(n) = 5*a(n-2) for n > 2; a(1) = 2, a(2) = 5.
- A162964 (program): a(n) = sigma(sigma(sigma(sigma(sigma(n))))).
- A162966 (program): Union of 1 and nonsquarefree numbers (A013929).
- A162968 (program): Number of pairs of consecutive non-fixed points in all permutations of {1,2,…,n}.
- A162970 (program): Number of 2-cycles in all involutions of {1,2,…,n}.
- A162973 (program): Number of cycles in all derangement permutations of {1,2,…,n}.
- A162988 (program): n appears A008578(n) times.
- A162990 (program): Triangle of polynomial coefficients related to 3F2([1,n+1,n+1],[n+2,n+2],z).
- A162991 (program): The first right hand column of triangle A162990
- A162992 (program): The second right hand column of triangle A162990
- A162993 (program): The second left hand column of triangle A162990
- A162994 (program): The third left hand column of triangle A162990
- A162995 (program): A scaled version of triangle A162990.
- A163000 (program): Count of integers x in [0,n] satisfying A000120(x) + A000120(n-x) = A000120(n) + 1.
- A163037 (program): Number of nX2 binary arrays with all 1s connected and a path of 1s from left column to right column
- A163057 (program): An alternating sum from the n-th odd number up to the n-th odd prime.
- A163058 (program): Primes in A163057.
- A163059 (program): An alternating sum from 4*n-3 up to the smaller of the n-th twin primes.
- A163061 (program): Sum of the first n primes plus the first n nonprimes.
- A163062 (program): a(n) = ((3+sqrt(5))*(1+sqrt(5))^n + (3-sqrt(5))*(1-sqrt(5))^n)/2.
- A163063 (program): Lucas(3n+2) = Fibonacci(3n+1) + Fibonacci(3n+3).
- A163064 (program): a(n) = ((3+sqrt(5))*(4+sqrt(5))^n + (3-sqrt(5))*(4-sqrt(5))^n)/2.
- A163065 (program): a(n) = ((3+sqrt(5))*(5+sqrt(5))^n + (3-sqrt(5))*(5-sqrt(5))^n)/2.
- A163066 (program): a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 2, a(1) = 17.
- A163067 (program): a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 2, a(1) = 19.
- A163068 (program): a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 2, a(1) = 21.
- A163069 (program): a(n) = ((4+sqrt(5))*(1+sqrt(5))^n + (4-sqrt(5))*(1-sqrt(5))^n)/2.
- A163070 (program): a(n) = ((4+sqrt(5))*(2+sqrt(5))^n + (4-sqrt(5))*(2-sqrt(5))^n)/2.
- A163071 (program): a(n) = ((4+sqrt(5))*(3+sqrt(5))^n + (4-sqrt(5))*(3-sqrt(5))^n)/2.
- A163072 (program): a(n) = ((4+sqrt(5))*(5+sqrt(5))^n + (4-sqrt(5))*(5-sqrt(5))^n)/2.
- A163073 (program): a(n) = ((5+sqrt(5))*(4+sqrt(5))^n + (5-sqrt(5))*(4-sqrt(5))^n)/10.
- A163085 (program): Product of first n swinging factorials (A056040).
- A163086 (program): Product of first n terms of A163085.
- A163094 (program): a(n) = A162796(n)/2.
- A163095 (program): a(n) = A000788(n)^2.
- A163102 (program): a(n) = n^2*(n+1)^2/2.
- A163103 (program): Decimal expansion of the astronomical unit (measured in meters).
- A163105 (program): a(n) = tau(sigma(tau(n))), where tau = number of divisors of n (A000005), and sigma = sum of divisors of n (A000203).
- A163106 (program): a(n) = sigma(sigma(tau(n))), where tau = number of divisors and sigma = sum of divisors.
- A163107 (program): a(n) = tau(tau(sigma(n))), where tau = A000005, the number of divisors, and sigma = A000203, the sum of divisors of n.
- A163108 (program): a(n) = sigma(tau(sigma(n))).
- A163109 (program): a(n) = phi(tau(n)).
- A163114 (program): a(n) = 5*a(n-2) for n > 2; a(1) = 3, a(2) = 5.
- A163116 (program): Partial sums of A161671.
- A163125 (program): Sum of digits of the n-th Self-number (or Colombian number), A003052(n).
- A163126 (program): a(1)=1. a(n) = the number of integers k, 1 <= k <= n-1, where a(k) is coprime to n-k.
- A163128 (program): a(n) is the n-th self-number minus n.
- A163139 (program): First differences of A163128.
- A163141 (program): a(n) = 5*a(n-2) for n > 2; a(1) = 4, a(2) = 5.
- A163146 (program): a(n) = 12*a(n-1)-31*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
- A163147 (program): a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
- A163148 (program): a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 13.
- A163162 (program): Numbers k such that sigma(k) is not prime.
- A163163 (program): a(n) = sigma(n) + tau(n) - n.
- A163164 (program): Positions n such that A163163(n) is not prime.
- A163165 (program): a(n) = 20*a(n-1) - 96*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A163166 (program): a(n) = 20*a(n-1)-95*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A163169 (program): a(n) = minimal number of consecutive integers required which when summed make n.
- A163173 (program): The n-th product of three primes divided by its central prime factor.
- A163176 (program): The n-th Minkowski number divided by the n-th factorial: a(n) = A053657(n)/n!.
- A163180 (program): a(n) = tau(n) + Sum_{k=1..n} (n mod k).
- A163190 (program): a(n) = Sum_{k=0..n} C(n,k)*sigma(n,k) for n>0 with a(0)=1.
- A163191 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*C(n,k)*sigma(n,k) for n>0 with a(0)=1.
- A163192 (program): a(n) = 20*a(n-1)-93*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A163194 (program): a(n) = F(n)^2 * L(n+1)^2 * F(n-1) * L(n+2), where F(n) and L(n) are the Fibonacci and Lucas numbers, respectively.
- A163195 (program): a(n) = (1/4)*F(n)^2 * L(n+1)^2 * F(n-1) * L(n+2), where F(n) and L(n) are the Fibonacci and Lucas numbers, respectively.
- A163196 (program): a(n) = L(n)^2 * F(n+1)^2 * L(n-1) * F(n+2), where F(n) and L(n) are the Fibonacci and Lucas numbers, respectively.
- A163197 (program): a(n) = (1/4)* L(n)^2 * F(n+1)^2 * L(n-1) * F(n+2), where F(n) and L(n) are the Fibonacci and Lucas numbers, respectively.
- A163198 (program): Sum of the cubes of the first n even-indexed Fibonacci numbers.
- A163199 (program): Sum of the cubes of the first n even-indexed Fibonacci numbers, minus 1.
- A163200 (program): Sum of the cubes of the first n odd-indexed Fibonacci numbers.
- A163201 (program): Alternating sum of the cubes of the first n even-indexed Fibonacci numbers.
- A163202 (program): Alternating sum of the cubes of the first n odd-indexed Fibonacci numbers.
- A163206 (program): a(n) = 20*a(n-1) - 92*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A163210 (program): Swinging Wilson quotients ((p-1)$ +(-1)^floor((p+2)/2))/p, p prime. Here ‘$’ denotes the swinging factorial function (A056040).
- A163213 (program): Swinging Wilson remainders ((p-1)$ + (-1)^floor((p+2)/2))/p mod p, p prime. Here ‘$’ denotes the swinging factorial function (A056040).
- A163227 (program): Fibonacci-accumulation sequence.
- A163241 (program): Simple self-inverse permutation: Write n in base 4, then replace each digit ‘2’ with ‘3’ and vice versa, then convert back to decimal.
- A163242 (program): Row sums of A163233 and A163235.
- A163248 (program): Sum of the n-th composite number plus the number of composite numbers less than the n-th noncomposite number.
- A163249 (program): Sum of prime(n) and number of numbers from this set less than n-th nonprime number (A018252(n)).
- A163250 (program): The number of nonisomorphic complete simple games with n voters of two different types.
- A163253 (program): An interspersion: the order array of the odd-numbered columns of the double interspersion at A161179.
- A163254 (program): Array of the nonsquares; the columns satisfy c(n)=c(n-1)+c(n-2)-c(n-3)+1.
- A163255 (program): An interspersion: the order array of A163254.
- A163256 (program): Fractal sequence of the interspersion A163253.
- A163259 (program): Triangle T(n,k) read by rows: mod(A007318(n,k+1);A007318(n,k)).
- A163260 (program): Row sums of A163259.
- A163267 (program): Partial sums of A118977.
- A163270 (program): First column in matrix inverse of (A047999*A154990).
- A163271 (program): Numerators of fractions in a ‘zero-transform’ approximation of sqrt(2) by means of a(n) = (a(n-1) + c)/(a(n-1) + 1) with c=2 and a(1)=0.
- A163274 (program): a(n) = n^4*(n+1)^2/2.
- A163275 (program): a(n) = n^5*(n+1)^2/2.
- A163276 (program): a(n) = n^6*(n+1)^2/2.
- A163277 (program): a(n) = n^7*(n+1)^2/2.
- A163279 (program): a(n) = (n^6 + 2n^5 + 2n^4 + n^3 + 2n)/2.
- A163282 (program): Triangle read by rows in which row n lists n+1 terms, starting with n^2 and ending with n^3, such that difference between successive terms is equal to n^2 - n.
- A163283 (program): Triangle read by rows in which row n lists n+1 terms, starting with n^3 and ending with n^4, such that the difference between successive terms is equal to n^3 - n^2.
- A163284 (program): Triangle read by rows in which row n lists n+1 terms, starting with n^4 and ending with n^5, such that the difference between successive terms is equal to n^4 - n^3.
- A163285 (program): Triangle read by rows in which row n lists n+1 terms, starting with n^5 and ending with n^6, such that the difference between successive terms is equal to n^5 - n^4.
- A163291 (program): Number of digits of n-th prime written in base 4.
- A163292 (program): a(n) = n-th prime minus (number of digits of n-th prime written in base 4).
- A163293 (program): a(n) = n-th prime minus (number of bits in binary expansion of n-th prime).
- A163295 (program): Binary order of n plus number of partitions of n-1.
- A163296 (program): Absolute value of the Sum_{x=0..A141468(n)} x*(-1)^x.
- A163297 (program): a(n) = sum of divisors of n plus length of the binary expansion of n.
- A163298 (program): Sum of divisors of n minus binary order of n.
- A163299 (program): a(n) = (the number of divisors of n)^(the binary order of n).
- A163300 (program): Zero together with the even nonprimes.
- A163301 (program): a(n) = Sum_{x=n-th even nonprime..n-th odd nonprime} -x*(-1)^x.
- A163303 (program): a(n) = n^3 + 73*n^2 + n + 67.
- A163305 (program): Numerators of fractions in the approximation of the square root of 5 satisfying: a(n)= (a(n-1)+ c)/(a(n-1)+1); with c=5 and a(1)=0. Also product of the powers of two and five times the Fibonacci numbers.
- A163306 (program): a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
- A163307 (program): a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
- A163308 (program): a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
- A163309 (program): a(n) = 18*a(n-1) - 76*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A163310 (program): a(n) = 20*a(n-1) - 95*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
- A163314 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
- A163322 (program): The 3rd Hermite Polynomial evaluated at n: H_3(n) = 8*n^3 - 12*n.
- A163323 (program): The 4th Hermite Polynomial evaluated at n: H_4(n) = 16n^4 - 48n^2 + 12.
- A163325 (program): Pick digits at the even distance from the least significant end of the ternary expansion of n, then convert back to decimal.
- A163326 (program): Pick digits at the odd distance from the least significant end of the ternary expansion of n, then convert back to decimal.
- A163327 (program): Self-inverse permutation of integers: swap the odd- and even-positioned digits in the ternary expansion of n, then convert back to decimal.
- A163343 (program): Central diagonal of A163334 and A163336.
- A163344 (program): Central diagonal of A163334 and A163336 divided by 4.
- A163346 (program): a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
- A163348 (program): a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
- A163349 (program): a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
- A163350 (program): a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
- A163366 (program): a(n) = (-1)^floor((prime(n)+2)/2) mod prime(n).
- A163367 (program): a(n) = phi(tau(sigma(n))).
- A163368 (program): a(n) = phi(sigma(tau(n))).
- A163369 (program): a(n) = sigma(sigma(phi(n))).
- A163370 (program): a(n) = phi(sigma(phi(n))).
- A163371 (program): a(n) = tau(phi(sigma(n)))
- A163372 (program): a(n) = sigma(phi(sigma(n))).
- A163373 (program): a(n) = phi(phi(sigma(n))).
- A163374 (program): a(n) = tau(tau(phi(n))).
- A163375 (program): a(n) = sigma(tau(phi(n))).
- A163376 (program): a(n) = phi(tau(phi(n))).
- A163377 (program): a(n) = tau(phi(tau(n))).
- A163378 (program): a(n) = sigma(phi(tau(n))).
- A163379 (program): a(n) = phi(phi(tau(n))).
- A163383 (program): a(n) = (n-1)*2^n - 1.
- A163385 (program): Primes p such that 3(p-3)-1 and 3(p-3)+1 are twin primes.
- A163388 (program): Primes p such that 6*(p-6) is an average of a twin prime pair.
- A163394 (program): The odd part of Minkowski(n)/n!
- A163395 (program): a(n) = (n-th even nonprime)^(n-th even number).
- A163399 (program): a(n)=(the binary order of n)^sigma(n)
- A163400 (program): Number of bits in binary expansion of n-th nonprime.
- A163403 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 2.
- A163405 (program): a(n) = (n-th nonprime) + (number of bits in binary expansion of n-th nonprime).
- A163406 (program): Numbers n which are not in A163405
- A163407 (program): Sum of semiprime divisors of n with repetition.
- A163408 (program): Positive integers n such that A008475(n) is composite.
- A163409 (program): Subsequence of composite terms of A008475.
- A163412 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n>1, a(0)=1, a(1)=10.
- A163413 (program): a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
- A163414 (program): a(n) = 16*a(n-1) - 62*a(n-2) for n>1, a(0)=1, a(1)=12.
- A163415 (program): a(n) = 18*a(n-1) - 79*a(n-2) for n>1, a(0)=1, a(1)=13.
- A163416 (program): a(n) = 20*a(n-1) - 98*a(n-2) for n>1, a(0)=1, a(1)=14.
- A163417 (program): a(n) = 2^(floor((n-1)/2)) - n*(n-1)/2.
- A163418 (program): Primes of the form ((p-1)/2)^2+((p+1)/2), where p is prime.
- A163419 (program): Primes of the form ((p+1)/2)^2+((p-1)/2), where p is prime.
- A163420 (program): Primes p such that p+(p^2-1)/4 is also prime.
- A163433 (program): Number of different fixed (possibly) disconnected trominoes bounded tightly by an n X n square.
- A163434 (program): Number of different fixed (possibly) disconnected tetrominoes bounded tightly by an n X n square.
- A163435 (program): Number of different fixed (possibly) disconnected pentominoes bounded tightly by an n X n square.
- A163444 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
- A163445 (program): a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
- A163446 (program): a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A163447 (program): a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
- A163448 (program): a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
- A163449 (program): A007582 written in base 2.
- A163450 (program): A028403 written in base 2.
- A163455 (program): a(n) = binomial(5*n-1,n).
- A163456 (program): a(n) = binomial(5*n,n)/5.
- A163458 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
- A163459 (program): a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
- A163460 (program): a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
- A163461 (program): a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A163462 (program): a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
- A163464 (program): Cumulative sum of a repeated shift-and-add operation on the base-7 representation of prime(n).
- A163466 (program): A permutation of two copies of the prime sequence, one moved to nonprime indices, the other to prime indices.
- A163467 (program): a(n) = floor(p/2) * floor(floor(p/2)/2) * floor(floor(floor(p/2)/2)/2) * … * 1, where p=prime(n).
- A163468 (program): Indices k such that half of the k-th nonprime nonnegative integer is prime.
- A163470 (program): a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0) = 3, a(1) = 15.
- A163471 (program): a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 3, a(1) = 18.
- A163472 (program): a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 3, a(1) = 21.
- A163473 (program): a(n) = 14*a(n-1) - 46*a(n-2) for n > 1; a(0) = 3, a(1) = 24.
- A163474 (program): a(n) = 16*a(n-1) - 61*a(n-2) for n > 1; a(0) = 3, a(1) = 27.
- A163475 (program): a(n) = 18*a(n-1) - 78*a(n-2) for n > 1; a(0) = 3, a(1) = 30.
- A163476 (program): a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 3, a(1) = 33.
- A163478 (program): Row sums of A163233 and A163235 divided by 3.
- A163480 (program): Row 0 of A163334 (column 0 of A163336).
- A163481 (program): Row 0 of A163336 (column 0 of A163334).
- A163489 (program): Indices n such that composite(n)/3 is prime.
- A163491 (program): A fractal sequence (if we delete the first occurrence of n we get the sequence itself).
- A163493 (program): Number of binary strings of length n which have the same number of 00 and 01 substrings.
- A163495 (program): a(0)=0, a(1)=1, a(2)=2. For n >= 3, a(n) = a(n-1) - min(a(n-2), a(n-3)).
- A163504 (program): a(n) = abs(n-th prime minus n-th odd nonprime).
- A163505 (program): a(n) = n-th odd nonprime mod n-th odd number.
- A163506 (program): a(n) = n-th odd nonprime * n-th odd number.
- A163508 (program): The sum of the prime factors (with repetition) of the sum of 2 successive primes.
- A163509 (program): Take n written in binary. Replace the leftmost run of 1’s with just a single 1. a(n) is the decimal equivalent of the result.
- A163511 (program): a(0)=1. a(n) = p(A000120(n)) * product{m=1 to A000120(n)} p(m)^A163510(n,m), where p(m) is the m-th prime.
- A163515 (program): If n-th composite is the product of k1-th prime, k2-th prime, …, kr-th prime then set a(n) = k1 + k2 + … + kr.
- A163517 (program): If m-th composite is the product of k1-th prime, k2-th prime,..,kr-th prime and prime=k1+k2+..+kr then set a(n)=m.
- A163520 (program): a(n) is the least integer x such that n < x and the product n*x is divisible by an integer y where n < y < x.
- A163522 (program): a(1)=2; for n>1, a(n) = sum of digits of a(n-1)^2.
- A163523 (program): a(n) = tau(n) + omega(n).
- A163528 (program): The X-coordinate of the n-th point in the Peano curve A163334.
- A163529 (program): The Y-coordinate of the n-th point in the Peano curve A163334.
- A163532 (program): The change in X-coordinate when moving from the n-1:th to the n-th point in the Peano curve A163334.
- A163533 (program): The change in Y-coordinate when moving from the n-1:th to the n-th point in the Peano curve A163334.
- A163550 (program): a(1)=a(2)=a(3)=1. a(n) = reverseDigits(a(n-1)+a(n-2)+a(n-3)) for n>=4.
- A163553 (program): First differences of A024816.
- A163563 (program): n occurs 1+a(n) times starting with a(1)=1.
- A163569 (program): Numbers of the form p^3*q^2*r where p, q and r are three distinct primes.
- A163575 (program): Remove all trailing bits equal to (n mod 2) in binary representation of n.
- A163577 (program): Count of indices x in [0,n] that satisfy the equation A000120(x) + A000120(n-x) = A000120(n) + 2.
- A163581 (program): Number of zeros of sin(x) in integer intervals starting with (0,1).
- A163584 (program): Number of singularities of tan(x) in integer intervals starting with (0,1).
- A163588 (program): Primes which are within 1 of a square number.
- A163590 (program): Odd part of the swinging factorial A056040.
- A163595 (program): Numbers k such that prime(k) == 5 (mod 9).
- A163602 (program): First differences of A161753.
- A163603 (program): Numbers k such that prime(k) == 5 (mod 7).
- A163604 (program): a(n) = ((3+2*sqrt(2))*(4+sqrt(2))^n + (3-2*sqrt(2))*(4-sqrt(2))^n)/2.
- A163605 (program): a(n) = ((3+2*sqrt(2))*(5+sqrt(2))^n + (3-2*sqrt(2))*(5-sqrt(2))^n)/2.
- A163606 (program): a(n) = ((3 + 2*sqrt(2))*(3 + sqrt(2))^n + (3 - 2*sqrt(2))*(3 - sqrt(2))^n)/2.
- A163607 (program): a(n) = ((5 + 2*sqrt(2))*(1 + sqrt(2))^n + (5 - 2*sqrt(2))*(1 - sqrt(2))^n)/2.
- A163608 (program): a(n) = ((5 + 2*sqrt(2))*(2 + sqrt(2))^n + (5 - 2*sqrt(2))*(2 - sqrt(2))^n)/2.
- A163609 (program): a(n) = ((5 + 2*sqrt(2))*(3 + sqrt(2))^n + (5 - 2*sqrt(2))*(3 - sqrt(2))^n)/2.
- A163610 (program): a(n) = ((5 + 2*sqrt(2))*(4 + sqrt(2))^n + (5 - 2*sqrt(2))*(4 - sqrt(2))^n)/2.
- A163611 (program): a(n) = ((5 + 2*sqrt(2))*(5 + sqrt(2))^n + (5 - 2*sqrt(2))*(5 - sqrt(2))^n)/2.
- A163613 (program): a(n) = ((1 + 3*sqrt(2))*(2 + sqrt(2))^n + (1 - 3*sqrt(2))*(2 - sqrt(2))^n)/2.
- A163614 (program): a(n) = ((1 + 3*sqrt(2))*(3 + sqrt(2))^n + (1 - 3*sqrt(2))*(3 - sqrt(2))^n)/2.
- A163615 (program): a(n) = ((1 + 3*sqrt(2))*(4 + sqrt(2))^n + (1 - 3*sqrt(2))*(4 - sqrt(2))^n)/2.
- A163616 (program): a(n) = ((1 + 3*sqrt(2))*(5 + sqrt(2))^n + (1 - 3*sqrt(2))*(5 - sqrt(2))^n)/2.
- A163617 (program): a(2*n) = 2*a(n), a(2*n + 1) = 2*a(n) + 2 + (-1)^n, for all n in Z.
- A163618 (program): a(2*n) = 2 * a(n). a(2*n - 1) = 2 * a(n) - 2 - (-1)^n, for all n in Z.
- A163621 (program): Square array read by antidiagonals: Write n and m in binary with n on the left. Concatenate. a(n,m) is the decimal equivalent of the result.
- A163623 (program): Primes of the form 120*k + 1.
- A163624 (program): Numbers n such that 120n+1 is prime.
- A163626 (program): Triangle read by rows: The n-th derivative of the logistic function written in terms of y, where y = 1/(1 + exp(-x)).
- A163627 (program): Numbers n such that 42n + 5 is prime.
- A163628 (program): Integers such that the two adjacent integers are a prime and three times a prime.
- A163631 (program): Partial sums of the odd nonprimes, A014076.
- A163632 (program): Triple and reverse digits.
- A163634 (program): a(n) = (p*(p+4)+1)/2 where (p,p+4) are the n-th cousin prime pair.
- A163636 (program): The sum of all odd numbers from 2n-1 up to the n-th odd nonprime.
- A163637 (program): The sum of all odd numbers from 2n-1 to prime(n).
- A163639 (program): The count of odd numbers from prime(n) up to the n-th odd nonprime, A014076(n).
- A163640 (program): The radical of the swinging factorial A056040 for odd indices.
- A163641 (program): The radical of the swinging factorial A056040.
- A163644 (program): Product of primes which do not exceed n and do not divide the swinging factorial n$ (A056040).
- A163650 (program): Subswing - the inverse binomial transform of the swinging factorial (A056040).
- A163652 (program): Triangle read by rows where T(n,m)=2*m*n + m + n + 6.
- A163654 (program): The sum of the n-th and (n+1)st isolated prime.
- A163655 (program): a(n) = n*(2*n^2 + 5*n + 13)/2.
- A163656 (program): Arithmetic mean of the n-th and (n+1)st twin prime member A001097.
- A163657 (program): Triangle T(m,n) = 2*m*n + m + n + 8 read by rows.
- A163658 (program): G.f.: A(x) = exp( Sum_{n>=1} A163659(n)^2*x^n/n ), where x*exp(Sum_{n>=1} A163659(n)*x^n/n) = S(x) is the g.f. of Stern’s diatomic series (A002487).
- A163659 (program): L.g.f.: Sum_{n>=1} a(n)*x^n/n = log(S(x)/x) where S(x) is the g.f. of Stern’s diatomic series (A002487).
- A163661 (program): a(n) = n*(2*n^2 + 5*n + 17)/2.
- A163662 (program): A020988 written in base 2.
- A163663 (program): a(0) = 0 and A059153(n-1) written in base 2 otherwise.
- A163664 (program): a(n) = 10^(2*n) + 10^n.
- A163671 (program): Expansion of Sum_( x^k / (1 - x^(k^2)) ).
- A163672 (program): Triangle T(n,m) = 2mn + m + n + 7 read by rows.
- A163673 (program): a(n) = n*(2*n^2 + 5*n + 15)/2.
- A163674 (program): Triangle T(n,m) = 2*m*n + m + n + 9 read by rows.
- A163675 (program): a(n) = n*(2*n^2 + 5*n + 19)/2.
- A163676 (program): Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.
- A163683 (program): a(n) = n^2*(2*n + 5).
- A163685 (program): Number of nX2 binary arrays with all 1s connected, a path of 1s from upper left corner to lower right corner, and no 1 having more than two 1s adjacent
- A163695 (program): Number of n X 2 binary arrays with all 1s connected, a path of 1s from top row to lower right corner, and no 1 having more than two 1s adjacent.
- A163704 (program): Number of n X 2 binary arrays with all 1s connected, a path of 1s from left column to lower right corner, and no 1 having more than two 1s adjacent.
- A163714 (program): Number of n X 2 binary arrays with all 1s connected, a path of 1s from top row to bottom row, and no 1 having more than two 1s adjacent.
- A163723 (program): Number of nX2 binary arrays with all 1s connected, a path of 1s from left column to right column, and no 1 having more than two 1s adjacent
- A163733 (program): Number of n X 2 binary arrays with all 1’s connected, all corners 1, and no 1 having more than two 1’s adjacent.
- A163746 (program): Expansion of (theta_3(q)^2 + 3 * theta_3(q^3)^2) / 4 - 1 in powers of q.
- A163747 (program): Expansion of e.g.f. 2*exp(x)*(1-exp(x))/(1+exp(2*x)).
- A163750 (program): a(n) = (n-th even nonprime mod n-th prime).
- A163751 (program): a(n) = n-th even nonprime minus n-th nonprime.
- A163755 (program): a(0)=1. For n>=1, write n in binary. Let b(n,m) be the length of the m-th run of 0’s or 1’s, reading right to left. Then a(n) = product{m=1 to M} p(m)^b(n,m), where p(m) is the m-th prime, and M is the number of runs of 0’s and 1’s in binary n.
- A163756 (program): 14 times triangular numbers.
- A163758 (program): a(n) = 9*n*(n+1).
- A163761 (program): a(n) = 10*n*(n+1).
- A163765 (program): Inverse binomial transform of A048775 (assuming offset zero in both sequences)
- A163767 (program): a(n) = tau_{n}(n) = number of ordered n-factorizations of n.
- A163769 (program): Primes p such that 2*p+3 is not prime.
- A163770 (program): Triangle read by rows interpolating the swinging sub-factorial (A163650) with the swinging factorial (A056040).
- A163771 (program): Triangle interpolating the swinging factorial (A056040) restricted to even indices with its binomial inverse. Same as interpolating the central trinomial coefficients (A002426) with the central binomial coefficients (A000984).
- A163772 (program): Triangle interpolating the swinging factorial (A056040) restricted to odd indices with its binomial inverse.
- A163773 (program): Row sums of the swinging derangement triangle (A163770).
- A163774 (program): Row sums of the central coefficients triangle (A163771).
- A163775 (program): Row sums of triangle A163772.
- A163777 (program): Even terms in the sequence of Queneau numbers A054639.
- A163778 (program): Odd terms in A054639.
- A163779 (program): Numbers k of the form 4*j + 1 such that 2*k + 1 is a prime with primitive root 2.
- A163780 (program): Terms in A054639 equal to 3 mod 4.
- A163782 (program): a(n) is the n-th J_2-prime (Josephus_2 prime).
- A163801 (program): a(n)=n-a(a(n-2)) with a(0)=0,a(1)=1
- A163804 (program): Expansion of (1 - x) * (1 - x^4) / ((1 - x^2) * (1 - x^3)) in powers of x.
- A163805 (program): Expansion of (1 - x) * (1 - x^6) / ((1 - x^3) * (1 - x^4)) in powers of x.
- A163806 (program): Expansion of (1 - x^3) * (1 - x^4) / ((1 - x) * (1 - x^6)) in powers of x.
- A163807 (program): Reverse the order of inner digits (all digits but the first and last) of n written in binary. a(n) = the decimal value of the result.
- A163808 (program): Write n in binary. Place a 0 right of every 1 without a 0 right of it. a(n) = the decimal value of the result.
- A163809 (program): Write n in binary. Insert a 0 in the middle of each pair of two consecutive 1’s. a(n) = the decimal value of the result.
- A163810 (program): Expansion of (1 - x) * (1 - x^2) * (1 - x^3) / (1 - x^6) in powers of x.
- A163811 (program): Expansion of (1 - x) * (1 - x^10) / ((1 - x^5) * (1 - x^6)) in powers of x.
- A163812 (program): Expansion of (1 - x^5) * (1 - x^6) / ((1 - x) * (1 - x^10)) in powers of x.
- A163815 (program): a(n) = n*(2*n^2 + 5*n + 3).
- A163817 (program): Expansion of (1 - x^2) * (1 - x^5) / ((1 - x) * (1 - x^6)) in powers of x.
- A163818 (program): Expansion of (1 - x) * (1 - x^6) / ((1 - x^2) * (1 - x^5)) in powers of x.
- A163822 (program): Number of divisors d of 2n such that gcd(d-1,2n/d-1) = 1.
- A163823 (program): Number of initial segments of signature sequences of length n.
- A163826 (program): G.f.: Sum_{n>=1} n * 2^(n^2) * x^n / (1 - 2^n*x)^(n+1).
- A163827 (program): a(n) = 6n^3 + 1, solution z in Diophantine equation x^3 + y^3 = z^3 - 2. It may be considered a Fermat near miss by 2.
- A163830 (program): The n-th composite minus the product of the indices of the primes in its prime factorization.
- A163831 (program): a(n) is the n-th composite minus the sum of the indices of the primes in its prime factorization.
- A163832 (program): a(n) = n*(2*n^2 + 5*n + 1).
- A163833 (program): a(n) = n*(6*n^2 + 15*n + 5)/2.
- A163834 (program): a(n) = (4^n + 5)/3.
- A163838 (program): a(n) = (n-th composite) * (number of nontrivial divisors of n-th composite).
- A163839 (program): a(n) = (2^n-1)*4^(2*n-1).
- A163840 (program): Triangle interpolating the binomial transform of the swinging factorial (A163865) with the swinging factorial (A056040).
- A163841 (program): Triangle interpolating the swinging factorial (A056040) restricted to even indices with its binomial transform. Same as interpolating bilateral Schroeder paths (A026375) with the central binomial coefficients (A000984).
- A163842 (program): Triangle interpolating the swinging factorial (A056040) restricted to odd indices with its binomial transform. Same as interpolating the beta numbers 1/beta(n,n) (A002457) with (A163869).
- A163843 (program): Row sums of triangle A163840.
- A163844 (program): Row sums of triangle A163841.
- A163845 (program): Row sums of triangle A163842.
- A163864 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
- A163865 (program): The binomial transform of the swinging factorial (A056040).
- A163866 (program): Partial sums of A007318.
- A163868 (program): a(n) = (4^n + 11)/3.
- A163869 (program): Binomial transform of the beta numbers 1/beta(n+1,n+1) (A002457).
- A163870 (program): Triangle read by rows: row n lists the nontrivial divisors of the n-th composite.
- A163871 (program): The n-th composite plus the sum of its nontrivial divisors.
- A163872 (program): Inverse binomial transform of the beta numbers 1/beta(n+1,n+1) (A002457).
- A163873 (program): a(n) = n - a(a(n-2)) with a(0) = a(1) = 0.
- A163876 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
- A163888 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 4.
- A163895 (program): Positions where A163894 obtains record values.
- A163901 (program): The positions i where A163355(i) = i, that is, the fixed points of permutation A163355.
- A163927 (program): Numerators of the higher order exponential integral constants alpha(k,4).
- A163929 (program): Denominators of the higher order exponential integral constants alpha(2,n).
- A163933 (program): Third right hand column of triangle A163932
- A163935 (program): Third right hand column of triangle A163934
- A163941 (program): Fourth right hand column of triangle A163940.
- A163942 (program): Fifth right hand column of triangle A163940.
- A163943 (program): Third left hand column of triangle A163940.
- A163944 (program): Fourth left hand column of triangle A163940.
- A163945 (program): Triangle interpolating between (-1)^n (A033999) and the swinging factorial function (A056040) restricted to odd indices (2n+1)$ (A002457).
- A163960 (program): Decimal expansion of 2*(sqrt(2) - 1).
- A163961 (program): First differences of A116533.
- A163963 (program): First differences of A080735.
- A163975 (program): n-th nonprime - (-1)^(n-th nonprime).
- A163976 (program): prime(n) -(-1)^(n-th nonprime).
- A163978 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 4.
- A163979 (program): a(n) = n*(n-1) + A144437(n+2).
- A163980 (program): a(n) = 2*n + (-1)^n.
- A163982 (program): Real part of the coefficient [x^n] of the expansion of (1+i)/(1-i*exp(x)) - 1 multiplied by 2*n!, where i is the imaginary unit.
- A163984 (program): First differences of A056737.
- A163985 (program): Sum of all isolated parts of all partitions of n.
- A163987 (program): First differences of A160119.
- A164001 (program): Spiral of triangles around a hexagon.
- A164004 (program): Zero together with row 4 of the array in A163280.
- A164005 (program): Zero together with row 5 of the array in A163280.
- A164006 (program): Zero together with row 6 of the array in A163280.
- A164013 (program): 3 times centered triangular numbers: 9*n*(n+1)/2 + 3.
- A164015 (program): 5 times centered pentagonal numbers: 5*(5*n^2 + 5*n + 2)/2.
- A164016 (program): 6 times centered hexagonal numbers: 18*n*(n+1) + 6.
- A164018 (program): The index values of the smallest and the largest n-digit Fibonacci numbers.
- A164019 (program): Table read by rows: row n contains the primes between n and 2n.
- A164020 (program): Denominators of Bernoulli numbers interleaved with even numbers.
- A164021 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 3, a(1) = 22.
- A164028 (program): The n-th composite minus 3.
- A164029 (program): a(n) = nonprime(n) + (-1)^(nonprime(n)).
- A164031 (program): a(n) = ((2+3*sqrt(2))*(5+sqrt(2))^n+(2-3*sqrt(2))*(5-sqrt(2))^n)/4.
- A164032 (program): Number of “ON” cells in a certain 2-dimensional cellular automaton.
- A164033 (program): a(n) = ((4+3*sqrt(2))*(3+sqrt(2))^n + (4-3*sqrt(2))*(3-sqrt(2))^n)/4.
- A164034 (program): a(n) = ((4+3*sqrt(2))*(4+sqrt(2))^n + (4-3*sqrt(2))*(4-sqrt(2))^n)/4.
- A164035 (program): a(n) = ((4+3*sqrt(2))*(5+sqrt(2))^n + (4-3*sqrt(2))*(5-sqrt(2))^n)/4.
- A164037 (program): Expansion of (5-9*x)/(1-6*x+7*x^2).
- A164038 (program): Expansion of (5-19*x)/(1-10*x+23*x^2).
- A164039 (program): a(n+1) = 3*a(n) - n.
- A164040 (program): 2*alpha^4*e^(Pi/(4*alpha))*(e/2)^(1/4), where alpha is the fine structure constant A003673.
- A164041 (program): Primes of the form 2*p^2 + 4*p + 1, where p is also prime.
- A164042 (program): Primes p such that 2*p^2+4*p+1 is also prime.
- A164044 (program): a(n+1) = 4*a(n) - n.
- A164045 (program): a(n+1) = 5*a(n) - n.
- A164046 (program): A001445 written in base 2.
- A164051 (program): a(n) = 2^(2n) + 2^(n-1).
- A164053 (program): Partial sums of A162255.
- A164055 (program): Triangular numbers that are one plus a perfect square.
- A164056 (program): Triangle of 2^n terms by rows, derived from A088696 as to length of continued fractions, lengths increase = 1, decrease = 0. A088696 can be generated using the following algorithm: Rows 0 and 1 begin 1; 1,2; then for all further rows, bring down current row then append to the right: (1 added to each term in current row). Row 2 (1, 2, 3, 2) then becomes: (1, 2, 3, 2, 3, 4, 3, 2).
- A164057 (program): Complement to A164056, change A164056 bits (0->1; 1->0). Provides a coding template for Petoukhov matrices, relating to DNA codons.
- A164072 (program): a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
- A164073 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 3.
- A164080 (program): Perfect squares one less than a triangular number.
- A164086 (program): Beatty sequence for 4*Pi/3 = 4.1887902… .
- A164087 (program): Beatty sequence for 4*Pi/(4*Pi-3) = 1.3135986… .
- A164089 (program): For n >=4, a(n) = the numerical value of the substring of binary n containing all digits but the first and last. a(1) = a(2) = a(3) = 0.
- A164090 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 2, a(2) = 3.
- A164092 (program): Triangle by 2^n term rows, codes used for generating Petoukhov matrices in a Gray code format.
- A164093 (program): 9*4^n+2.
- A164094 (program): a(n) = 3*2^n + 2.
- A164095 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.
- A164096 (program): Partial sums of A164095.
- A164097 (program): Numbers n such that 6n + 7 is a perfect square.
- A164102 (program): Decimal expansion of 2*Pi^2.
- A164103 (program): Decimal expansion of 8*Pi^2/15.
- A164104 (program): Decimal expansion of 8*Pi^2/3.
- A164105 (program): Decimal expansion of Pi^3/6.
- A164106 (program): Decimal expansion of 16*Pi^3/105.
- A164107 (program): Decimal expansion of 16*Pi^3/15.
- A164108 (program): Decimal expansion of Pi^4/24.
- A164109 (program): Decimal expansion of Pi^4/3.
- A164110 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 5, a(1) = 36.
- A164111 (program): Expansion of (1-x)/(1+4*x^2).
- A164114 (program): Numbers k such that Chowla(k) + phi(k) is prime.
- A164115 (program): Expansion of (1 - x^5) / ((1 - x) * (1 - x^4)) in powers of x.
- A164116 (program): Expansion of (1 - x) * (1 - x^4) / (1 - x^5) in powers of x.
- A164117 (program): Expansion of (1 - x) * (1 - x^10) / ((1 - x^2) * (1 - x^4) * (1 - x^5)) in powers of x.
- A164118 (program): Expansion of (1 - x^2) * (1 - x^4) * (1 - x^5) / ((1 - x) * (1 - x^10)) in powers of x.
- A164120 (program): Partial sums of A162396.
- A164123 (program): Partial sums of A162436.
- A164126 (program): First differences of A006995.
- A164131 (program): Numbers k such that k^2 == 2 (mod 31).
- A164135 (program): Numbers k such that k^2 == 2 (mod 47).
- A164136 (program): a(n) = 11*n*(n+1).
- A164141 (program): Number of binary strings of length n with equal numbers of 001 and 010 substrings.
- A164143 (program): Number of binary strings of length n with equal numbers of 001 and 100 substrings
- A164158 (program): Number of binary strings of length n with equal numbers of 0001 and 0101 substrings
- A164161 (program): Number of binary strings of length n with equal numbers of 0001 and 1000 substrings.
- A164203 (program): Number of binary strings of length n with equal numbers of 00001 and 10000 substrings.
- A164229 (program): Number of binary strings of length n with equal numbers of 00011 and 00101 substrings
- A164265 (program): Partial sums of A162766.
- A164267 (program): A Fibonacci convolution.
- A164269 (program): Expansion of q * f(q^9)^3 * phi(q) / (f(q^3) * phi(q^3)^3) in powers of q where f(), phi() are Ramanujan theta functions.
- A164270 (program): Expansion of f(x^3)^3 * phi(x^3) / (f(x) * phi(x)^3) in powers of x where f(), phi() are Ramanujan theta functions.
- A164271 (program): Expansion of ( f(-q^2) * f(q^3) * f(-q^6) / f(q)^3 )^2 in powers of q where f() is a Ramanujan theta function.
- A164274 (program): (n-th isolated prime) plus (n-th isolated composite).
- A164275 (program): The absolute value of (the n-th isolated composite minus the n-th isolated prime).
- A164276 (program): The non-isolated nonprimes.
- A164278 (program): a(n) = (6*n + 1)^(2*n) - 1.
- A164279 (program): Triangle of 2^n terms per row, a Petoukhov sequence generated from (3,2).
- A164281 (program): Triangle read by rows, a Petoukhov sequence (cf. A164279) generated from (1,2).
- A164282 (program): Hypotenuses of more than two Pythagorean triangles.
- A164284 (program): a(n) = 15*n-7.
- A164285 (program): a(n) = 7*2^n + 3.
- A164292 (program): Binary sequence identifying the twin primes (characteristic function of twin primes: 1 if n is a twin prime else 0).
- A164295 (program): Triangle T(n,k) read by rows: sum of the triangles A054521 and A051731.
- A164296 (program): Let S(n) be the set of all positive integers that are <= n and are coprime to n. a(n) = the number of members of S(n) that are each coprime to every other member of S(n).
- A164297 (program): Let S(n) be the set of all positive integers that are <= n and are coprime to n. a(n) = the number of members of S(n) that are each non-coprime with at least one other member of S(n).
- A164298 (program): a(n) = ((1+4*sqrt(2))*(2+sqrt(2))^n + (1-4*sqrt(2))*(2-sqrt(2))^n)/2.
- A164299 (program): a(n) = ((1+4*sqrt(2))*(3+sqrt(2))^n + (1-4*sqrt(2))*(3-sqrt(2))^n)/2.
- A164300 (program): a(n) = ((1+4*sqrt(2))*(4+sqrt(2))^n + (1-4*sqrt(2))*(4-sqrt(2))^n)/2.
- A164301 (program): a(n) = ((1+4*sqrt(2))*(5+sqrt(2))^n + (1-4*sqrt(2))*(5-sqrt(2))^n)/2.
- A164302 (program): a(n) = 2* (the n-th positive (odd) integer that is a palindrome when written in base 2).
- A164303 (program): a(n) = 2*a(n-1) + a(n-2) for n > 1; a(0) = 3, a(1) = 11.
- A164304 (program): a(n) = 4*a(n-1) - 2*a(n-2) for n > 1; a(0) = 3, a(1) = 14.
- A164305 (program): a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 3, a(1) = 17.
- A164306 (program): Triangle read by rows: T(n, k) = k / gcd(k, n), 1 <= k <= n.
- A164308 (program): Triangle read by rows, binomial distribution of the terms (1, 3, 9, 27, …).
- A164309 (program): Triangle read by rows, generated from the binomial expansion of (5x + 2).
- A164310 (program): a(n) = 6*a(n-1) - 6*a(n-2) for n > 1; a(0) = 4, a(1) = 15.
- A164311 (program): a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 4, a(1) = 27.
- A164313 (program): LCM of all differences of odd primes up to prime(n).
- A164314 (program): Largest prime factor of n^2 - 2.
- A164315 (program): Number of binary strings of length n with no substrings equal to 000 or 011.
- A164316 (program): Number of binary strings of length n with no substrings equal to 000, 001, or 010.
- A164317 (program): Number of binary strings of length n with no substrings equal to 000, 010, or 111.
- A164318 (program): Primes p such that the sum of divisors of p-1 is larger than 2*p.
- A164343 (program): A positive integer is included if it is a square that contains the same number of 0’s as 1’s when represented in binary.
- A164344 (program): Positive integers whose square contains the same number of 0’s as 1’s when represented in binary.
- A164346 (program): a(n) = 3 * 4^n.
- A164349 (program): The limit of the string “0, 1” under the operation ‘repeat string twice and remove last symbol’.
- A164355 (program): Expansion of (1 - x^2)^4 * (1 - x^5) / ((1 - x)^5 * (1 - x^4)^2) in powers of x.
- A164356 (program): Expansion of (1 - x^2)^4 / ((1 - x)^4 * (1 - x^4)) in powers of x.
- A164357 (program): Expansion of (1 - x^2)^5 / ((1 - x)^4 * (1 - x^6)) in powers of x.
- A164358 (program): Expansion of (1 - x^2)^2 * (1 - x^3) / ((1 - x)^3 * (1 - x^4)) in powers of x.
- A164359 (program): Expansion of (1 - x^2)^3 / ((1 - x)^3 * (1 - x^3)) in powers of x.
- A164360 (program): Period 3: repeat [5, 4, 3].
- A164362 (program): The number of 0’s in the n-th stage of A164349.
- A164363 (program): The number of 1’s in the n-th stage of A164349
- A164364 (program): a(n) = A164349(2^n).
- A164367 (program): a(n) = A164051(n) in base 2.
- A164370 (program): Sequence A005418 written in base 2.
- A164376 (program): Nonprime numbers that are not a sum of 2 primes.
- A164383 (program): Composite numbers of the form 4 + some prime.
- A164384 (program): Positive nonprimes of the form p-4 where p is prime.
- A164385 (program): Composite numbers n such that n+4 and n-4 are both prime.
- A164386 (program): Numbers which are not 1 larger than a nonzero square.
- A164387 (program): Number of binary strings of length n with no substrings equal to 0000 or 0010.
- A164388 (program): Number of binary strings of length n with no substrings equal to 0000 or 0011.
- A164389 (program): Number of binary strings of length n with no substrings equal to 0000 or 0101.
- A164390 (program): Number of binary strings of length n with no substrings equal to 0000 or 0110.
- A164391 (program): Number of binary strings of length n with no substrings equal to 0000 or 0111.
- A164392 (program): Number of binary strings of length n with no substrings equal to 0001 or 0010.
- A164393 (program): Number of binary strings of length n with no substrings equal to 0001 or 0011.
- A164394 (program): Number of binary strings of length n with no substrings equal to 0001 or 0100.
- A164395 (program): Number of binary strings of length n with no substrings equal to 0001 or 0101.
- A164396 (program): Number of binary strings of length n with no substrings equal to 0001 or 0110.
- A164397 (program): Number of binary strings of length n with no substrings equal to 0001 or 0111.
- A164398 (program): Number of binary strings of length n with no substrings equal to 0001 or 1000.
- A164399 (program): Number of binary strings of length n with no substrings equal to 0001 or 1010
- A164400 (program): Number of binary strings of length n with no substrings equal to 0001 or 1100.
- A164401 (program): Number of binary strings of length n with no substrings equal to 0010 or 0101.
- A164402 (program): Number of binary strings of length n with no substrings equal to 0010 or 0110.
- A164403 (program): Number of binary strings of length n with no substrings equal to 0010 or 1001
- A164404 (program): Number of binary strings of length n with no substrings equal to 0010 or 1011
- A164405 (program): Number of binary strings of length n with no substrings equal to 0010 or 1100.
- A164406 (program): Number of binary strings of length n with no substrings equal to 0011 or 0101.
- A164407 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0010
- A164408 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0011.
- A164409 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0100
- A164410 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0101
- A164411 (program): Number of binary strings of length n with no substrings equal to 0000, 0001, or 0110.
- A164412 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0111.
- A164413 (program): Number of binary strings of length n with no substrings equal to 0000, 0001 or 1001.
- A164414 (program): Number of binary strings of length n with no substrings equal to 0000, 0001, or 1010.
- A164415 (program): Number of binary strings of length n with no substrings equal to 0000, 0001, or 1100.
- A164416 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 1111
- A164417 (program): Number of binary strings of length n with no substrings equal to 0000, 0010, or 0100.
- A164418 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 0101
- A164419 (program): Number of binary strings of length n with no substrings equal to 0000, 0010, or 0110.
- A164420 (program): Number of binary strings of length n with no substrings equal to 0000, 0010, or 0111.
- A164421 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1001
- A164422 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1010
- A164423 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1100
- A164424 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1101
- A164425 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1111
- A164427 (program): Number of binary strings of length n with no substrings equal to 0000 0011 or 0110
- A164428 (program): Number of binary strings of length n with no substrings equal to 0000, 0011, or 1001.
- A164429 (program): Number of binary strings of length n with no substrings equal to 0000, 0011, or 1011.
- A164431 (program): Number of binary strings of length n with no substrings equal to 0000 0011 or 1101
- A164432 (program): Number of binary strings of length n with no substrings equal to 0000 0101 or 0110
- A164433 (program): Number of binary strings of length n with no substrings equal to 0000 0101 or 0111
- A164436 (program): Number of binary strings of length n with no substrings equal to 0000 0101 or 1110.
- A164438 (program): Number of binary strings of length n with no substrings equal to 0000 0110 or 0111
- A164439 (program): Number of binary strings of length n with no substrings equal to 0000 0110 or 1001
- A164440 (program): Number of binary strings of length n with no substrings equal to 0000 0110 or 1011
- A164442 (program): Number of binary strings of length n with no substrings equal to 0000 0111 or 1001
- A164443 (program): Number of binary strings of length n with no substrings equal to 0000 0111 or 1110
- A164444 (program): Number of binary strings of length n with no substrings equal to 0000 1001 or 1011
- A164445 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 0100
- A164446 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 0101
- A164447 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 0110
- A164448 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 0111
- A164449 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 1010
- A164450 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 1011
- A164451 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 1100
- A164452 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 1101.
- A164453 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 0100
- A164454 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 0101
- A164455 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 0111
- A164456 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 1000
- A164457 (program): Number of binary strings of length n with no substrings equal to 0001, 0011, or 1010.
- A164458 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 1011
- A164460 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 1101
- A164461 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 1110
- A164462 (program): Number of binary strings of length n with no substrings equal to 0001 0100 or 0101
- A164463 (program): Number of binary strings of length n with no substrings equal to 0001 0100 or 0110
- A164464 (program): Number of binary strings of length n with no substrings equal to 0001, 0100, or 0111.
- A164465 (program): Number of binary strings of length n with no substrings equal to 0001 0100 or 1010
- A164466 (program): Number of binary strings of length n with no substrings equal to 0001, 0100, or 1011.
- A164467 (program): Number of binary strings of length n with no substrings equal to 0001 0100 or 1101
- A164468 (program): Number of binary strings of length n with no substrings equal to 0001, 0100, or 1110.
- A164469 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 0110
- A164470 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 0111
- A164471 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1000
- A164472 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1010
- A164473 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1011
- A164474 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1100
- A164475 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1110
- A164476 (program): Number of binary strings of length n with no substrings equal to 0001, 0110, or 0111.
- A164477 (program): Number of binary strings of length n with no substrings equal to 0001 0110 or 1000.
- A164478 (program): Number of binary strings of length n with no substrings equal to 0001 0110 or 1010
- A164479 (program): Number of binary strings of length n with no substrings equal to 0001 0110 or 1011
- A164480 (program): Number of binary strings of length n with no substrings equal to 0001, 0110 or 1100.
- A164481 (program): Number of binary strings of length n with no substrings equal to 0001 0110 or 1101.
- A164482 (program): Number of binary strings of length n with no substrings equal to 0001, 0110, or 1110.
- A164483 (program): Number of binary strings of length n with no substrings equal to 0001 0111 or 1010.
- A164484 (program): Number of binary strings of length n with no substrings equal to 0001 0111 or 1100
- A164485 (program): Number of binary strings of length n with no substrings equal to 0001, 1000 or 1001.
- A164487 (program): Number of binary strings of length n with no substrings equal to 0001, 1010, or 1100.
- A164488 (program): Number of binary strings of length n with no substrings equal to 0001 1010 or 1101
- A164489 (program): Number of binary strings of length n with no substrings equal to 0001 1011 or 1100
- A164490 (program): Number of binary strings of length n with no substrings equal to 0010 0011 or 0110
- A164491 (program): Number of binary strings of length n with no substrings equal to 0010 0100 or 1001
- A164492 (program): Number of binary strings of length n with no substrings equal to 0010 0101 or 0110
- A164493 (program): Number of binary strings of length n with no substrings equal to 0010 0101 or 1001
- A164494 (program): Number of binary strings of length n with no substrings equal to 0010 0101 or 1010
- A164495 (program): Number of binary strings of length n with no substrings equal to 0010 0101 or 1011
- A164497 (program): Number of binary strings of length n with no substrings equal to 0010 0110 or 1011
- A164498 (program): Number of binary strings of length n with no substrings equal to 0010 0110 or 1100
- A164499 (program): Number of binary strings of length n with no substrings equal to 0010 0110 or 1101
- A164500 (program): Number of binary strings of length n with no substrings equal to 0010 1001 or 1010
- A164501 (program): Number of binary strings of length n with no substrings equal to 0010 1001 or 1100
- A164503 (program): Number of binary strings of length n with no substrings equal to 0011 0101 or 0110
- A164504 (program): Number of binary strings of length n with no substrings equal to 0011 0101 or 1010
- A164505 (program): Number of binary strings of length n with no substrings equal to 0011 0101 or 1100
- A164506 (program): Number of binary strings of length n with no substrings equal to 0011 0110 or 1001
- A164508 (program): Number of binary strings of length n with no substrings equal to 0101, 0110, or 1001.
- A164509 (program): Number of binary strings of length n with no substrings equal to 0101, 0110, or 1010.
- A164510 (program): First differences of A071904 (Odd composite numbers).
- A164513 (program): Primes with gap to the next prime no less than 20.
- A164514 (program): 1 followed by numbers that are not squares.
- A164515 (program): Positive numbers not of the form n^2+2.
- A164532 (program): a(n) = 6*a(n-2) for n > 2; a(1) = 1, a(2) = 4.
- A164533 (program): a(n) = sigma(sigma(n))*sigma(n).
- A164534 (program): (n-th isolated prime) -(-1)^(n-th isolated prime).
- A164535 (program): a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.
- A164536 (program): a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 3, a(1) = 23.
- A164537 (program): a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 5, a(1) = 28.
- A164538 (program): a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
- A164539 (program): a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 13.
- A164540 (program): a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 14.
- A164541 (program): a(n) = 6*a(n-1) - a(n-2) for n > 1; a(0) = 1, a(1) = 15.
- A164542 (program): a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 16.
- A164543 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 17.
- A164544 (program): a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
- A164545 (program): a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
- A164546 (program): a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A164547 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
- A164549 (program): a(n) = 4*a(n-1) + 2*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
- A164550 (program): a(n) = 6*a(n-1) - 3*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
- A164551 (program): a(n) = 10*a(n-1)-19*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
- A164552 (program): a(n) = 12*a(n-1)-30*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A164553 (program): a(n) = 14*a(n-1)-43*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
- A164555 (program): Numerators of the “original” Bernoulli numbers; also the numerators of the Bernoulli polynomials at x=1.
- A164559 (program): a(n) = 6^n/3 - 1.
- A164560 (program): Partial sums of A164532.
- A164561 (program): Triangle with elements A120070(m,n)/A120072(m,n) read by rows, m>=2, 1<=n<m.
- A164569 (program): Primes p such that 11*p+8 are prime numbers.
- A164575 (program): a(n) = n! * [x^n] 2*(tan(x))^2*(sec(x) + tan(x)).
- A164576 (program): Integer averages of the set of the first positive squares up to some n^2.
- A164577 (program): Integer averages of the first perfect cubes up to some n^3.
- A164578 (program): Integers of the form (k+1)*(2k+1)/12.
- A164579 (program): Integer averages of halves of first cubes of natural numbers (n^3)/2 for some n.
- A164581 (program): a(n) = 5*a(n - 1) + a(n - 2), with a(0)=1, a(1)=2.
- A164582 (program): a(n) = 5*a(n - 1) - a(n - 2), with n>2, a(1)=2, a(2)=3.
- A164583 (program): a(n)=4^n*(2n + 1)^2.
- A164584 (program): Expansion of (1 + 6*x - 12*x^2 - 8*x^3)/(1 - 24*x^2 + 16*x^4).
- A164587 (program): a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.
- A164588 (program): a(n) = ((3 + sqrt(18))*(5 + sqrt(8))^n + (3 - sqrt(18))*(5 - sqrt(8))^n)/6.
- A164589 (program): a(n) = ((4 + 3*sqrt(2))*(1 + 2*sqrt(2))^n + (4 - 3*sqrt(2))*(1 - 2*sqrt(2))^n)/8.
- A164591 (program): a(n) = ((4 + sqrt(18))*(4 + sqrt(8))^n + (4 - sqrt(18))*(4 - sqrt(8))^n)/8 .
- A164592 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
- A164593 (program): a(n) = ((5 + sqrt(18))*(2 + sqrt(8))^n + (5 - sqrt(18))*(2 - sqrt(8))^n)/2.
- A164594 (program): a(n) = ((5 + sqrt(18))*(4 + sqrt(8))^n + (5 - sqrt(18))*(4 - sqrt(8))^n)/2.
- A164595 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 5, a(1) = 37.
- A164597 (program): a(n) = the largest integer such that {the n-th prime} + k(k + 1) is prime for all k where 0 <= k <= a(n).
- A164598 (program): a(n) = 12*a(n-1) - 34*a(n-2), for n > 1, with a(0) = 1, a(1) = 14.
- A164599 (program): a(n) = 14*a(n-1) - 47*a(n-2), for n > 1, with a(0) = 1, a(1) = 15.
- A164600 (program): a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 17.
- A164602 (program): a(n) = ((1+4*sqrt(2))*(1+2*sqrt(2))^n + (1-4*sqrt(2))*(1-2*sqrt(2))^n)/2.
- A164603 (program): a(n) = ((1+4*sqrt(2))*(2+2*sqrt(2))^n + (1-4*sqrt(2))*(2-2*sqrt(2))^n)/2.
- A164604 (program): a(n) = ((1+4*sqrt(2))*(3+2*sqrt(2))^n + (1-4*sqrt(2))*(3-2*sqrt(2))^n)/2.
- A164605 (program): a(n) = ((1+4*sqrt(2))*(4+2*sqrt(2))^n + (1-4*sqrt(2))*(4-2*sqrt(2))^n)/2.
- A164606 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 21.
- A164607 (program): a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
- A164608 (program): Expansion of (1+4*x)/(1-8*x+8*x^2).
- A164609 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 13.
- A164611 (program): Expansion of (1 + x + 2*x^2 - x^3)/(1 - 2*x + 3*x^2 - 2*x^3 + x^4).
- A164614 (program): Expansion of (chi(q) / chi^3(q^3))^2 in powers of q where chi() is a Ramanujan theta function.
- A164616 (program): Expansion of c(-q) * c(-q^3) / c(q^2)^2 in powers of q where c() is a cubic AGM theta function.
- A164617 (program): Expansion of (phi^3(q^3) / phi(q)) * (psi(-q^3) / psi^3(-q)) in powers of q where phi(), psi() are Ramanujan theta functions.
- A164619 (program): Integers of the form A164577(k)/3.
- A164629 (program): Expansion of phi (golden ratio) in base 5.
- A164632 (program): a(1)=1 followed by 2^k appearing 2^(2*k-1) times for k>0.
- A164640 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
- A164651 (program): Number of permutations of length n that avoid both 1243 and 2134.
- A164653 (program): a(1) = 1, for n>=2: a(n) = sum of two consecutive noncomposite numbers A008578.
- A164654 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 8.
- A164655 (program): Numerators of partial sums of Theta(3) = sum(1/(2*j-1)^3, j=1..infinity).
- A164656 (program): Numerators of partial sums of Theta(5) = sum( 1/(2*j-1)^5, j=1..infinity ).
- A164657 (program): Denominators of partial sums of Theta(5) = sum(1/(2*j-1)^5, j=1..infinity).
- A164658 (program): Numerators of coefficients of integrated Chebyshev polynomials T(n,x) (in increasing order of powers of x).
- A164659 (program): Denominators of coefficients of integrated Chebyshev polynomials T(n,x) (in increasing order of powers of x).
- A164660 (program): Numerators of row sums of triangle of rationals A164658/A164659. Definite integral of Chebyshev polynomials of the first kind: Integral_{x=0..1} T(n,x).
- A164661 (program): Denominators of row sums of triangle of rationals A164658/A164659. Definite integral of Chebyshev polynomials of the first kind: Integral_{x=0..1} T(n,x).
- A164662 (program): Row sums of triangle A164658 (numerators of coefficients from Integral_{x} T(n,x), with T(n,x) Chebyshev polynomials of the first kind).
- A164663 (program): Row sums of triangle A164659 (denominators of coefficients from int(T(n,x),x), with T(n,x) Chebyshev polynomials of the first kind).
- A164675 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 12.
- A164677 (program): For a binary reflected Gray code, the (Hamming/Euclidean) distance between 2 subsequent points x and y is 1, say in coordinate k. If y has a 1 in coordinate k and x has a 0, than (x,y) is indicated by k, if it is the other way around, (x,y) is indicated by -k. The sequence has a fractal character such that G(d+1) = G(d) d+1 R(G(d)) where R(G(d)) alters d –> -d and leaves all other numbers invariant.
- A164680 (program): Expansion of x/((1-x)^3*(1-x^2)^3*(1-x^3)).
- A164682 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 8.
- A164683 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 8.
- A164689 (program): If p and q are (odd) twin primes and q > p then p*q^2+(p+q)+1 is divisible by 3; a(n) = (p*q^2+(p+q)+1)/3.
- A164703 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 16.
- A164705 (program): T(n,k)=Binomial(2n-k,n)*2^(k-1) for n>=1,0<=k<=n
- A164711 (program): Those positive integers missing from sequence A164710. Those positive integers that, when written in binary, contain at least two runs of 0’s that are of differing lengths.
- A164737 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 5, a(2) = 12.
- A164738 (program): Triangle read by rows. Row 0 = {2}; left half of row n+1 = row n, right half = row n reversed with each term replaced by the next prime.
- A164740 (program): (2^p-(p+2))/p as p runs through the primes.
- A164743 (program): Digital root of 3*A000045(n).
- A164754 (program): Number of n X 2 1..4 arrays with all 1’s connected, all 2’s connected, all 3’s connected, all 4’s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.
- A164765 (program): Partial sums of [A080782^2].
- A164768 (program): First differences of A003592.
- A164783 (program): 7^n-6.
- A164784 (program): a(n) = 6^n-5.
- A164785 (program): a(n) = 5^n - 4.
- A164786 (program): a(n) = 8^n-7.
- A164826 (program): Sequences A087800 and A077416 interleaved.
- A164827 (program): Generalized Lucas numbers: a(n) = a(n-1) + 10 a(n-2); with a(1)=2 a(2)=1
- A164844 (program): Generalized Pascal Triangle - satisfying the same recurrence as Pascal’s triangle, but with a(n,0)=1 and a(n,n)=10^n (instead of both being 1).
- A164845 (program): a(n) = (6 + 10*n + 5*n^2 + n^3)/2.
- A164847 (program): (100^n,1) Pascal triangle
- A164848 (program): a(n) = A026741(n)/A051712(n+1).
- A164849 (program): Diagonal sum of (100^n,1) Pascal Triangle
- A164851 (program): Generalized Lucas-Pascal triangle; (11*10^n, 1).
- A164852 (program): Diagonal sum of generalized Lucas-Pascal triangle;(11*10^n,1)
- A164854 (program): Diagonal sum of generalized Pascal triangle; (10^n,1).
- A164855 (program): Generalized Lucas-Pascal triangle: (101*100^n,1)
- A164856 (program): Row sums of generalized Lucas-Pascal triangle: A164855
- A164861 (program): Odd positive integers that are not palindromes when written in binary.
- A164866 (program): (101^n,1)-Pascal triangle
- A164869 (program): n*A027642(n).
- A164870 (program): The number of permutations of length n that can be sorted by 2 pop stacks in parallel.
- A164874 (program): Triangle read by rows: T(1,1)=2; T(n,k)=2*T(n-1,k)+1, 1<=k<n; T(n,n)=2*(T(n-1,n-1)+1).
- A164877 (program): First bisection of A164869.
- A164881 (program): Inverse of A164844
- A164884 (program): a(n) = image of n under the base-2 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).
- A164894 (program): Base-10 representation of the binary string formed by appending 10, 100, 1000, 10000, …, etc., to 1.
- A164897 (program): a(n) = 4*n*(n+1) + 3.
- A164898 (program): First differences of numbers having only odd digits in their decimal representation.
- A164899 (program): Binomial matrix (1,10^n) read by antidiagonals.
- A164900 (program): a(2n) = 4*n*(n+1) + 3; a(2n+1) = 2*n*(n+2) + 3.
- A164901 (program): a(1)=1, a(2) = 2. For n >=3, a(n) = the smallest integer > a(n-1) that is coprime to every sum of any two distinct earlier terms of this sequence.
- A164907 (program): a(n) = (3*3^n-(-1)^n)/2.
- A164908 (program): a(n) = (3*4^n - 0^n)/2.
- A164910 (program): Partial sums of A088748
- A164913 (program): Expansion of x/(1-9*x-11*x^2+10*x^3).
- A164915 (program): Inverse of binomial matrix (10^n,1 )A164899. (Subtraction instead of addition)
- A164921 (program): a(1)=0, a(2)=1. For n >=3, a(n) = the smallest integer > a(n-1) that is coprime to every sum of any two distinct earlier terms of this sequence.
- A164925 (program): Array binomial(j-i,j) read by rising antidiagonals.
- A164931 (program): n times the n-th noncomposite.
- A164938 (program): a(n) = (n^5 - n)/10, which is always an integer.
- A164940 (program): Partial sums of A138202.
- A164942 (program): Triangle, read by rows, T(n,k) = (-1)^k*binomial(n, k)*3^(n-k).
- A164943 (program): Decimal value of the concatenation of first n odd numbers in binary.
- A164944 (program): Decimal value of the concatenation of first n even numbers in binary.
- A164945 (program): Decimal value of the concatenation of first n multiples of 3 in binary.
- A164948 (program): Fibonacci matrix read by antidiagonals. (Inverse of A136158.)
- A164950 (program): 1 if there is a winning strategy for misère Sprouts with n initial points, else 0.
- A164955 (program): Sequence obtained from Fibonacci numbers by taking the factorials of each digit and summing.
- A164961 (program): Triangle read by rows: T[n,m] = quadruple factorials A001813(n) * binomials A007318(n,m)
- A164965 (program): Cumulative sums of A010892.
- A164977 (program): Numbers m such that the set {1..m} has only one nontrivial decomposition into subsets with equal element sum.
- A164978 (program): Number of divisors of n*(n+1)/2 that are >= n.
- A164981 (program): A triangle with Pell numbers in the first column.
- A164984 (program): Odd (Jacobsthal) triangle
- A164985 (program): Denominators of ternary BBP-type series for log(5)
- A164990 (program): Number of square involutions of n.
- A164991 (program): Number of triangular involutions of n. A triangular involution is a square involution with at most three faces.
- A164993 (program): a(n) = image of n under the base-3 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order)
- A164994 (program): A164993(n)/2
- A165020 (program): Length of cycle mentioned in A165019
- A165024 (program): Length of cycle mentioned in A165023
- A165027 (program): Number of n-digit fixed points under the base-4 Kaprekar map A165012
- A165051 (program): a(n) = image of n under the base-6 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order)
- A165052 (program): A165051(n)/5
- A165063 (program): Length of cycle mentioned in A165062
- A165130 (program): a(n) = (2^(n+4)-1)*(2^n-1).
- A165133 (program): a(n) = (2^(n+4)-1)*(2^n+1).
- A165145 (program): Partial sums of A058183.
- A165147 (program): a(n) = (3*7^n-3^n)/2.
- A165148 (program): a(n) = (3*8^n-4^n)/2.
- A165149 (program): a(n) = (3*9^n-5^n)/2.
- A165150 (program): a(n) = (3*10^n-6^n)/2.
- A165151 (program): a(n) = (3*11^n-7^n)/2.
- A165152 (program): a(n) = (3*12^n-8^n)/2.
- A165154 (program): a(n) = 100*a(n-1) +/- 9^(n-1) for n>0, a(0)=0.
- A165155 (program): a(n) = 100*a(n-1)+ 11^(n-1) for n>0, a(0)=0.
- A165156 (program): n^(2*n-1)-(2*n-1)^n.
- A165157 (program): Zero followed by partial sums of A133622.
- A165162 (program): Triangle T(n,m) with 2n-1 entries per row, read by rows: the first n entries count down from n to 1, the remaining n-1 entries down from n-1 to 1.
- A165163 (program): Sequence is obtained from Catalan numbers (A000108) by taking the factorial of each digit and adding them up.
- A165186 (program): a(n) = Sum_{k=1..n} (k*(n-k) mod n).
- A165187 (program): a(n) = n^3*(n+1)^2*(n+2)/12.
- A165188 (program): Interleaving of A014125 and zero followed by A014125.
- A165189 (program): Partial sums of partial sums of (A001840 interleaved with zeros).
- A165190 (program): G.f.: 1/((1-x^4)*(1-x^5)).
- A165191 (program): Irregular triangle B(n,i) = i-th significant bit of Gray code of n.
- A165192 (program): a(0) = 1, a(1) = 2, a(3) = 3, a(n) = a(n-1) - a(n-3).
- A165195 (program): Rows of triangle A165194 tend to this sequence; generated from A000110.
- A165198 (program): Primes from integers by taking the factorial of each digit and adding them up.
- A165199 (program): a(n) is obtained by flipping every second bit in the binary representation of n starting at the second-most significant bit and on downwards.
- A165201 (program): Expansion of 1/(1-x*c(x)^3), c(x) the g.f. of A000108.
- A165202 (program): Expansion of (1+x)/(1 - x + x^2)^2.
- A165203 (program): Expansion of (1+x)*c(x)^3/(1-x*c(x)^3), c(x) the g.f. of A000108.
- A165204 (program): Hankel transform of A165203.
- A165205 (program): a(n) = C(2n-1,n) + C(2n+1,n+1) - C(0,n).
- A165206 (program): a(n) = (3-4*n)*F(2*n-2) + (4-7*n)*F(2*n-1).
- A165207 (program): Period 4: repeat [2, 2, 4, 4].
- A165211 (program): Period 8: repeat [0,1,0,1,1,0,1,0].
- A165220 (program): Numbers n such that 8*n+1 is a cube.
- A165221 (program): The Padovan sequence analog of the Fibonacci “rabbit” constant binary expansion. Starting with 0 and using the transitions 0->1,1->10,10->01 the subsequences 0,1,10,01,110,1001,01110,1101001,100101110,011101101001… are formed where each subsequence has P sub n ones and length P sub (n-1) binary digits, where P sub n is the n-th Padovan number. This sequence is the concatenation of all the subsequences. Also note that the n-th subsequence is the concatenation of the n-th-3 and n-th-2 subsequences.
- A165222 (program): a(n) = (2^(n+4)+1)*(2^n+1).
- A165224 (program): a(0)=1, a(1)=9, a(n) = 18*a(n-1) - 49*a(n-2) for n > 1.
- A165225 (program): a(0)=1, a(1)=5, a(n) = 10*a(n-1) - 5*a(n-2) for n > 1.
- A165226 (program): Numerator of 1 - A164555(n)/A027642(n).
- A165229 (program): a(n) = 12*a(n-1) - 6*a(n-2), with a(0)=1, a(1)=6.
- A165230 (program): a(0)=1, a(1)=7, a(n)=14*a(n-1)-7*a(n-2) for n>1 .
- A165231 (program): a(0)=1, a(1)=8, a(n)=16*a(n-1)-8*a(n-2) for n>1 .
- A165232 (program): a(0)=1, a(1)=9, a(n)=18*a(n-1)-9*a(n-2) for n>1 .
- A165233 (program): Signed denominators of terms in series expansion of cos(x)+sin(x).
- A165240 (program): Integers of the form (a+b+c+..+z)/z where (a,b,c,..,z) is a list of 2 or more distinct consecutive nonprimes.
- A165241 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,1,0,0,0,0,0,0,0,…] DELTA [1,0,1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A165242 (program): The larger member of the n-th twin prime pair, modulo 8.
- A165244 (program): The numbers commonly displayed with 7 segments in electric clocks, in ascending order of number of segments lit.
- A165246 (program): a(n) = (10^n + 53)/9
- A165247 (program): a(n) = (10^n + 71)/9.
- A165248 (program): Quintisection A061037(5*n+2).
- A165253 (program): Triangle T(n,k), read by rows given by [1,0,1,0,0,0,0,0,0,…] DELTA [0,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A165254 (program): a(n) = 9 + n^17.
- A165256 (program): Numbers whose number of distinct prime factors equals the number of digits in the number.
- A165257 (program): Triangle in which n-th row is binomial(n+k-1,k), for column k=1..n.
- A165259 (program): Sum of odd powers of 4 and 9 divided by 13
- A165263 (program): A sequence similar to the Fibonacci rabbit sequence for the Padovan sequence
- A165280 (program): If p and q are twin primes then pq + 1 is always divisible by 3, except for (p,q)=(3,5). Sequence gives values of (pq + 1)/3.
- A165281 (program): a(n) = (n+1)*(6*n^4 - 51*n^3 + 161*n^2 - 251*n + 251).
- A165283 (program): a(n) = (2*n + 1)*16^n.
- A165293 (program): Inverse of A038303, and generalization of A130595.
- A165294 (program): The larger member of a prime pair (p, p+100).
- A165295 (program): The larger member of a prime pair (p,p + 1000).
- A165310 (program): a(0)=1, a(1)=3, a(n) = 7*a(n-1) - 9*a(n-2) for n > 1.
- A165311 (program): a(0)=1, a(1)=4, a(n)=9*a(n-1)-16*a(n-2) for n>1.
- A165312 (program): a(0)=1, a(1)=5, a(n)=11*a(n-1)-25*a(n-2) for n>1.
- A165313 (program): Triangle T(n,k) = A091137(k-1) read by rows.
- A165314 (program): a(0)=1, a(1)=6, a(n)=13*a(n-1)-36*a(n-2) for n>1.
- A165316 (program): a(n) = the number of digits in the binary representation of n that each either precede and/or follow a similarly valued digit.
- A165317 (program): a(n) = the number of digits in the binary representation of n that each do not precede or follow a similarly valued digit.
- A165322 (program): a(0)=1, a(1)=7, a(n)=15*a(n-1)-49*a(n-2) for n>1.
- A165323 (program): a(0)=1, a(1)=8, a(n)=17*a(n-1)-64*a(n-2) for n>1.
- A165324 (program): a(0)=1, a(1)=9, a(n)= 19*a(n-1)-81*a(n-2) for n>1.
- A165326 (program): a(0)=a(1)=1, a(n) = -a(n-1) for n > 1.
- A165327 (program): E.g.f: Sum_{n>=0} 2^(n(n-1)) * exp(2^n*x) * x^n/n!.
- A165342 (program): a(n) = A061037(n+2)/A000265(n+4).
- A165349 (program): Primes p such that (p^2-1)/4-p is also prime.
- A165351 (program): Numerator of 3*n/2.
- A165352 (program): Primes of the form p + (p^2 - 1)/8, where p is also prime.
- A165353 (program): Primes p such that p+(p^2-1)/8 is a prime number.
- A165355 (program): a(n) = 3n + 1 if n is even, or a(n) = (3n + 1)/2 if n is odd.
- A165367 (program): Trisection a(n) = A026741(3n + 2).
- A165372 (program): Number of slanted n X 3 (i=1..n) X (j=i..3+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, and 4 in the lower right corner.
- A165378 (program): Number of slanted n X 4 (i=1..n) X (j=i..4+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.
- A165392 (program): Number of slanted 2 X n (i=1..2) X (j=i..n+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.
- A165394 (program): Number of slanted 2 X n (i=1..2) X (j=i..n+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 3 neighbors with the same value.
- A165402 (program): a(n) = (10^n*2 - 11)/9.
- A165403 (program): The positions of zeros in A163898 and A163899.
- A165404 (program): The positions of zeros in the top row of A163898 (and A163899).
- A165405 (program): a(0)=1, a(1)=3,a(n)=6*a(n-2)-a(n-1).
- A165406 (program): Sequence A165404 shown in binary, or equivalently, sequence A163901 in quaternary base.
- A165407 (program): Expansion of 1/(1-x-x^3*c(x^3)), c(x) the g.f. of A000108.
- A165410 (program): Hankel transform of the transform of 2^n given by A165409.
- A165412 (program): Divisors of 2520.
- A165413 (program): a(n) is the number of distinct lengths of runs in the binary representation of n.
- A165415 (program): a(n) = the smallest positive integer that contains more digits written in binary than n has written in binary, and which does not contain binary n as a substring in its binary representation.
- A165420 (program): a(1) = 1, a(2) = 2, a(n) = product of the previous terms for n >= 3.
- A165421 (program): a(1) = 1, a(2) = 3, a(n) = product of the previous terms for n >= 3.
- A165422 (program): a(1) = 1, a(2) = 4, a(n) = product of the previous terms for n >= 3.
- A165431 (program): A transform of the central binomial coefficients.
- A165433 (program): A transform of the double factorial numbers A001147.
- A165443 (program): a(n) = ( 16^(2*n+1) + 81^(2*n+1) )/97.
- A165447 (program): T(n,k) = n^4 - 2*k^2*n^2 + k^4 = A120070(n, k)^2.
- A165451 (program): Sum of factorial of digits is prime.
- A165453 (program): Linear interpolation of the sequence that maps an entry of A002378 to the corresponding entry of A006331.
- A165457 (program): a(n) = (2*n+1)!*(2*n+3)/3.
- A165458 (program): a(0)=1, a(1)=4, a(n) = 12*a(n-2) - a(n-1).
- A165470 (program): a(0)=1, a(1)=5, a(n) = 20*a(n-2) - a(n-1).
- A165478 (program): Positions of zeros in A165477.
- A165479 (program): a(n) = Least i in range [A165478(n),A165478(n+1)] for which abs(A165477(i)) gets the maximum value in that range.
- A165491 (program): a(0)=1, a(1)=6, a(n) = 30*a(n-2) - a(n-1).
- A165505 (program): a(0)=1, a(1)=7, a(n) = 42*a(n-2) - a(n-1).
- A165506 (program): a(0) = 1, a(1) = 8, a(n) = 56*a(n-2) - a(n-1).
- A165507 (program): Triangle T(n,m) read by rows: numerator of 1/(1+n-m)^2 - 1/m^2.
- A165510 (program): a(0)=1, a(1)=9, a(n) = 72*a(n-2) - a(n-1).
- A165511 (program): a(0)=1, a(1)=10, a(n) = 90*a(n-2) - a(n-1).
- A165513 (program): Trapezoidal numbers.
- A165516 (program): Perfect squares (A000290) that can be expressed as the sum of three consecutive triangular numbers (A000217).
- A165517 (program): Indices of the least triangular numbers (A000217) for which three consecutive triangular numbers sum to a perfect square (A000290).
- A165518 (program): Perfect squares (A000290) that can be expressed as the sum of four consecutive triangular numbers (A000217).
- A165520 (program): Antidiagonal writing from three rows trio A165351,A165355,A165367 (first,second and third trisections of A026741).
- A165530 (program): Number of permutations of length n which avoid the patterns 4321 and 3142.
- A165538 (program): Number of permutations of length n which avoid the patterns 4312 and 3142.
- A165543 (program): Number of permutations of length n which avoid the patterns 3241 and 4321.
- A165552 (program): a(1) = 1, and then a(n) is sum of k*a(k) where k<n and k divides n.
- A165553 (program): a(n) = (3/2)*(1+(-3)^(n-1)).
- A165556 (program): A symmetric version of the Josephus problem read modulo 2.
- A165557 (program): Primes of the form (p^2-1)/4-p where p are also primes.
- A165559 (program): Product of the arithmetic derivatives from 2 to n.
- A165560 (program): The arithmetic derivative of n, modulo 2.
- A165562 (program): Numbers n for which n+n’ is prime, n’ being the arithmetic derivative of n.
- A165563 (program): a(n) = 1 + 2*n + n^2 + 2*n^3 + n^4.
- A165568 (program): a(n) = -1 - 2*n + n^2 + 2*n^3 + n^4.
- A165613 (program): Primes of the form 1 + prime(k) + (prime(k+1))^2, any k.
- A165618 (program): a(n) = binomial(n+8,8) - 1.
- A165620 (program): Riordan array ((1-x)/(1-x^4),x/(1+x^2)).
- A165621 (program): Riordan array (c(x^2)*(1+xc(x^2)), xc(x^2)).
- A165622 (program): a(n)=(-4)*a(n-1)+8 with a(0)=1.
- A165625 (program): a(n)=(5/3)*(1+2*(-5)^(n-1)).
- A165634 (program): Start with x=1 and repeat: if x is a prime number then (append i and then x, with x=prime(i)) else (only append x), continue with x:=x+1.
- A165635 (program): Primes of the form (p^2 - 3)/2 where p is also prime.
- A165636 (program): a(n) = A091137(n)/2^n.
- A165638 (program): a(n)=(6/7)*(2+5*(-6)^(n-1)).
- A165639 (program): a(n)=(7/4)*(1+3*(-7)^(n-1)).
- A165640 (program): Number of distinct multisets of n integers, each of which is -2, +1, or +3, such that the sum of the members of each multiset is 3.
- A165641 (program): A091137(n) / A001316(n) .
- A165652 (program): Number of disconnected 2-regular graphs on n vertices.
- A165662 (program): Period 5: repeat 4,4,8,6,8.
- A165663 (program): Decimal expansion of 3 + sqrt(3).
- A165664 (program): First digit of the decimal expansion of (n^2-2)/7 after the decimal point.
- A165665 (program): a(n) = (3*2^n - 2) * 2^n.
- A165669 (program): First digit of the decimal expansion of (n^2+2)/7 after the decimal point.
- A165674 (program): Triangle generated by the asymptotic expansions of the E(x,m=2,n).
- A165675 (program): Triangle read by rows. T(n, k) = (n - k + 1)! * H(k, n - k), where H are the hyperharmonic numbers. For 0 <= k <= n.
- A165676 (program): Fourth right hand column of triangle A165674
- A165677 (program): Fifth right hand column of triangle A165674
- A165678 (program): Sixth right hand column of triangle A165674.
- A165679 (program): Seventh right hand column of triangle A165674
- A165680 (program): Triangle of the divisors of the coefficients of triangles A138771 and A165675
- A165682 (program): Primes p such that 3*p*(p-1)+1 is also prime.
- A165683 (program): Primes of form 3*p*(p-1)+1 with p also a prime.
- A165684 (program): Dimension of the space of Siegel cusp forms of genus 2 and dimension 2n (associated with full modular group Gamma_2).
- A165686 (program): Dimension of the space of Siegel cusp forms of genus 2 and weight 2k which are not Saito-Kurokawa lifts of forms of genus 1.
- A165717 (program): Integers of the form k*(5+k)/4.
- A165718 (program): Integers of the form k*(k+7)/6.
- A165719 (program): Integers of the form k*(k+9)/8.
- A165720 (program): Integers of the form k*(k+11)/10.
- A165721 (program): Integers of the form k*(k+13)/12.
- A165722 (program): Positive integers k such that the sum of decimal digits of (16^k - 1) equals 6*k.
- A165723 (program): The (d+1)th digit after the decimal point in the decimal representation of 1/n, where d is the number of digits of n.
- A165725 (program): Largest divisor of n coprime to 30. I.e., a(n) = max { k | gcd(n, k) = k and gcd(k, 30) = 1 }.
- A165728 (program): If we divide the sequence into these subsequences, the pattern is obvious. {{1,1}, {0,1}, {1,1}}, {{0,1,0,1}, {1,1,1,1}, {0,1,0,1}}, {{1,1,1,1,1,1,1,1}, {0,1,0,1,0,1,0,1}, {1,1,1,1,1,1,1,1}}, {{0,1,0,1,0,1,0,1,0,1,0,1,0,1,0}, {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}, {0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1}}, …
- A165734 (program): Period 2: repeat 6,30.
- A165735 (program): Surviving integers under the double-count Josephus problem (see A054995), modulo 3.
- A165743 (program): The greatest common divisor of n and 210.
- A165746 (program): a(n) = 3 - 2*3^n.
- A165747 (program): a(n) = 1-2n.
- A165748 (program): a(n) = (8/9)*(2+7*(-8)^(n-1)).
- A165749 (program): a(n) = (9/5)*(1+4*(-9)^(n-1)).
- A165750 (program): a(n) = (10/11)*(2+9*(-10)^(n-1)).
- A165751 (program): a(n) = 4 - 3*2^n.
- A165752 (program): a(n) = (8-5*4^n)/3.
- A165753 (program): Number of trailing zeros in sequence of factorials of Fibonacci numbers.
- A165754 (program): a(n) = nimsum(n+(n+1)+(n+2)).
- A165755 (program): a(n) = (5-3*5^n)/2.
- A165758 (program): a(n) = (12-7*6^n)/5.
- A165759 (program): a(n) = (7-4*7^n)/3.
- A165760 (program): a(n) = (16-9*8^n)/7.
- A165775 (program): n + (least square >= n), i.e., n + A048761(n).
- A165776 (program): n + (least square > n), i.e., n + A048761(n+1).
- A165781 (program): a(n) = (2^A002326(n)-1)/(2*n+1).
- A165783 (program): a(n) = A002326(n-1) + A000120(A165781(n-1)).
- A165789 (program): a(n) is the smallest positive integer k that when written in binary, and leading 0’s of k are ignored, contains the reversal of the digits of binary n.
- A165792 (program): a(0)=1, a(n) = n*(a(n-1)+2).
- A165793 (program): a(0)=1, a(n)=n*(a(n-1)-2).
- A165795 (program): Array A(n, k) = numerator of 1/n^2 - 1/k^2 with A(0,k) = 1 and A(n,0) = -1, read by antidiagonals.
- A165797 (program): a(n) = n^( sigma(n) - tau(n) ).
- A165798 (program): a(n) = 65*n^2.
- A165800 (program): Powers of 50.
- A165801 (program): f(n), f(f(n)), … are all prime, where f(n) = (n-1)/2. Stop when f(…f(n)…) is less than 4.
- A165804 (program): Numbers of the form i*8^j-1 (i=1..7, j >= 0).
- A165805 (program): Integers that start a trajectory x -> A008619(x) which contains only primes until terminating at 2 or 3.
- A165806 (program): a(n) = 15n^2 + 3n + 1.
- A165810 (program): Primes p such that 18*p+1 is also a prime.
- A165811 (program): Primes of the form 18*p+1, where p is also a prime.
- A165813 (program): a(n) = n*(a(n-1)+3), a(0)=1.
- A165814 (program): a(n)=n*(a(n-1)-3), a(0)=1.
- A165817 (program): Number of compositions (= ordered integer partitions) of n into 2n parts.
- A165824 (program): Totally multiplicative sequence with a(p) = 3.
- A165825 (program): Totally multiplicative sequence with a(p) = 4.
- A165826 (program): Totally multiplicative sequence with a(p) = 5.
- A165827 (program): Totally multiplicative sequence with a(p) = 6.
- A165828 (program): Totally multiplicative sequence with a(p) = 7.
- A165829 (program): Totally multiplicative sequence with a(p) = 8.
- A165830 (program): Totally multiplicative sequence with a(p) = 9.
- A165831 (program): Totally multiplicative sequence with a(p) = 10.
- A165832 (program): Totally multiplicative sequence with a(p) = 11.
- A165833 (program): Totally multiplicative sequence with a(p) = 12.
- A165834 (program): Totally multiplicative sequence with a(p) = 13.
- A165835 (program): Totally multiplicative sequence with a(p) = 14.
- A165836 (program): Totally multiplicative sequence with a(p) = 15.
- A165837 (program): Totally multiplicative sequence with a(p) = 16.
- A165838 (program): Totally multiplicative sequence with a(p) = 17.
- A165839 (program): Totally multiplicative sequence with a(p) = 18.
- A165840 (program): Totally multiplicative sequence with a(p) = 19.
- A165841 (program): Totally multiplicative sequence with a(p) = 20.
- A165842 (program): Totally multiplicative sequence with a(p) = 21.
- A165843 (program): Totally multiplicative sequence with a(p) = 22.
- A165844 (program): Totally multiplicative sequence with a(p) = 23.
- A165845 (program): Totally multiplicative sequence with a(p) = 24.
- A165846 (program): Totally multiplicative sequence with a(p) = 25.
- A165847 (program): Totally multiplicative sequence with a(p) = 26.
- A165848 (program): Totally multiplicative sequence with a(p) = 27.
- A165849 (program): Totally multiplicative sequence with a(p) = 28.
- A165850 (program): Totally multiplicative sequence with a(p) = 29.
- A165851 (program): Totally multiplicative sequence with a(p) = 30.
- A165852 (program): Totally multiplicative sequence with a(p) = 31.
- A165853 (program): Totally multiplicative sequence with a(p) = 32.
- A165854 (program): Totally multiplicative sequence with a(p) = 33.
- A165855 (program): Totally multiplicative sequence with a(p) = 34.
- A165856 (program): Totally multiplicative sequence with a(p) = 35.
- A165857 (program): Totally multiplicative sequence with a(p) = 36.
- A165858 (program): Totally multiplicative sequence with a(p) = 37.
- A165859 (program): Totally multiplicative sequence with a(p) = 38.
- A165860 (program): Totally multiplicative sequence with a(p) = 39.
- A165861 (program): Totally multiplicative sequence with a(p) = 40.
- A165862 (program): Totally multiplicative sequence with a(p) = 41.
- A165863 (program): Totally multiplicative sequence with a(p) = 42.
- A165864 (program): Totally multiplicative sequence with a(p) = 43.
- A165865 (program): Totally multiplicative sequence with a(p) = 44.
- A165866 (program): Totally multiplicative sequence with a(p) = 45.
- A165867 (program): Totally multiplicative sequence with a(p) = 46.
- A165868 (program): Totally multiplicative sequence with a(p) = 47.
- A165869 (program): Totally multiplicative sequence with a(p) = 48.
- A165870 (program): Totally multiplicative sequence with a(p) = 49.
- A165871 (program): Totally multiplicative sequence with a(p) = 50.
- A165872 (program): Totally multiplicative sequence with a(p) = - 2.
- A165886 (program): a(n) = A165641(n+1)/A165641(n).
- A165897 (program): a(n) = a(n-1) + largest proper divisor of a(n-1), a(1)=4.
- A165900 (program): Values of Fibonacci polynomial n^2 - n - 1.
- A165901 (program): a(0)=0, a(1)=1, a(n) = a(n-1) + 2^(n-3)*a(n-2).
- A165902 (program): a(0)=0, a(1)=1, a(n) = a(n-1) + 3^(n-3)*a(n-2).
- A165903 (program): a(n) = (a(n-1)^2 + a(n-2)^2 + a(n-1)*a(n-2))/a(n-3) with three initial ones.
- A165904 (program): Somos-4 recurrence with a(i)=2^i for 0<=i<=3.
- A165905 (program): Somos-4 recurrence with a(0)=1, a(1)=2, a(2)=4, a(3)=16
- A165907 (program): Minimal m for packing the first n primes in a prime(n) X m rectangle
- A165922 (program): Decimal expansion of 2*sqrt(3)/(9*Pi).
- A165928 (program): a(n) = 2^(n^2)*(2^(2n+1)/3 + 1/3).
- A165930 (program): a(1) = 1, for n > 1: a(n) = tau(sum of the previous terms) where tau(k) = number of the divisors of k.
- A165933 (program): Least integer, k, whose value is n in A165413.
- A165935 (program): a(n) = (-1)^(n-1)*n*(4n^2-5)^2.
- A165937 (program): G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)*x^n/n ).
- A165938 (program): a(n) = A002203(n^2) for n>=1.
- A165943 (program): Heptasection A061037(7*n+2).
- A165944 (program): Primes of the form p^2 +3p + 1, where p is also a prime.
- A165947 (program): Primes of the form 2q + 3 where q is composite.
- A165949 (program): a(n) = A027762(n)/A165734(n).
- A165951 (program): a(n) = (Sum of the quadratic non-residues of prime(n) - Sum of the quadratic residues of prime(n)) / prime(n)
- A165952 (program): Decimal expansion of 2*sqrt(3)/(3*Pi).
- A165955 (program): n-th odd nonprime plus n-th even nonprime.
- A165957 (program): Product of the digits of the n-th nonprime.
- A165958 (program): The digits on a number pad from lower right to upper left.
- A165960 (program): Number of permutations of length n without modular 3-sequences.
- A165961 (program): Number of circular permutations of length n without 3-sequences.
- A165966 (program): Triangular numbers that are sums of twin prime pairs.
- A165968 (program): Number of pairings disjoint to a given pairing, and containing a given pair not in the given pairing.
- A165971 (program): The n-th odd nonprime minus the n-th even nonprime.
- A165972 (program): Nonprimes k such that the sum of the smallest and largest divisor of k is prime.
- A165978 (program): Largest prime factor of number formed from a(n-1) with a 1 added at the end, a(1)=2.
- A165983 (program): Period 16: repeat 1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4.
- A165984 (program): Number of ways to put n indistinguishable balls into n^3 distinguishable boxes.
- A165986 (program): Even semiprimes n such that (the largest prime factor of n) + 4 is prime.
- A165988 (program): First trisection of A022998.
- A165993 (program): a(n) = sum_{j=1..prime(n)-1} floor (j^2/prime(n)).
- A165994 (program): a(n) is the number of nonzero values of floor (j^2/prime(n)), over 1 <= j < prime(n).
- A165998 (program): Denominators of Taylor series expansion of 1/(3*x)*log((1+x)/(1-x)^2)
- A166005 (program): Primes p such that 8*p+15 is also a prime.
- A166006 (program): Distance from the origin using the binary expansion of Pi to walk the number line: Start at the origin; subtract one for each ‘0’ digit, and add one for each ‘1’ digit.
- A166008 (program): Number of ones in the binary representation of the average of twin prime pairs.
- A166009 (program): Primes of the form 7 + 2*p, where p is a prime.
- A166010 (program): a(n) = prime(n)^2-4.
- A166011 (program): Least common multiple of prime(n)-3 and prime(n)+3.
- A166012 (program): a(n) = 2*(A000045(n)-(n mod 2)) + 1 + (n mod 2).
- A166013 (program): Inverse permutation to A138606.
- A166021 (program): a(n) = 2*A000124(A003056(n-1)) if A002262(n-1)=0, otherwise a(n-1)+1.
- A166022 (program): a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +3*a(n-4) -2*a(n-5) for n > 4, with initial values as shown.
- A166023 (program): a(n) = 6*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
- A166024 (program): Define dsf(n) = A045503(n) = n_1^{n_1}+n_2^{n_2}+n_3^{n_3} + n_m^{n_m}, where {n_1,n_2,n_3,…n_m} is the list of the decimal digits of n. dsf(421845123) = 16780890 and dsf(16780890) = 421845123, so these 2 numbers make a loop for the function dsf.
- A166025 (program): a(0) = 6, a(1) = 17, a(n+1) = a(n) + a(n-1) for n>0.
- A166027 (program): a(n) = 6*a(n-2) for n > 2; a(1) = 4, a(2) = 1.
- A166033 (program): a(n) = 11/4 +11*n/2 + 29*(-1)^n/4.
- A166035 (program): a(n) = (3^n+6*(-4)^n)/7.
- A166036 (program): a(n) = (4^n+8*(-5)^n)/9.
- A166037 (program): Numbers that are the sum of 2 successive nonprimes A141468.
- A166039 (program): Sums of three consecutive nonprimes A141468.
- A166060 (program): a(n) = 4*3^n - 3*2^n.
- A166061 (program): 19-rough numbers: positive integers that have no prime factors less than 19.
- A166063 (program): 23-rough numbers: positive integers that have no prime factors less than 23.
- A166065 (program): Triangle, read by rows, given by [0,1,1,0,0,0,0,0,0,0,…] DELTA [2,-1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A166067 (program): Fibonacci sequence beginning 1, 69.
- A166070 (program): Sorted sequence of primes and multiply perfect numbers.
- A166074 (program): a(n) = n^2 - [largest Fibonacci number <= n^2].
- A166077 (program): a(n)=2^(n(3n-1)/2).
- A166078 (program): Expansion of (3(1-x)-sqrt(1+6x-7x^2))/(2(1-x)(1-2x)).
- A166079 (program): Given a row of n payphones, all initially unused, how many people can use the payphones, assuming (1) each always chooses one of the most distant payphones from those in use already, (2) the first person takes a phone at the end, and (3) no people use adjacent phones?
- A166080 (program): Nonprimes of the form (k^2+1)/2.
- A166081 (program): Natural numbers that not are the sum of two distinct primes.
- A166101 (program): Integers k such that A166100(k)/A005408(k) is not an integer.
- A166102 (program): Odd numbers k such that A166100((k-1)/2)/k is not an integer.
- A166103 (program): Squares of A166104.
- A166104 (program): Natural numbers whose prime factors are all congruent to 3 or 5 mod 6 (i.e., are in the sequence A045410).
- A166105 (program): Quadratic recurrence from Sylvester’s sequence, but starting with a(0)=1 and a(1)=2.
- A166106 (program): a(n) = a(n-1) + a(n-2) + F(n), with a(0) = 0, a(1) = 1, a(2) = a(1) + a(0), a(3) = a(2) + a(1), a(4) = a(3) + a(2) + 2.
- A166114 (program): a(n) = (6-(-4)^n)/5.
- A166117 (program): a(0)=0, a(1)=1, a(2)=2 and a(n) = a(n-1) - 2a(n-2) + a(n-3).
- A166118 (program): Fixed points of the mapping f(x) = (x + 2^x) mod (17 + x).
- A166119 (program): a(n)=A165966(n)/12.
- A166120 (program): a(n) = A027642(n-1) / A089026(n).
- A166122 (program): a(n) = (7-(-5)^n)/6.
- A166123 (program): If n is prime, a(n) = 1; otherwise, a(n) is gcd(n, d) where d is the denominator of the (n-1)-th Bernoulli number.
- A166124 (program): Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,…] DELTA [2,-1,0,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A166125 (program): Decimal expansion of sqrt(229).
- A166126 (program): Decimal expansion of 1/(imaginary part of (15+2*I)^(1/2))^2.
- A166127 (program): Minimum value of j such that floor(j^2 / prime(n)) > 0.
- A166132 (program): a(n) = 1 + (4*9^n - 9*4^n) / 5.
- A166135 (program): Number of possible paths to each node that lies along the edge of a cut 4-nomial tree, that is rooted one unit from the cut.
- A166136 (program): a(n) = n*(n+3)/2 + 7.
- A166137 (program): a(n) = 5*n*(n+1)/2 - 4.
- A166138 (program): Trisection A022998(3n+1).
- A166139 (program): Triangle T(n,k) read by rows. A080305(A126988(n,k)) if k|n, 0 otherwise.
- A166140 (program): Product of the nonzero elements of the n-th row of A166139.
- A166142 (program): Row products of A166141; Product of such divisors of n that are squarefree and have an even number of prime factors.
- A166143 (program): a(n) = 3*n^2 + 3*n - 5.
- A166144 (program): a(n) = (11*n^2 + 11*n - 20)/2.
- A166146 (program): a(n) = (7*n^2 + 7*n - 12)/2.
- A166147 (program): a(n) = 4n^2 + 4n - 7.
- A166148 (program): a(n) = (9*n^2 + 9*n - 16)/2.
- A166149 (program): a(n) = (5^n + 10*(-6)^n)/11.
- A166150 (program): a(n) = 5n^2 + 5n - 9.
- A166151 (program): (5n^2 + 5n - 6)/2.
- A166152 (program): a(n) = (6^n+12*(-7)^n)/13.
- A166153 (program): a(n) = (7^n+14*(-8)^n)/15.
- A166154 (program): 7*n*(n+1)/2 - 5.
- A166155 (program): Numbers n such that number of divisors of n + number of perfect partitions of (n-1) is prime.
- A166157 (program): a(n) = (8^n+16*(-9)^n)/17.
- A166160 (program): a(n) = (n-th odd prime + n-th odd nonprime)/2 - 1.
- A166168 (program): G.f.: exp( Sum_{n>=1} Lucas(n^2)*x^n/n ) where Lucas(n) = A000204(n).
- A166169 (program): a(n) = Lucas(n^2) = A000204(n^2) for n >= 1.
- A166173 (program): Digit sum of n-th twin prime pair.
- A166189 (program): Number of 3 X 3 X 3 triangular nonnegative integer arrays with all sums of an element and its neighbors <= n.
- A166213 (program): Number of 5 X 5 X 5 triangular nonnegative integer arrays, symmetric under 120 degree rotation, with all sums of an element and its neighbors <= n.
- A166226 (program): Bell number n modulo n.
- A166228 (program): Alternating sum of large Schroeder numbers.
- A166229 (program): Expansion of (1-2x-sqrt(1-8x+8x^2))/(2x).
- A166231 (program): a(n) = 2^C(n+1,2)*A006012(n).
- A166232 (program): a(n) = A166231(n)/4^n.
- A166236 (program): Absolute value of (n-th odd prime minus n-th odd nonprime)/2.
- A166237 (program): Differences between consecutive products of two distinct primes: a(n) = A006881(n+1) - A006881(n).
- A166238 (program): Horizontal para-Narayana sequence: says which column of 3rd-order Zeckendorf array (starting column count at 0) contains n.
- A166242 (program): Sequence generated from A014577, the dragon curve.
- A166245 (program): Numbers n such that the Collatz trajectory of n (iterate T(k)=k/2 if k is even, (3k+1)/2 if k is odd, A014682, starting at n and stopping if you reach 1) never exceeds n.
- A166247 (program): Number of perfect partitions of n-1 plus sum of remainders of n mod k, for k=1,2,3,..,n.
- A166248 (program): a(n) is the absolute value of n minus sum of all the remainders modulo the numbers below n.
- A166249 (program): a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4) for n>3, a(0)=a(1)=1, a(2)=0, a(3)=2.
- A166250 (program): a(n) = n-1 plus the largest proper divisor of n.
- A166253 (program): String substitution 0 -> 01110, 1 -> 10001, started with 1.
- A166257 (program): Odd numbers not of the form prime(k) + phi(prime(k)).
- A166260 (program): a(n) = A089026(n) - 1.
- A166265 (program): Numbers of the form 1+x^2+y^2, x, y integers >= 1.
- A166266 (program): Number of 1’s in binary expansion of A000110(n).
- A166267 (program): Number of 1’s in the binary representation of A000129(n).
- A166279 (program): Triangle, read by rows: T(0,0) = 1, T(n,k) = T(n-1,k-1) (mod 2) + T(n-1,k) (mod 2), T(n,k) = 0 if k < 0 or k > n.
- A166280 (program): Stirling2 triangle mod 2, T(n,k) = A008277(n,k) mod 2.
- A166281 (program): Number of perfect partitions of the nonprimes A018252.
- A166282 (program): Matrix inverse of Sierpinski’s triangle (A047999, Pascal’s triangle mod 2).
- A166287 (program): Number of peak plateaux in all Dyck paths of semilength n with no UUU’s and no DDD’s (U=(1,1), D=(1,-1)).
- A166289 (program): Number of Dyck paths with no UUU’s and no DDD’s, of semilength n and having no UDUD’s (U=(1,1), D=(1,-1)).
- A166290 (program): Number of UDUD’s in all Dyck paths of semilength n with no UUU’s and no DDD’s (U=(1,1), D=(1,-1)).
- A166294 (program): Number of peaks at even level in all Dyck paths of semilength n with no UUU’s and no DDD’s, (U=(1,1), D=(1,-1)). These Dyck paths are counted by the secondary structure numbers (A004148).
- A166297 (program): Number of UUDUDD’s starting at level 0 in all Dyck paths of semilength n with no UUU’s and no DDD’s (U=(1,1), D=(1,-1)).
- A166300 (program): Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no UUDD’s starting at level 0.
- A166304 (program): Third trisection of A022998.
- A166305 (program): Even semiprimes k such that the largest prime factor + 8 is a prime. Also semiprimes k such that k+16 is semiprime.
- A166306 (program): Denominator of Bernoulli_n multiplied by the sum of the associated inverse primes in the Staudt-Clausen theorem, n=1, 2, 4, 6, 8, 10,…
- A166311 (program): Numbers whose sum of digits is 11.
- A166312 (program): Number of 1’s in binary expansion of A000326(n).
- A166314 (program): Number of 1’s in binary expansion of A000124(n).
- A166329 (program): Products of squares of 2 successive primes.
- A166333 (program): The largest prime that divides A027642(n) (the denominator of the Bernoulli number B_n), or 1 if A027642(n) is 1.
- A166334 (program): a(n) = (3*n)!/(2^n*n!).
- A166335 (program): Exponential Riordan array [1+x*sinh(x), x].
- A166336 (program): Expansion of (1 - 4*x + 7*x^2 - 4*x^3 + x^4)/(1 - 7*x + 17*x^2 - 17*x^3 + 7*x^4 - x^5).
- A166337 (program): a(n)=(2n+0^n)*C(4n,2n).
- A166338 (program): a(n) = (4*n)!/n!.
- A166350 (program): Table T(n,m) = m! read by rows.
- A166356 (program): Expansion of e.g.f. 1 + x*arctanh(x), even powers only.
- A166357 (program): Exponential Riordan array [1+x*arctanh(x), x].
- A166358 (program): Row sums of exponential Riordan array [1+x*arctanh(x), x], A166357.
- A166359 (program): Diagonal sums of the exponential Riordan array [1+x*arctanh(x), x], A166357.
- A166360 (program): Triangle of Narayana numbers mod 2, T(n,k) = A001263(n,k) mod 2.
- A166361 (program): Scale degrees of the roots of chords in a traditional “twelve-bar blues” in Western music.
- A166362 (program): a(n) = phi(nonprime(n)).
- A166370 (program): Numbers whose sum of digits is 17.
- A166373 (program): Triangle read by rows for floor(j^2 / n) with n >= 2 and 1<=j<n.
- A166375 (program): a(n) = sum (floor (j^2/n)) taken over 1 <= j <= n-1.
- A166380 (program): Diagonal sums of exponential Riordan array [1+x^2*sec(x),x], A166378.
- A166381 (program): a(n) = Sum_{j>n} floor(n^2/j).
- A166387 (program): a(n) = sum (floor (j^2/n), 1 <= j <= n-1) - floor ((n-1)(n-2)/3), n >= 2.
- A166389 (program): Multiples of 7 whose reversal + 1 is also a multiple of 7.
- A166390 (program): Multiples of 13 whose reversal + 1 is also a multiple of 13.
- A166394 (program): Multiples of 7 whose reversal - 1 is also a multiple of 7.
- A166397 (program): Multiples of 13 whose reversal - 1 is also a multiple of 13.
- A166401 (program): Positive integers n where (the largest divisor of n that is <= sqrt(n)) divides (the smallest divisor of n that is >= sqrt(n)).
- A166444 (program): a(0) = 0, a(1) = 1 and for n > 1, a(n) = sum of all previous terms.
- A166445 (program): Hankel transform of A025276.
- A166446 (program): Period 12: repeat [1,1,1,1,0,0,-1,-1,-1,-1,0,0].
- A166447 (program): a(n) = n*round(sqrt(n)).
- A166448 (program): Sum of first n primes minus next prime.
- A166450 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
- A166452 (program): Binomial transform of A166242
- A166453 (program): Triangle read by rows, square of Sierpinski’s gasket, (A047999)^2
- A166454 (program): Triangle read by rows: T(n, k) = (1/2)*(A007318(n,k) - A047999(n,k)).
- A166456 (program): Row sums of triangle A166455.
- A166457 (program): Numbers n such that n*100+1 is prime.
- A166458 (program): Numbers k such that 10*k - (-1)^k is prime.
- A166459 (program): Numbers whose sum of digits is 19.
- A166460 (program): Numbers k such that k + (-1)^k is not prime.
- A166464 (program): a(n) = (3+2n+6n^2+4n^3)/3.
- A166465 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
- A166466 (program): Trisection a(n) = A000265(3n).
- A166469 (program): Number of divisors of n which are not multiples of consecutive primes.
- A166470 (program): a(n) = 2^F(n+1)*3^F(n), where F(n) is the n-th Fibonacci number, A000045(n).
- A166474 (program): a(1)=1; a(2)=2; for n>2, a(n)=a(n-1)+A000217(n-1)*a(n-2).
- A166479 (program): Lesser of twin primes, written in base 6.
- A166480 (program): Greater of twin primes, written in base 6.
- A166481 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 7.
- A166482 (program): a(n) = Sum_{k=0..n} binomial(n+k,2k)*Fibonacci(2k+1).
- A166486 (program): Periodic sequence [0,1,1,1] of length 4.
- A166492 (program): Table of numerators of A120070(n,m)/A002260(n,m), 1 <= m < n.
- A166494 (program): Irregular triangle T(n,k) = greatest common divisor of n-th row terms of A143753.
- A166496 (program): Prime plus the next composite.
- A166502 (program): The n-th power of the product prime(n)*prime(n+1) of 2 successive primes.
- A166514 (program): Zig-zag function for first two columns of a matrix (take numbers in consecutive pairs).
- A166515 (program): Partial sum of A166514.
- A166516 (program): A product of consecutive doubled Fibonacci numbers.
- A166517 (program): a(n) = (3 + 5*(-1)^n + 6*n)/4.
- A166519 (program): a(n) = 1 + 2*(-1)^n + 2*n.
- A166520 (program): a(n) = (10*n + 11*(-1)^n + 5)/4.
- A166521 (program): a(n) = (6*n + 7*(-1)^n + 3)/2.
- A166522 (program): a(n) = 7*n - a(n-1), with a(1) = 1.
- A166523 (program): a(n) = 8*n - a(n-1), with n>1, a(1)=1.
- A166524 (program): a(n) = 9*n - a(n-1), with n>1, a(1)=1.
- A166525 (program): a(n) = 10*n - a(n-1), with n>1, a(1)=1.
- A166526 (program): a(n) = 12*n - a(n-1), with n>1, a(1)=1.
- A166527 (program): Complement of A076537.
- A166536 (program): A product of consecutive doubled Fibonacci numbers.
- A166539 (program): a(n) = (10*n + 7*(-1)^n + 5)/4.
- A166542 (program): a(n) = 6*n - a(n-1), with n>1, a(1)=2.
- A166544 (program): a(n) = 7*n - a(n-1), with n>1, a(1)=2.
- A166545 (program): a(n) = 13*n - a(n-1), (with a(1)=13).
- A166546 (program): Natural numbers n such that d(n) + 1 is prime.
- A166547 (program): Primes of the form 100*n+7.
- A166549 (program): The number of halving steps of the Collatz 3x+1 map to reach 1 starting from 2n-1.
- A166552 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 4.
- A166554 (program): a(0)=1, a(n) = n*(a(n-1)-1) for n>0.
- A166555 (program): Triangle read by rows, Sierpinski’s gasket, A047999 * (1,2,4,8,…) diagonalized.
- A166556 (program): Triangle read by rows, A000012 * A047999
- A166560 (program): Primes of the form 100*n+9.
- A166563 (program): Numbers n such that 12*n+5 is not prime.
- A166569 (program): Numbers n such that 12*n+7 is not prime.
- A166570 (program): Numbers n such that 12*n+11 is not prime.
- A166574 (program): If p, q are successive primes, and there is a number k with p < k <= q such that r = p+k is a prime, then r is in the sequence.
- A166575 (program): Primes p>=5 with the property: if Prime(k)<p/2<Prime(k+1), then p>=Prime(k)+ Prime(k+1)
- A166577 (program): Inverse binomial transform of A166517.
- A166578 (program): a(n) = a(n-3) + 2^(n-4) with a(1) = 1, a(2) = 2, a(3) = 1.
- A166586 (program): Totally multiplicative sequence with a(p) = p - 2 for prime p.
- A166587 (program): A signed variant of the Motzkin numbers.
- A166588 (program): Partial sums of A097331; binomial transform of A166587.
- A166589 (program): Totally multiplicative sequence with a(p) = p-3 for prime p.
- A166590 (program): Totally multiplicative sequence with a(p) = p+2 for prime p.
- A166591 (program): Totally multiplicative sequence with a(p) = p+3 for prime p.
- A166592 (program): Hankel transform of A166588(n-1).
- A166593 (program): Partial sums of A166592.
- A166594 (program): Maximal prime gap q-p encountered from 0 to least prime > n.
- A166595 (program): The number of vertices of a hypercube modulo the number of largest-dimensional surface tiles, in the first fourteen cases of the residue being greater than the dimension number.
- A166597 (program): Let p = largest prime <= n, with p(0)=p(1)=0, and let q = smallest prime > n; then a(n) = q-p.
- A166598 (program): a(n) = 5*n - a(n-1), with n>1, a(1)=5.
- A166602 (program): Numbers k such that Sum_{i=1..k} i^2 divides Product_{i=1..k} i^2.
- A166621 (program): a(n) = 10*n - a(n-1), with n>1, a(1)=5.
- A166624 (program): Totally multiplicative sequence with a(p) = 3p for prime p.
- A166625 (program): Totally multiplicative sequence with a(p) = 4p for prime p.
- A166626 (program): Totally multiplicative sequence with a(p) = 5p for prime p.
- A166627 (program): Totally multiplicative sequence with a(p) = 6p for prime p.
- A166628 (program): Totally multiplicative sequence with a(p) = 7p for prime p.
- A166629 (program): Totally multiplicative sequence with a(p) = 8p for prime p.
- A166630 (program): Totally multiplicative sequence with a(p) = 9p for prime p.
- A166631 (program): Totally multiplicative sequence with a(p) = 10p for prime p.
- A166632 (program): Totally multiplicative sequence with a(p) = 2*(p-1) for prime p.
- A166633 (program): Totally multiplicative sequence with a(p) = 3*(p-1) for prime p.
- A166634 (program): Totally multiplicative sequence with a(p) = 4*(p-1) for prime p.
- A166635 (program): Totally multiplicative sequence with a(p) = 5*(p-1) for prime p.
- A166636 (program): Totally multiplicative sequence with a(p) = 6*(p-1) for prime p.
- A166637 (program): Totally multiplicative sequence with a(p) = 7*(p-1) for prime p.
- A166638 (program): Totally multiplicative sequence with a(p) = 8*(p-1) for prime p.
- A166639 (program): a(n) = 6*n + 3 + 4*(-1)^n.
- A166640 (program): Totally multiplicative sequence with a(p) = 9*(p-1) for prime p.
- A166641 (program): Totally multiplicative sequence with a(p) = 10*(p-1) for prime p.
- A166642 (program): Totally multiplicative sequence with a(p) = 2*(p+1) for prime p.
- A166643 (program): Totally multiplicative sequence with a(p) = 3*(p+1) for prime p.
- A166644 (program): Totally multiplicative sequence with a(p) = 4*(p+1) for prime p.
- A166645 (program): Totally multiplicative sequence with a(p) = 5*(p+1) for prime p.
- A166646 (program): Totally multiplicative sequence with a(p) = 6*(p+1) for prime p.
- A166647 (program): Totally multiplicative sequence with a(p) = 7*(p+1) for prime p.
- A166648 (program): Totally multiplicative sequence with a(p) = 8*(p+1) for prime p.
- A166649 (program): Totally multiplicative sequence with a(p) = 9*(p+1) for prime p.
- A166650 (program): Totally multiplicative sequence with a(p) = 10*(p+1) for prime p.
- A166651 (program): Totally multiplicative sequence with a(p) = 2p-1 for prime p.
- A166652 (program): Totally multiplicative sequence with a(p) = 3p-1 for prime p.
- A166653 (program): Totally multiplicative sequence with a(p) = 4p-1 for prime p.
- A166654 (program): Totally multiplicative sequence with a(p) = 5p-1 for prime p.
- A166655 (program): Totally multiplicative sequence with a(p) = 6p-1 for prime p.
- A166656 (program): Totally multiplicative sequence with a(p) = 7p-1 for prime p.
- A166657 (program): Totally multiplicative sequence with a(p) = 8p-1 for prime p.
- A166658 (program): Totally multiplicative sequence with a(p) = 9p-1 for prime p.
- A166659 (program): Totally multiplicative sequence with a(p) = 10p-1 for prime p.
- A166660 (program): Totally multiplicative sequence with a(p) = 2p+1 for prime p.
- A166661 (program): Totally multiplicative sequence with a(p) = 3p+1 for prime p.
- A166662 (program): Totally multiplicative sequence with a(p) = 4p+1 for prime p.
- A166663 (program): Totally multiplicative sequence with a(p) = 5p+1 for prime p.
- A166664 (program): Totally multiplicative sequence with a(p) = 6p+1 for prime p.
- A166665 (program): Totally multiplicative sequence with a(p) = 7p+1 for prime p.
- A166666 (program): Totally multiplicative sequence with a(p) = 8p+1 for prime p.
- A166667 (program): Totally multiplicative sequence with a(p) = 9p+1 for prime p.
- A166668 (program): Totally multiplicative sequence with a(p) = 10p+1 for prime p.
- A166669 (program): Totally multiplicative sequence with a(p) = 3p-2 for prime p.
- A166670 (program): Totally multiplicative sequence with a(p) = 5p-2 for prime p.
- A166671 (program): Totally multiplicative sequence with a(p) = 7p-2 for prime p.
- A166672 (program): Totally multiplicative sequence with a(p) = 9p-2 for prime p.
- A166673 (program): Totally multiplicative sequence with a(p) = 3p+2 for prime p.
- A166674 (program): Totally multiplicative sequence with a(p) = 5p+2 for prime p.
- A166675 (program): Totally multiplicative sequence with a(p) = 7p+2 for prime p.
- A166676 (program): Totally multiplicative sequence with a(p) = 9p+2 for prime p.
- A166677 (program): a(n)= n*(a(n-1)+4), a(0)=1.
- A166680 (program): a(n) = n*(a(n-1)-4), a(0) = 1.
- A166684 (program): Numbers n such that d(n)<4.
- A166685 (program): Odd numbers that are the sum of two consecutive nonprimes.
- A166687 (program): Numbers of the form x^2 + y^2 + 1, x, y integers.
- A166692 (program): Triangle T(n,k) read by rows: T(n,k) = 2^(k-1), k>0. T(n,0) = (n+1) mod 2.
- A166694 (program): A transform of the large Schroeder numbers, A006318.
- A166695 (program): Alternating smallest odd/even number not in list followed by that number of consecutive odd/even numbers, sequence commencing with 1.
- A166696 (program): A transform of A103210.
- A166697 (program): A “Morgan Voyce” transform of A103210.
- A166698 (program): Totally multiplicative sequence with a(p) = a(p-1) - 1 for prime p.
- A166711 (program): Permutation of the integers: two positives, one negative.
- A166720 (program): Trisection A165342(3n).
- A166724 (program): a(n) = PrimePi(A166546(n)).
- A166725 (program): a(n) = (2*n+1)*25^n.
- A166726 (program): Nonnegative integers with English names ending in “o”.
- A166727 (program): Positive integers with English names ending in “r”.
- A166728 (program): Positive integers with English names ending in “x”.
- A166729 (program): Positive integers with English names ending in “t”.
- A166730 (program): Positive integers with English names ending in “y”.
- A166731 (program): Positive integers with English names ending in “d”.
- A166733 (program): Numbers n with the property that the concatenation of the trivial divisors of n (i.e., 1 and n) is a prime.
- A166741 (program): E.g.f.: exp(2*arcsin(x)).
- A166743 (program): a(n) = (2^p - p^2 - 1)/6 where p = prime(n).
- A166748 (program): E.g.f.: exp(6*arcsin(x)).
- A166750 (program): a(n) = (A001147(n))^3 = 2^(3*n)*GAMMA(n+1/2)^3/Pi^(3/2).
- A166752 (program): Interleave A007583 and A000012.
- A166753 (program): Partial sums of A166752.
- A166754 (program): a(n) = 4*A061547(n+1) - 3*A166753(n).
- A166756 (program): Number of nX2 1..3 arrays containing at least one of each value, and all equal values connected.
- A166761 (program): Number of nX3 1..2 arrays containing at least one of each value, and all equal values connected.
- A166776 (program): Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.
- A166781 (program): Number of nX3 1..2 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.
- A166796 (program): Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
- A166805 (program): Number of n X 4 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
- A166808 (program): Number of n X 5 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
- A166810 (program): Number of n X 6 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
- A166812 (program): Number of n X 7 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
- A166813 (program): Number of n X 8 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
- A166814 (program): Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in increasing order.
- A166830 (program): Number of n X 3 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nonincreasing order.
- A166842 (program): Number of n X 3 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in decreasing order.
- A166849 (program): Primes with digital root 1, 2, 4 or 8.
- A166863 (program): a(1)= 1; a(2)= 5; thereafter a(n)= a(n-1) + a(n-2) + 5.
- A166864 (program): Primes p that divide n! - 1 for some n > 1 other than p-2.
- A166866 (program): Mixed fractal sequence mf(n). Mix fractals A158405, A002260.
- A166867 (program): a(n) = Pell(n+3) - Jacobsthal(n+4).
- A166868 (program): Convolution of Jacobsthal(n+2) and Pell(n+1).
- A166871 (program): Permutation of the integers: 3 positives, 2 negatives.
- A166873 (program): a(n) = a(n-1) + 12*n for n > 1; a(1) = 1.
- A166876 (program): a(n) = a(n-1) + Fibonacci(n), a(1)=1983.
- A166879 (program): G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)/2*x^n/n ).
- A166894 (program): G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^n * x^k] * x^n/n ), an integer series in x.
- A166895 (program): a(n) = Sum_{k=0..[n/2]} C(n-k,k)^(n-k)*n/(n-k), n>=1.
- A166896 (program): G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k] * x^n/n ), an integer series in x.
- A166897 (program): a(n) = Sum_{k=0..[n/2]} C(n-k,k)^3*n/(n-k), n>=1.
- A166898 (program): G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^4 * x^k] * x^n/n ), an integer series in x.
- A166899 (program): a(n) = Sum_{k=0..[n/2]} C(n-k,k)^4*n/(n-k), n>=1.
- A166911 (program): a(n) = (9 + 14*n + 12*n^2 + 4*n^3)/3.
- A166914 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 21, a(1) = 340.
- A166915 (program): a(n) = 20*a(n-1) - 64*a(n-2) - 45 for n>1; a(0) = 399, a(1) = 5695.
- A166916 (program): a(n) = 20*a(n-1) - 64*a(n-2) - 15 for n > 1; a(0) = 357, a(1) = 5525.
- A166917 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 85, a(1) = 1364.
- A166918 (program): Triangle T(n,k) read by rows: T(n,0) = n mod 2. T(n,k) = 2^(k-1), 0<k<=n.
- A166920 (program): a(n) = 2^n - (1 + (-1)^n)/2.
- A166922 (program): E.g.f. exp(-x)*exp(exp(2*x)/2-1/2)/2 + 1/2.
- A166923 (program): Digital root of prime(n)^2.
- A166925 (program): Digital root of square of n-th triangular number.
- A166926 (program): A000004 preceded by 1, 2, 4.
- A166927 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 18.
- A166929 (program): Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some coprime integers a, b, c.
- A166931 (program): Numbers n with property that n mod k is k-1 for all k = 2..9.
- A166939 (program): Numerators of partial sums (n+1)/n (not sorted).
- A166941 (program): Product plus sum of four consecutive nonnegative numbers.
- A166942 (program): One fifth of product plus sum of five consecutive nonnegative numbers.
- A166943 (program): One third of product plus sum of six consecutive nonnegative numbers.
- A166944 (program): a(1)=2; a(n) = a(n-1) + gcd(n, a(n-1)) if n is even, a(n) = a(n-1) + gcd(n-2, a(n-1)) if n is odd.
- A166946 (program): a(n) = 1 if n is a rounded multiple of phi (1.618033989…), the larger golden ratio value; else a(n) = 0.
- A166948 (program): The count of smallest prime factors in n-th composite.
- A166949 (program): The count of largest prime factors in n-th composite.
- A166952 (program): G.f. satisfies: A(x) = theta_3(x*A(x)) where Jacobi theta_3(x) = 1 + 2*Sum_{n>=1} x^(n^2).
- A166956 (program): a(n) = 2^n +(-1)^n - 2.
- A166957 (program): a(n) = 841*n^3 + 261*n^2 + 28*n + 1.
- A166959 (program): Numbers congruent to (12,32) mod 44.
- A166963 (program): Number of permutations in S_{2n} avoiding 123 and 1432 whose matrices are 180-degree symmetric.
- A166965 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 19.
- A166966 (program): Eigensequence of A047999, Sierpinski’s gasket.
- A166976 (program): Array of A002450 in the top row and higher-order differences in subsequent rows, read by antidiagonals.
- A166977 (program): Jacobsthal-Lucas numbers A014551, except a(0) = 0.
- A166978 (program): a(n) = 4*( 1-(-1)^n) -2^n.
- A166982 (program): Natural numbers with number of perfect partitions equal to a perfect power.
- A166983 (program): The n-th composite minus the number of its divisors.
- A166984 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 20.
- A166985 (program): Primes of the form phi(n)/2.
- A166986 (program): a(n) = 2*floor((n+2)/log(2)) - 4.
- A166989 (program): G.f.: A(x) = 1/(1 - 2*x - 7*x^2 - 2*x^3 + x^4).
- A166990 (program): G.f.: A(x) = exp( Sum_{n>=1} A000172(n)*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
- A166991 (program): G.f.: A(x) = exp( Sum_{n>=1} A000172(n)*x^n/(2*n) ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
- A166992 (program): G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/n ) where A005260(n) = Sum_{k=0..n} C(n,k)^4.
- A166993 (program): G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/(2*n) ), where A005260(n) = Sum_{k=0..n} C(n,k)^4.
- A167001 (program): Least possible nonnegative coefficients of x^n in G(x)^(2^n), n>=0, for an integer series G(x) such that G’(0)=G(0)=1; the G(x) that satisfies this condition equals the g.f. of A167000.
- A167004 (program): Least possible nonnegative coefficients of x^n in G(x)^(3^n), n>=0, such that G(x) is an integer series with G’(0)=G(0)=1; the G(x) that satisfies this condition equals the g.f. of A167003.
- A167006 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, n*k) ).
- A167007 (program): G.f.: A(x) = exp( Sum_{n>=1} A167010(n)*x^n/n ) where A167010(n) = Sum_{k=0..n} binomial(n,k)^n.
- A167008 (program): a(n) = Sum_{k=0..n} C(n,k)^k.
- A167009 (program): a(n) = Sum_{k=0..n} C(n^2, n*k).
- A167010 (program): a(n) = Sum_{k=0..n} C(n,k)^n.
- A167020 (program): a(n) = 1 iff 6n-1 is prime.
- A167021 (program): a(n) = 1 iff 6n+1 is prime.
- A167022 (program): Expansion of sqrt(1 - 2*x - 3*x^2) in powers of x.
- A167024 (program): Triangle read by rows: T(n, m) = binomial(n, m)* Sum_{k=0..m} binomial(n, k) for 0 <= m <= n.
- A167028 (program): Number of terms in the expansion of the determinant of a skew-symmetric matrix of order n.
- A167030 (program): a(n) = (2^n - (-1)^n - 3)/3.
- A167031 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.
- A167032 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 1; a(0) = 1, a(1) = 21.
- A167033 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 1; a(0) = 1, a(1) = 22.
- A167034 (program): Triangle t(n,m)= (m+1)^n*binomial(n,m) if m <= n/2, otherwise t(n,m) = t(n,n-m).
- A167040 (program): Triangle T(n, k) = (n-k)^n * binomial(n, n-k) for n < 2*k, k^n * binomial(n, k) for n >= 2*k with T(n, 0) = T(n, n) = 1, read by rows.
- A167050 (program): Squarefree numbers with as many decimal digits as distinct prime factors.
- A167051 (program): Start at 1, then add the first term (which is one here) plus 1 for the second term; then add the second term plus 2 for the third term; then add the third term to the sum of the first and second term; this gives the fourth term. Restart the sequence by adding 1 to the fourth term, etc. (From a sixth grade math extra credit assignment)
- A167055 (program): Numbers n such that 12*n + 5 is prime.
- A167056 (program): Numbers n such that 12*n + 7 is prime.
- A167057 (program): Numbers n such that 12*n + 11 is prime.
- A167060 (program): Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}}
- A167120 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 2; a(0) = 1, a(1) = 22, a(2) = 376.
- A167121 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 2; a(0) = 1, a(1) = 22, a(2) = 377.
- A167122 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 2; a(0) = 1, a(1) = 22, a(2) = 378.
- A167129 (program): n^7 mod 21.
- A167130 (program): Primes of the form A002808(n) + A062502(n+1).
- A167131 (program): Numbers k such that A002808(k) - A144925(k) is prime.
- A167132 (program): Gaps between twin prime pairs.
- A167134 (program): Primes congruent to {2, 3, 5, 7} mod 11.
- A167135 (program): Primes congruent to {2, 3, 5, 7, 11} mod 12.
- A167136 (program): a(n) = b(n)-th highest positive integer not equal to any a(k), 1 <= k <= n-1, where b(n) = noncomposite numbers = A008578(n).
- A167140 (program): Self-convolution of A155200.
- A167149 (program): 10000-gonal numbers: a(n) = n + 4999 * n * (n-1).
- A167153 (program): Numbers not appearing in A167152.
- A167154 (program): Numbers where terms in A167153 change parity: a(n)+1 is in A167153, but a(n)-1 is not.
- A167155 (program): Exponential primorial constant sum( 1/A140319(k), k>=0 )
- A167156 (program): Number of n-vertex 4-hedrites.
- A167166 (program): a(n) = n^7 mod 16.
- A167167 (program): A001045 with a(0) replaced by -1.
- A167170 (program): a(6) = 14, for n >= 7, a(n) = a(n-1) + gcd(n, a(n-1)).
- A167171 (program): Squarefree semiprimes together with primes.
- A167172 (program): Triangle T(n,k) read by rows: T(n,k) = binomial(n, k) + A140356(n, k) - 1.
- A167175 (program): Numbers with a nonprime number of prime divisors (counted with multiplicity).
- A167176 (program): n^3 mod 9.
- A167179 (program): The number of additional armies one receives in Parker Brothers’ (now part of Hasbro) game of Risk for turning in the n-th set of three different or alike cards.
- A167180 (program): a(n) = pi(n) plus the number of nonprimes less than prime(n).
- A167181 (program): Squarefree numbers such that all prime factors are == 3 mod 4.
- A167182 (program): a(0)=1, a(1)=2; for n>=2, a(n) = 2^A042950(n-2).
- A167184 (program): Smallest prime power >= n that is not prime.
- A167185 (program): Largest prime power <= n that is not prime.
- A167192 (program): Triangle read by rows: T(n,k) = (n-k)/gcd(n,k), 1 <= k <= n.
- A167193 (program): a(n) = (1/3)*(1 - (-2)^n + 3*(-1)^n ) = (-1)^(n+1)*A167030(n).
- A167194 (program): Triangle read by rows. A130713 in the columns.
- A167195 (program): a(2)=3, for n>=3, a(n)=a(n-1)+gcd(n, a(n-1)).
- A167196 (program): Triangle T(n,k) read by rows: matrix inverse of A106246.
- A167197 (program): a(6) = 7, for n >= 7, a(n) = a(n - 1) + gcd(n, a(n - 1))
- A167198 (program): Fractal sequence of the interspersion A083047.
- A167199 (program): First column of A167196.
- A167204 (program): Triangle read by rows in which row n lists the first 2^(n-1) terms of A003602.
- A167205 (program): a(n) = (3^n+1)/(3-(-1)^n).
- A167206 (program): Binomial transform of A164555.
- A167207 (program): Numbers that are not divisible by a smaller number that is a square greater than 1
- A167208 (program): Append two digits, each increasing by one modulo 10 from the last digit the of the positive integers. 0 -> 12 1 -> 123 2 -> 234 .. 9 -> 901 10 -> 1012.
- A167211 (program): Numbers n such that number of perfect partitions of n-1 divides n.
- A167214 (program): a(n) = (sum of first n primes) * n.
- A167227 (program): Number of 2-self-hedrites with n vertices.
- A167230 (program): The matrix exponential of Sierpiński’s triangle (A047999) scaled by exp(-1).
- A167231 (program): Append three digits, each increasing by one modulo 10 from the last digit the of the nonnegative integers. 0 -> 123, 1 -> 1234 2 -> 2345, … , 9 -> 9012, 10 -> 10123, etc.
- A167237 (program): Lower trim of the Wythoff fractal sequence, A003603.
- A167238 (program): Number of ways to partition a 2*n X 2 grid into 4 connected equal-area regions
- A167239 (program): Number of ways to partition a 5*n X 2 grid into 5 connected equal-area regions
- A167268 (program): Janet’s sequence: Number of elements for each successively filled electronic subshell of an atom.
- A167269 (program): Triangle read by rows, Pascal’s triangle columns interleaved with 1’s.
- A167270 (program): a(n) = Fibonacci(n + 2) + floor(n/2).
- A167274 (program): Triangle read by rows, = 2*A047999 - A047999^(-1); = twice Sierpinski’s gasket minus the inverse of Sierpinski’s gasket.
- A167275 (program): Row sums of triangle A167274 (a variant of Gould’s sequence A001316).
- A167277 (program): Largest nonprime<n-th single (or isolated or non-twin) prime.
- A167278 (program): Smallest prime>n-th single (or isolated or non-twin) prime.
- A167280 (program): Period length 12: 0,0,1,2,4,7,4,8,7,4,8,5 (and repeat).
- A167291 (program): a(n) = A137505(2n) + A137505(2n+1).
- A167294 (program): Totally multiplicative sequence with a(p) = 2*(p-2) for prime p.
- A167295 (program): Totally multiplicative sequence with a(p) = 3*(p-2) for prime p.
- A167296 (program): Totally multiplicative sequence with a(p) = 4*(p-2) for prime p.
- A167297 (program): Totally multiplicative sequence with a(p) = 5*(p-2) for prime p.
- A167298 (program): Totally multiplicative sequence with a(p) = 6*(p-2) for prime p.
- A167299 (program): Totally multiplicative sequence with a(p) = 7*(p-2) for prime p.
- A167300 (program): Totally multiplicative sequence with a(p) = 8*(p-2) for prime p.
- A167301 (program): Totally multiplicative sequence with a(p) = 9*(p-2) for prime p.
- A167302 (program): Totally multiplicative sequence with a(p) = 10*(p-2) for prime p.
- A167303 (program): Totally multiplicative sequence with a(p) = 2*(p+2) for prime p.
- A167304 (program): Totally multiplicative sequence with a(p) = 3*(p+2) for prime p.
- A167305 (program): Totally multiplicative sequence with a(p) = 4*(p+2) for prime p.
- A167306 (program): Totally multiplicative sequence with a(p) = 5*(p+2) for prime p.
- A167307 (program): Totally multiplicative sequence with a(p) = 6*(p+2) for prime p.
- A167308 (program): Totally multiplicative sequence with a(p) = 7*(p+2) for prime p.
- A167309 (program): Totally multiplicative sequence with a(p) = 8*(p+2) for prime p.
- A167310 (program): Totally multiplicative sequence with a(p) = 9*(p+2) for prime p.
- A167311 (program): Totally multiplicative sequence with a(p) = 10*(p+2) for prime p.
- A167312 (program): Totally multiplicative sequence with a(p) = 2*(p-3) for prime p.
- A167313 (program): Totally multiplicative sequence with a(p) = 3*(p-3) for prime p.
- A167314 (program): Totally multiplicative sequence with a(p) = 4*(p-3) for prime p.
- A167315 (program): Totally multiplicative sequence with a(p) = 5*(p-3) for prime p.
- A167316 (program): Totally multiplicative sequence with a(p) = 6*(p-3) for prime p.
- A167317 (program): Totally multiplicative sequence with a(p) = 7*(p-3) for prime p.
- A167318 (program): Totally multiplicative sequence with a(p) = 8*(p-3) for prime p.
- A167319 (program): Totally multiplicative sequence with a(p) = 9*(p-3) for prime p.
- A167320 (program): Totally multiplicative sequence with a(p) = 10*(p-3) for prime p.
- A167321 (program): Totally multiplicative sequence with a(p) = 2*(p+3) for prime p.
- A167322 (program): Totally multiplicative sequence with a(p) = 3*(p+3) for prime p.
- A167323 (program): Totally multiplicative sequence with a(p) = 4*(p+3) for prime p.
- A167324 (program): Totally multiplicative sequence with a(p) = 5*(p+3) for prime p.
- A167325 (program): Totally multiplicative sequence with a(p) = 6*(p+3) for prime p.
- A167326 (program): Totally multiplicative sequence with a(p) = 7*(p+3) for prime p.
- A167327 (program): Totally multiplicative sequence with a(p) = 8*(p+3) for prime p.
- A167328 (program): Totally multiplicative sequence with a(p) = 9*(p+3) for prime p.
- A167329 (program): Totally multiplicative sequence with a(p) = 10*(p+3) for prime p.
- A167330 (program): Totally multiplicative sequence with a(p) = 2*(2p-1) = 4p-2 for prime p.
- A167331 (program): Totally multiplicative sequence with a(p) = 2*(3p-1) = 6p-2 for prime p.
- A167332 (program): Totally multiplicative sequence with a(p) = 2*(4p-1) = 8p-2 for prime p.
- A167333 (program): Totally multiplicative sequence with a(p) = 2*(5p-1) = 10p-2 for prime p.
- A167334 (program): Totally multiplicative sequence with a(p) = 2*(2p+1) = 4p+2 for prime p.
- A167335 (program): Totally multiplicative sequence with a(p) = 2*(3p+1) = 6p+2 for prime p.
- A167336 (program): Totally multiplicative sequence with a(p) = 2*(4p+1) = 8p+2 for prime p.
- A167337 (program): Totally multiplicative sequence with a(p) = 2*(5p+1) = 10p+2 for prime p.
- A167338 (program): Totally multiplicative sequence with a(p) = p*(p+1) = p^2+p for prime p.
- A167339 (program): Totally multiplicative sequence with a(p) = p*(p-2) = p^2-2p for prime p.
- A167340 (program): Totally multiplicative sequence with a(p) = p*(p+2) = p^2+2p for prime p.
- A167341 (program): Totally multiplicative sequence with a(p) = p*(p-3) = p^2-3p for prime p.
- A167342 (program): Totally multiplicative sequence with a(p) = p*(p+3) = p^2+3p for prime p.
- A167343 (program): Totally multiplicative sequence with a(p) = (p-1)^2 = p^2-2p+1 for prime p.
- A167344 (program): Totally multiplicative sequence with a(p) = (p-1)*(p+1) = p^2-1 for prime p.
- A167345 (program): Totally multiplicative sequence with a(p) = (p-1)*(p-2) = p^2-3p+2 for prime p.
- A167346 (program): Totally multiplicative sequence with a(p) = (p-1)*(p+2) = p^2+p-2 for prime p.
- A167347 (program): Totally multiplicative sequence with a(p) = (p-1)*(p-3) = p^2-4p+3 for prime p.
- A167349 (program): Totally multiplicative sequence with a(p) = (p+1)^2 = p^2+2p+1 for prime p.
- A167350 (program): Totally multiplicative sequence with a(p) = (p+1)*(p-2) = p^2-p-2 for prime p.
- A167351 (program): Totally multiplicative sequence with a(p) = (p+1)*(p+2) = p^2+3p+2 for prime p.
- A167352 (program): Totally multiplicative sequence with a(p) = (p+1)*(p-3) = p^2-2p-3 for prime p.
- A167353 (program): Totally multiplicative sequence with a(p) = (p+1)*(p+3) = p^2+4p+3 for prime p.
- A167354 (program): Totally multiplicative sequence with a(p) = (p-2)^2 = p^2-4p+4 for prime p.
- A167355 (program): Totally multiplicative sequence with a(p) = (p-2)*(p+2) = p^2-4 for prime p.
- A167356 (program): Totally multiplicative sequence with a(p) = (p-2)*(p-3) = p^2-5p+6 for prime p.
- A167357 (program): Totally multiplicative sequence with a(p) = (p-2)*(p+3) = p^2+p-6 for prime p.
- A167358 (program): Totally multiplicative sequence with a(p) = (p+2)^2 = p^2+4p+4 for prime p.
- A167359 (program): Totally multiplicative sequence with a(p) = (p+2)*(p-3) = p^2-p-6 for prime p.
- A167360 (program): Totally multiplicative sequence with a(p) = (p+2)*(p+3) = p^2+5p+6 for prime p.
- A167361 (program): Totally multiplicative sequence with a(p) = (p-3)^2 = p^2-6p+9 for prime p.
- A167362 (program): Totally multiplicative sequence with a(p) = (p-3)*(p+3) = p^2-9 for prime p.
- A167363 (program): Totally multiplicative sequence with a(p) = (p+3)^2 = p^2+6p+9 for prime p.
- A167366 (program): Triangle read by rows, 2*A047999 - A097806 (signed) = twice Sierpinski’s gasket - the signed pair sum operator.
- A167367 (program): a(n) = sigma(n!!) where n!! is A006882(n).
- A167371 (program): Triangle, read by rows, given by [0,1,-1,0,0,0,0,0,0,0,0,…] DELTA [1,0,-1,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A167373 (program): Expansion of (1+x)*(3*x+1)/(1+x+x^2).
- A167374 (program): Triangle, read by rows, given by [ -1,1,0,0,0,0,0,0,0,…] DELTA [1,0,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A167375 (program): a(n)=3*a(n-1)-a(n-2) with a(0)=1, a(1)=3, a(2)=11.
- A167376 (program): Complement of the partition numbers.
- A167379 (program): Let p and q be twin primes, excluding the pair (3,5). Then p+q is always divisible by 6 and we set a(n) = (p+q)/6.
- A167380 (program): a(1)=1, a(2)=2, and continued periodically with 4, 5, 1, -4, -5, -1 .
- A167381 (program): The numbers read down the left-center column of an arrangement of the natural numbers in square blocks.
- A167385 (program): a(n)= sum_{i=7..n+6} A000931(i).
- A167386 (program): a(n) = (-1)^n*n*(n+1)*(2*n-5)/6.
- A167387 (program): a(n) = (-1)^(n+1) * n*(n-1)*(n-4)*(n+1)/12.
- A167388 (program): Prime numbers ending in the prime number 31.
- A167389 (program): (arg(exp(-w)) + Im(w)) / (2*Pi), with w = W(n,-log(2)/2)/log(2), where W is the Lambert W function.
- A167392 (program): Characteristic function of partition numbers.
- A167393 (program): Characteristic function of the range of A000009.
- A167394 (program): Largest single or isolated prime < n-th single or isolated composite.
- A167397 (program): n-th single (or isolated or non-twin) prime minus n.
- A167398 (program): a(n) = Fibonacci(11*n).
- A167403 (program): Number of decimal numbers having n or fewer digits and having the sum of their digits equal to n.
- A167406 (program): Sequence a(n) gives the number of ways to seat 2n people around a circular table so that person i does not sit across from person n+i for any 1 <= i <= n.
- A167407 (program): T(m,n) is -m if n=0, 1 elsewhere.
- A167418 (program): G.f.: 1/(1 - 4*x + 5*x^2 - 100*x^3).
- A167420 (program): 2^n mod 14.
- A167421 (program): 2^n mod 22.
- A167422 (program): Expansion of (1+x)*c(x), c(x) the g.f. of A000108.
- A167423 (program): Hankel transform of a simple Catalan convolution.
- A167425 (program): 2^n mod 26.
- A167426 (program): a(n) = 2^n mod 28.
- A167427 (program): Largest non-isolated nonprime < n-th non-isolated (or twin) prime.
- A167430 (program): Fractal sequence of the interspersion A163255.
- A167431 (program): Riordan array (1-4x+4x^2, x(1-2x)).
- A167432 (program): Riordan array (c(2x)^2,xc(2x)), c(x) the g.f. of A000108.
- A167433 (program): Row sums of the Riordan array (1-4x+4x^2, x(1-2x)) (A167431).
- A167434 (program): Diagonal sums of the Riordan array (1-4*x+4*x^2, x*(1-2*x)) (A167431).
- A167435 (program): Hankel transform of A084076.
- A167436 (program): 3rd Fibonacci polynomial evaluated at n^n.
- A167440 (program): 5th GegenbauerC polynomial evaluated at powers of 2 (multiplied by 5).
- A167441 (program): Prime numbers ending in the prime number 71.
- A167442 (program): Prime numbers ending in the prime number 11.
- A167443 (program): Prime numbers ending in the prime number 41.
- A167444 (program): Fibonacci(n)!!.
- A167445 (program): Prime numbers ending in the prime number 61.
- A167449 (program): a(0)=1; a(1)=1; for a>1, a(n)=a(n-1)+((n-1)^3)*a(n-2).
- A167461 (program): Anagram multiples of 123456789.
- A167462 (program): Primes p such that 2*p-5 is composite.
- A167463 (program): a(n) = n mod 15.
- A167465 (program): n^5 mod 16.
- A167467 (program): a(n) = 25*n^3 - n*(5*n+1)/2 + 1.
- A167469 (program): a(n) = 3*n*(5*n-1)/2.
- A167471 (program): Janet periodic table of the elements and structured hexagonal diamond numbers. a(n) = A166911(2n) + A166911(2n+1).
- A167477 (program): Expansion of (1-3x+5x^2-x^3)/(1-3x+x^2)^2.
- A167478 (program): Expansion of (1-2x+6x^2-x^3)/(1-3x+x^2)^2.
- A167479 (program): Convolution of the Catalan numbers A000108(n) and (-2)^n.
- A167480 (program): a(n)= primepi(n) if n is prime, otherwise a(n)=prime(n).
- A167481 (program): Convolution of the central binomial coefficients A000984(n) and (-2)^n.
- A167482 (program): a(n)=n-1 if n is prime, otherwise a(n)=n+1.
- A167484 (program): For n people on one side of a river, the number of ways they can all travel to the opposite side following the pattern of 2 sent, 1 returns, 2 sent, 1 returns, …, 2 sent.
- A167487 (program): a(n) = n*(n + 3)/2 + 8.
- A167489 (program): Product of run lengths in binary representation of n.
- A167493 (program): a(1) = 2; thereafter a(n) = a(n-1) + gcd(n, a(n-1)) if n is odd, and a(n) = a(n-1) + gcd(n-2, a(n-1)) if n is even.
- A167498 (program): a(n) = 6+32*n^2+8*n*(7+8*n^2)/3.
- A167499 (program): a(n) = n*(n+3)/2 + 6.
- A167512 (program): Number of Simple Alternating Transit (SAT) mazes with exactly two extreme values.
- A167515 (program): The sum over the divisors of n, except the maximum-prime-power divisors collected in A008475.
- A167520 (program): Positions of nonzero digits in this sequence, when all terms are concatenated.
- A167527 (program): n^5 mod 49.
- A167528 (program): a(n) = n^5 mod 50.
- A167531 (program): a(n) = Sum_{d divides n} d*(n/d)^(d-1).
- A167533 (program): a(n) = 71*n - a(n-1) for n>0, a(0)=12.
- A167534 (program): a(n) = 79*n - a(n-1) for n>0, a(0)=9.
- A167539 (program): a(n) = Sum_{k=0..[n/2]} C(n-k,k)^2 * n/(n-k), n>=1.
- A167541 (program): a(n) = -(n - 4)*(n - 5)*(n - 12)/6.
- A167542 (program): Natural numbers, swapped in pairs, with decimal digits reversed.
- A167543 (program): a(n) = (n-5)*(n-6)*(n-7)*(n-16)/24.
- A167544 (program): a(n) = (n-3)*(n-8)/2.
- A167545 (program): n^6 mod 16.
- A167547 (program): The fourth row of the ED1 array A167546.
- A167548 (program): The fifth row of the ED1 array A167546
- A167549 (program): The sixth row of the ED1 array A167546.
- A167550 (program): The a(n,n+1) diagonal of the ED1 array A167546
- A167554 (program): The second left hand column of triangle A167552.
- A167555 (program): The third left hand column of triangle A167552.
- A167557 (program): The lower left triangle of the ED1 array A167546.
- A167558 (program): The second right hand column of triangle A167557.
- A167559 (program): The row sums of triangle A167557.
- A167561 (program): The fourth row of the ED2 array A167560.
- A167562 (program): The fifth row of the ED2 array A167560.
- A167566 (program): The third left hand column of triangle A167565.
- A167569 (program): The lower left triangle of the ED2 array A167560.
- A167570 (program): The third right hand column of triangle A167569.
- A167571 (program): The row sums of triangle A167569.
- A167573 (program): The third row of the ED3 array A167572.
- A167574 (program): The fourth row of the ED3 array A167572.
- A167575 (program): The fifth row of the ED3 array A167572.
- A167576 (program): The first column of the ED3 array A167572.
- A167577 (program): The second column of the ED3 array A167572.
- A167578 (program): The third column of the ED3 array A167572.
- A167581 (program): The second left hand column of triangle A167580.
- A167585 (program): a(n) = 12*n^2 - 8*n + 9.
- A167586 (program): The fourth row of the ED4 array A167584.
- A167588 (program): The second column of the ED4 array A167584.
- A167589 (program): The third column of the ED4 array A167584.
- A167592 (program): The second left hand column of triangle A167591.
- A167596 (program): The number of isolated nonprimes between the nonisolated prime and the isolated prime.
- A167607 (program): Sum of cousin prime pairs.
- A167610 (program): Primes that are the sum of three consecutive nonprimes.
- A167611 (program): Nonprimes that are the sum of two consecutive nonprimes.
- A167614 (program): a(n) = (n^2 + 3*n + 8)/2.
- A167616 (program): a(n) = Fibonacci(n) - 5.
- A167617 (program): G.f.: x^2*(3+3*x+x^2) / ( (2*x+1) * (1+x) * (1+x+x^2) * (x^2-x+1) ) .
- A167618 (program): Convolution of A010054 with A052343.
- A167622 (program): n^3 mod n-th prime.
- A167623 (program): n^3 mod (n-th prime squared).
- A167624 (program): a(n) = n^6 mod 32.
- A167626 (program): Prime numbers ending in the prime number 101.
- A167628 (program): n^11 mod 13.
- A167632 (program): Smallest m such that A033183(m) = n.
- A167635 (program): Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no peaks at odd level.
- A167638 (program): Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no peaks at even level.
- A167655 (program): Riordan array (1-u,u) where u=x/(1+x+x^2).
- A167657 (program): Product of n-th block of identical consecutive values of A000720.
- A167660 (program): Chocolate dove bar numerator: a(n) = (Sum_{k=0..floor(n/2)} k*binomial(n+k,k)*binomial(n,n-2*k)) + (Sum_{k=0..ceiling(n/2)} k*binomial(n+k-1,k-1)*binomial(n,n-2*k+1)).
- A167666 (program): Triangle read by rows given by [1,1,-4,2,0,0,0,0,0,0,0,…] DELTA [1,0,0,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A167667 (program): Expansion of (1-x+4*x^2)/(1-2*x)^2.
- A167679 (program): Replace odd digits with 2 and even digits with 1.
- A167682 (program): Expansion of (1 - 2*x + 5*x^2) / (1 - 3*x)^2.
- A167683 (program): Hankel transform of A007325.
- A167684 (program): Triangle read by rows given by [2,-1,1,-2,0,0,0,0,0,0,0,…] DELTA [1,0,1,-1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
- A167692 (program): The even nonisolated nonprimes.
- A167700 (program): Number of partitions of n into distinct odd squares.
- A167704 (program): a(0)=1, a(1)=0, a(2)=2, a(3)=1, a(n)=a(n-2)+a(n-3)+a(n-4) for n>3.
- A167705 (program): Composite numbers having four composite nearest neighbors.
- A167706 (program): The single or isolated numbers. The union of single (or isolated or non-twin) primes and single (or isolated or average of twin prime pairs) nonprimes.
- A167707 (program): The non-single or nonisolated numbers. The union of non-single (or nonisolated or twin) primes and non-single (or nonisolated) nonprimes.
- A167710 (program): a(n) = 10*2^n - 3*A083658(n+2).
- A167711 (program): Numbers such that sum of digits is one more than a prime.
- A167713 (program): a(n) = 16^n * Sum_{k=0..n} binomial(2*k, k) / 16^k.
- A167716 (program): Squares that become a prime number when prefixed with a 1.
- A167717 (program): Squares that becomes a prime number when prefixed with a 2.
- A167718 (program): Squares that becomes primes when prefixed with a 3.
- A167719 (program): Squares that become a prime number when prefixed with a 4
- A167721 (program): Squares that become prime numbers when prefixed with a 6.
- A167722 (program): Squares that become prime numbers when prefixed with a 7.
- A167743 (program): Positive differences between distinct positive triangular numbers, with repetition.
- A167744 (program): Squares that become a prime number when some single digit is inserted in front of its decimal expansion.
- A167746 (program): Number of prime divisors of A001222 (counted with multiplicity), with a(1) = 1 by convention.
- A167747 (program): a(n) = phi(6^n).
- A167752 (program): Hankel transform of A167750.
- A167758 (program): Numbers n such that d(n)=nonisolated nonprime.
- A167759 (program): Numbers k such that d(k) is an isolated number (A167706).
- A167760 (program): The number of permutations w of [n] with no w(i)+1 == w(i+1) (mod n).
- A167761 (program): a(n) = sqrt(A167657(n).
- A167762 (program): a(n) = 2*a(n-1)+3*a(n-2)-6*a(n-3) starting a(0)=a(1)=0, a(2)=1.
- A167770 (program): a(n) = prime(n)^2 modulo prime(n+1).
- A167772 (program): Riordan array (c(x)/(1+x*c(x)), x*c(x)), c(x) the g.f. of A000108.
- A167774 (program): Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5*n+1).
- A167775 (program): Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5n+1).
- A167776 (program): Composite numbers having six composite nearest-neighbors.
- A167777 (program): Even single (or even isolated) numbers.
- A167778 (program): Subsequence of A167708 whose indices are 2 mod 5.
- A167779 (program): Subsequence of A167708 whose indices are congruent to 4 mod 5, i.e., a(n) = A167708(5n+4).
- A167780 (program): Subsequence of A167708 whose indices are 0 mod 5, that is, a(n) = A167708(5n+5).
- A167784 (program): a(n) = 2^n - (1 - (-1)^n)*3^((n-1)/2).
- A167791 (program): Numbers with primitive root 2.
- A167796 (program): Numbers with primitive root 8.
- A167808 (program): Numerator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/2.
- A167816 (program): Numerator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/3; denominator=A167817.
- A167817 (program): Period 4: repeat [1, 3, 3, 3].
- A167820 (program): Subsequence of A167709 whose indices are congruent to 0 mod 5, i.e., a(n) = A167709(5*n).
- A167821 (program): a(n) is the number of n-tosses having a run of 3 or more heads or a run of 3 or more tails for a fair coin (i.e., probability is a(n)/2^n).
- A167822 (program): Subsequence of A167709 whose indices are congruent to 1 mod 5, i.e., a(n) = A167709(5*n+1).
- A167823 (program): Subsequence of A167709 whose indices are congruent to 2 mod 5, i.e., a(n) = A167709(5*n+2).
- A167824 (program): Subsequence of A167709 whose indices are congruent to 3 mod 5, i.e., a(n) = A167709(5*n+3).
- A167825 (program): Subsequence of A167709 whose indices are congruent to 4 mod 5, i.e., a(n) = A167709(5*n+4).
- A167826 (program): a(n) is the number of n-tosses having a run of 3 or more heads and a run of 3 or more tails for a fair coin.
- A167831 (program): Largest m<=n such that no carry occurs when adding m to n in decimal arithmetic.
- A167832 (program): A167831(n) + n.
- A167858 (program): A000004 preceded by 3, 14, 36, 36, 12.
- A167859 (program): a(n) = 4^n * Sum_{k=0..n} binomial(2*k, k)^2 / 4^k.
- A167865 (program): Number of partitions of n into distinct parts greater than 1, with each part divisible by the next.
- A167867 (program): a(n) = 2^n * Sum_{k=0..n} binomial(2*k,k)^3 / 2^k.
- A167868 (program): a(n) = 3^n * Sum_{k=0..n} binomial(2*k,k)^3 / 3^k.
- A167869 (program): a(n) = 4^n * Sum_{k=0..n} binomial(2*k,k)^3 / 4^k.
- A167870 (program): a(n) = 16^n * Sum_{k=0..n} binomial(2*k,k)^3 / 16^k.
- A167871 (program): a(n) = 64^n * Sum_{k=0..n} binomial(2*k,k)^3 / 64^k.
- A167872 (program): A sequence of moments connected with Feynman numbers (A000698): Half the number of Feynman diagrams of order 2(n+1), for the electron self-energy in quantum electrodynamics (QED), i.e., all proper diagrams including Furry vanishing diagrams (those that vanish in 4-dimensional QED because of Furry theorem).
- A167873 (program): Period 4: repeat [10, 6, 10, 4].
- A167875 (program): One third of product plus sum of three consecutive nonnegative integers; a(n)=(n+1)(n^2+2n+3)/3.
- A167876 (program): A000004 preceded by 1, 3, 4, 2.
- A167877 (program): Largest m<=n such that no carry occurs when adding m to n in ternary arithmetic.
- A167878 (program): A167877(n) + n.
- A167885 (program): n-th single or isolated number*n-th non-single or nonisolated number.
- A167886 (program): n-th single or isolated number minus n-th non-single or nonisolated number.
- A167887 (program): n-th single or isolated number plus n-th non-single or nonisolated number.
- A167888 (program): n-th single or isolated number^n-th non-single or nonisolated number.
- A167889 (program): a(n) = (-7*3^n+(-3)^n+6*4^n) / 42.
- A167891 (program): A000004 preceded by 1, 4, 2.
- A167892 (program): a(n) = Sum_{k=1..n} Catalan(k)^2.
- A167893 (program): a(n) = Sum_{k=1..n} Catalan(k)^3.
- A167894 (program): Expansion of g.f.: 1/(Sum_{k >= 0} k!*x^k).
- A167909 (program): Differences between consecutive single (or isolated) numbers A167706.
- A167910 (program): a(n) = (4*3^n - 5*2^n + (-2)^n)/20.
- A167911 (program): Differences between consecutive non-single (or nonisolated) numbers A167707.
- A167915 (program): Primes which are the sums of two consecutive nonprimes (A141468).
- A167921 (program): Single or isolated numbers-1.
- A167925 (program): A triangular sequence of the Matrix Markov type based on the 2x2 matrix: m={{a,1},{-1,1}}; which has determinant equal to trace.
- A167928 (program): Number of partitions of n that do not contain 1 as a part and whose parts are not the same divisor of n.
- A167930 (program): Number of partitions of n in which some but not all parts are equal.
- A167932 (program): Number of partitions of n such that all parts are equal or all parts are distinct.
- A167934 (program): a(n) = A000041(n) - A032741(n).
- A167936 (program): 2^n - A108411(n).
- A167948 (program): Triangle read by rows, A101688 * (an infinite lower triangular matrix with A002083 as the main diagonal and the rest zeros).
- A167963 (program): a(n) = n*(n^5 + 1)/2.
- A167968 (program): Signature sequence of phi^4 = 0.14589803375032…, where phi is the golden ratio minus 1 (0.61803398874989…).
- A167972 (program): Signature sequence of Phi^4 = 6.8541019662497…, where Phi is the golden ratio 1.6180339887499… .
- A167987 (program): Number of (undirected) cycles in the graph of the n-orthoplex, n>=2.
- A167990 (program): Elements in A126988 (by row) that are not 1.
- A167991 (program): Blocks of size 2n, each with 2n-1 replicas of 2n followed by 2n+1; n=1, 2, 3, …
- A167993 (program): Expansion of x^2/((3*x-1)*(3*x^2-1)).
- A167998 (program): Numbers n with property that first digit of 5*n = last digit of n.
- A168007 (program): Jumping divisor sequence (see Comments lines for definition).
- A168008 (program): First differences of A168007.
- A168009 (program): Numbers of A168007, in sorted order.
- A168010 (program): a(n) = Sum of all numbers of divisors of all numbers k such that n^2 <= k < (n+1)^2.
- A168011 (program): a(n) = Sum of all numbers of divisors of all numbers < (n+1)^2.
- A168012 (program): a(n) = sum of all divisors of all numbers k such that n^2 <= k < (n+1)^2.
- A168013 (program): a(n) = Sum of all divisors of all numbers < (n+1)^2.
- A168014 (program): Sum of all parts of all partitions of n into equal parts that do not contain 1 as a part.
- A168015 (program): a(n) = A000041(n) + n*A032741(n).
- A168016 (program): Triangle T(n,k) read by rows in which row n list the number of partitions of n into parts divisible by k for k=n,n-1,…,1.
- A168017 (program): Triangle read by rows in which row n lists the number of partitions of n into parts divisible by d, where d is a divisor of n listed in decreasing order.
- A168018 (program): Triangle read by rows in which row n lists the number of partitions of n into parts divisible by d, where d is a divisor of n.
- A168020 (program): Square array read by antidiagonals in which row n lists the number of partitions of n into parts divisible by k.
- A168021 (program): Triangle T(n,k) read by rows in which row n lists the number of partitions of n into parts divisible by k.
- A168022 (program): Noncomposite numbers in the eastern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
- A168023 (program): Noncomposite numbers in the northern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
- A168024 (program): Noncomposite numbers in the northwestern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
- A168025 (program): Noncomposite numbers in the western ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
- A168026 (program): Noncomposite numbers in the southwestern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
- A168027 (program): Noncomposite numbers in the southern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
- A168029 (program): n*(n^6+1)/2.
- A168036 (program): Difference between n’ and n, where n’ is the arithmetic derivative of n (A003415).
- A168037 (program): Period length 18: repeat 0,1,2,0,8,7,0,4,5,0,5,4,0,7,8,0,2,1.
- A168038 (program): Squares closest to 2*n.
- A168039 (program): Squares closest to 3*n.
- A168043 (program): Let S(1)={1} and, for n>1 let S(n) be the smallest set containing x+1, x+2, and 2*x for each element x in S(n-1). a(n) is the number of elements in S(n).
- A168044 (program): Half of the even nonisolated nonprimes A167692.
- A168045 (program): a(n) = A167707(n) + n.
- A168046 (program): Characteristic function of zerofree numbers in decimal representation.
- A168048 (program): a(n) = C(n)*Pi(n) where C(n) = number of nonprimes <= n, Pi(n) = number of primes <= n.
- A168049 (program): Expansion of (3 -x -sqrt(1-2*x-3*x^2))/2.
- A168050 (program): Hankel transform of A168049.
- A168051 (program): Expansion of (1+x+sqrt(1-2x-3x^2))/2.
- A168052 (program): Hankel transform of a Motzkin variant.
- A168053 (program): Expansion of (1-2*x^2-3*x^3)/((1-x)^2*(1+x+x^2)).
- A168054 (program): Expansion of (1-8x^2-24x^3)/((1-2x)^2*(1+2x+4x^2)).
- A168055 (program): Expansion of 2 - x - sqrt(1-2x-3x^2).
- A168056 (program): Expansion of (1+2*x^2+x^3)/((1-x)^2*(1+x+x^2)).
- A168057 (program): Expansion of (1+8x^2+8x^3)/((1-2x)^2*(1+2x+4x^2)).
- A168058 (program): Expansion of x + sqrt(1-2x-3x^2).
- A168059 (program): Denominator of (n+2)/(n*(n+1)).
- A168061 (program): Denominator of (n+3) / ((n+2) * (n+1) * n).
- A168065 (program): If n = Product p(k)^e(k) then a(n) = {Product (p(k)+1)^e(k) + Product (p(k)-1)^e(k)}/2, a(1) = 1.
- A168066 (program): If n = Product p(k)^e(k) then a(n) = {Product (p(k)+1)^e(k) - Product (p(k)-1)^e(k)}/2, a(1) = 0.
- A168067 (program): n*(n^7+1)/2.
- A168068 (program): Array T(n,k) read by antidiagonals: T(n,2k+1) = 2k+1. T(n,2k) = 2^n*k.
- A168071 (program): Expansion of (1-3*x^2-4*x^3)/((1-x)^2*(1+x+x^2)).
- A168072 (program): Expansion of (1-27x^2-108x^3)/((1-3x)^2*(1+3x+9x^2)).
- A168073 (program): Expansion of 1 + 3*(1-x-sqrt(1-2*x-3*x^2))/2.
- A168075 (program): Expansion of (1+27x^2-54x^3)/((1+3x)^2*(1-3x+9 x^2)).
- A168076 (program): Expansion of 1 - 3*(1-x-sqrt(1-2*x-3*x^2))/2.
- A168077 (program): a(2n) = A129194(2n)/2; a(2n+1) = A129194(2n+1).
- A168081 (program): Lucas sequence U_n(x,1) over the field GF(2).
- A168088 (program): a(n) = 2^tetranacci(n).
- A168089 (program): a(n) = 2^pentanacci(n).
- A168090 (program): a(n) = (1 - (n mod 3) mod 2)*2^(floor(n/3) + (n mod 3)/2 ).
- A168092 (program): a(n) = number of natural numbers m such that n - 2 <= m <= n + 2.
- A168093 (program): a(n) = number of natural numbers m such that n - 3 <= m <= n + 3.
- A168094 (program): a(n) = number of natural numbers m such that n - 4 <= m <= n + 4.
- A168095 (program): a(n) = number of natural numbers m such that n - 5 <= m <= n + 5.
- A168096 (program): a(n) = number of natural numbers m such that n - 6 <= m <= n + 6.
- A168097 (program): a(n) = number of natural numbers m such that n - 7 <= m <= n + 7.
- A168098 (program): a(n) = number of natural numbers m such that n - 8 <= m <= n + 8.
- A168099 (program): a(n) = number of natural numbers m such that n - 9 <= m <= n + 9.
- A168100 (program): a(n) = number of natural numbers m such that n - 10 <= m <= n + 10.
- A168101 (program): a(n) = sum of natural numbers m such that n - 2 <= m <= n + 2.
- A168102 (program): a(n) = sum of natural numbers m such that n - 3 <= m <= n + 3.
- A168103 (program): a(n) = sum of natural numbers m such that n - 4 <= m <= n + 4.
- A168104 (program): a(n) = sum of natural numbers m such that n - 5 <= m <= n + 5.
- A168105 (program): a(n) = sum of natural numbers m such that n - 6 <= m <= n + 6.
- A168106 (program): a(n) = sum of natural numbers m such that n - 7 <= m <= n + 7.
- A168107 (program): a(n) = sum of natural numbers m such that n - 8 <= m <= n + 8.
- A168108 (program): a(n) = sum of natural numbers m such that n - 9 <= m <= n + 9.
- A168109 (program): a(n) = sum of natural numbers m such that n - 10 <= m <= n + 10.
- A168111 (program): Sum of the partition numbers of the proper divisors of n, with a(1) = 0.
- A168114 (program): If A168113 is regarded as a triangle then the rows converge to this sequence.
- A168116 (program): a(n) = n*(n^8+1)/2.
- A168118 (program): n*(n^9+1)/2.
- A168119 (program): n*(n^10+1)/2.
- A168120 (program): Square array T(n,k) read by antidiagonals in which column k lists each number A000009 followed by k-1 zeros, for k>0.
- A168121 (program): Triangle T(n,k) read by rows in which column k lists each number A000009 followed by k-1 zeros, for k>0.
- A168122 (program): n^2*(n^4+1)/2.
- A168123 (program): a(n) = n^2*(n^5+1)/2.
- A168124 (program): a(n) = n^2*(n^6+1)/2.
- A168125 (program): a(n) = n^2*(n^7+1)/2.
- A168126 (program): a(n) = n^2*(n^8+1)/2.
- A168134 (program): Numbers not of the form 7*k+11*m (with nonnegative k, m).
- A168135 (program): Numbers expressible as 7*k+11*m (with nonnegative k, m) exactly in one way.
- A168136 (program): a(n) = Bernoulli(2n)*(2n+1)!/n!.
- A168138 (program): a(n) = Fibonacci(n+1)^tau(n).
- A168141 (program): a(n) = pi(n + 1) - pi(n - 2), where pi is the prime counting function.
- A168142 (program): Count downwards from 2, then from 8, then from 18, then from … 2*k^2, k>=1.
- A168143 (program): a(17)=37; for n>=17, a(n)=3n-14 if gcd(n,a(n-1))>1 and all prime divisors of n more than 17; a(n)=a(n-1)+1, otherwise
- A168145 (program): Numbers n such that to abs(phi(n) - pi(n)) = 1.
- A168146 (program): Numbers n such that phi(n) > pi(n).
- A168147 (program): Primes of the form 10*n^3 + 1.
- A168150 (program): Inverse binomial transform of A026741.
- A168152 (program): a(n) = prime(prime(n)) - prime(n).
- A168153 (program): a(n) = n^2*(n^9 + 1)/2.
- A168160 (program): Number of 0’s in the matrix whose lines are the binary expansion of the numbers 1,…,n.
- A168175 (program): Expansion of 1/(1 - 4*x + 7*x^2).
- A168176 (program): a(n) = n^2*(n^10 + 1)/2.
- A168178 (program): a(n) = n^3*(n^2 + 1)/2.
- A168179 (program): a(n) = n^3*(n^4 + 1)/2.
- A168180 (program): a(n) = n^3*(n^5 + 1)/2.
- A168181 (program): Characteristic function of numbers that are not multiples of 8.
- A168182 (program): Characteristic function of numbers that are not multiples of 9.
- A168183 (program): Numbers that are not multiples of 9.
- A168184 (program): Characteristic function of numbers that are not multiples of 10.
- A168185 (program): Characteristic function of numbers that are not multiples of 12.
- A168186 (program): Positive numbers that are not multiples of 12.
- A168187 (program): a(n) = n^3*(n^6 + 1)/2.
- A168188 (program): a(n) = n^3*(n^7 + 1)/2.
- A168189 (program): a(n) = n^3*(n^8 + 1)/2.
- A168190 (program): a(n) = n^3*(n^9 + 1)/2.
- A168191 (program): a(n) = n^3*(n^10 + 1)/2.
- A168192 (program): a(n) = n^4*(n^2 + 1)/2.
- A168193 (program): a(n) = a(n-1) + a(n-2) + 4, with a(0)=0, a(1)=2.
- A168194 (program): a(n) = n^4*(n^3 + 1)/2.
- A168195 (program): a(n) = 2*n - a(n-1) + 1 with n>1, a(1)=5.
- A168196 (program): a(n) = n^4*(n^5 + 1)/2.
- A168197 (program): a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=0.
- A168198 (program): a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=1.
- A168199 (program): a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=2.
- A168200 (program): a(n) = 3*n - a(n-1) + 1, with a(1)=4.
- A168201 (program): Number of representations of n in the form 7*k+11*m (with nonnegative k, m).
- A168202 (program): a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=5.
- A168203 (program): a(n) = 4*n - a(n-1) + 1 with n>1, a(1)=0.
- A168204 (program): a(n) = 4*n - a(n-1) + 1 with n>1, a(1)=1.
- A168205 (program): a(n) = 4*n - a(n-1) + 1 with n>1, a(1)=2.
- A168206 (program): a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=0.
- A168207 (program): a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=2.
- A168209 (program): a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=3.
- A168210 (program): a(n) = 6*n - a(n-1) + 1 with n>1, a(1)=0.
- A168211 (program): a(n) = (9 + 14*n + 23*(-1)^n)/4.
- A168212 (program): a(n) = 7*n - a(n-1) + 1 with n>1, a(1)=4.
- A168213 (program): a(n) = (11 + 18*n + 9*(-1)^n)/4.
- A168216 (program): Riordan array (1/(1-x),xc(x)/(1-xc(x))) where c(x)is the g.f. of A000108.It factorizes as A007318*A106566.
- A168219 (program): Naturals n for which 1 + 10*n^3 (A168147) is prime.
- A168220 (program): a(n) = n^4*(n^6 + 1)/2.
- A168221 (program): a(n) = A006368(A006368(n)).
- A168222 (program): a(n) = A006369(A006369(n)).
- A168224 (program): Where record values occur in A168223.
- A168225 (program): a(n) = n^4*(n^7 + 1)/2.
- A168227 (program): a(n) = n^4*(n^8 + 1)/2.
- A168230 (program): a(n) = n + 2 - a(n-1) for n>1; a(1) = 0.
- A168232 (program): a(n) = (2*n - 3*(-1)^n - 1)/2.
- A168233 (program): a(n) = 3*n - a(n-1) - 1 for n>0, a(1)=1.
- A168235 (program): 1+5*n+7*n^2.
- A168236 (program): a(n) = (6*n - 3*(-1)^n - 1)/4.
- A168237 (program): a(n) = (6*n + 3*(-1)^n - 3)/4.
- A168240 (program): 1+7*n+13*n^2.
- A168241 (program): n-th squarefree number plus n-th non-single or nonisolated number.
- A168243 (program): Expansion of e.g.f. Product_{i>=1} (1 + x^i)^(1/i).
- A168244 (program): a(n) = 1 + 3*n - 2*n^2.
- A168245 (program): prime(prime(n+1))-2*prime(n).
- A168249 (program): n-th single or isolated number minus n-th squarefree number.
- A168251 (program): a(n) = n^2 if n is odd, n^2*2^(n-2) if n is even.
- A168255 (program): n appears n-th nonprime number times.
- A168256 (program): Triangle read by rows: Catalan number C(n) repeated n+1 times.
- A168258 (program): Triangle read by rows, A101688 * A000012 as infinite lower triangular matrices.
- A168259 (program): Eigensequence of triangle A168258.
- A168265 (program): a(n) = A003557(A060735(n)).
- A168269 (program): a(n) = 2*n - (-1)^n.
- A168273 (program): a(n) = 2*n + (-1)^n - 1.
- A168276 (program): a(n) = 2*n - (-1)^n - 1.
- A168277 (program): a(n) = 2*n - (-1)^n - 2.
- A168278 (program): (10*n + 5*(-1)^n + 3)/4.
- A168279 (program): (n+1)-th prime nonprime minus (n+1)-th prime.
- A168280 (program): (1 - 5*(-1)^n + 10*n)/4.
- A168281 (program): Triangle T(n,m) = 2*(min(n - m + 1, m))^2 read by rows.
- A168282 (program): (10*n + 5*(-1)^n - 1)/4.
- A168283 (program): a(n) = (10*n - 5*(-1)^n - 3)/4.
- A168284 (program): a(n) = (10*n + 5*(-1)^n - 5)/4.
- A168285 (program): a(n) = ((n-th nonprime)-th prime) - (n-th nonprime).
- A168286 (program): a(n) = (6*n + 3*(-1)^n + 1)/2.
- A168297 (program): a(n) = n^3 + (1-n)^2.
- A168298 (program): a(n) = 1 - n^2*2^n.
- A168299 (program): a(n) = 1 + 3^n * n^3.
- A168300 (program): a(n) = 6*n - a(n-1) - 2 with a(1)=5.
- A168301 (program): a(n) = (6*n + 3*(-1)^n - 1)/2.
- A168309 (program): Period 2: repeat 4,-3.
- A168313 (program): Triangle read by rows, retain 1’s as rightmost diagonal of A101688 and replace all other 1’s with 2’s.
- A168314 (program): Eigensequence of triangle A168313
- A168316 (program): Triangle read by rows, square of triangle A101688.
- A168319 (program): a(-1)=0. a(n)=a(n-1)^2-2^n.
- A168321 (program): a(n) = n +6 - a(n-1), with a(1) = 0.
- A168324 (program): Number of distinct permutations of the list of prime factors of n (with multiplicity), where a(1)=0.
- A168326 (program): a(n) = (6*n - 3*(-1)^n - 1)/2.
- A168328 (program): a(n) = 6 * floor( n/2 ).
- A168329 (program): a(n) = (3/2)*(2*n - (-1)^n - 1).
- A168330 (program): Period 2: repeat [3, -2].
- A168331 (program): a(n) = (5 + 14*n + 7*(-1)^n)/4.
- A168332 (program): a(n) = 6 + 7 * floor((n-1)/2).
- A168333 (program): a(n) = (14*n + 7*(-1)^n + 1)/4.
- A168336 (program): a(n) = 5 + 7*floor((n-1)/2).
- A168337 (program): a(n) = 1 + 7*floor(n/2).
- A168338 (program): Sum of the largest digit of the divisors of n.
- A168343 (program): n-th single or isolated number minus n.
- A168345 (program): a(n) = n^4*(n^9 + 1)/2.
- A168346 (program): a(n) = n^4*(n^10 + 1)/2.
- A168350 (program): Sum of first n non-single or nonisolated numbers.
- A168351 (program): a(n) = n^5*(n+1)/2.
- A168356 (program): A000796(n-2) - A000796(n)
- A168358 (program): Self-convolution square of A001246, which is the squares of Catalan numbers.
- A168360 (program): n-b(n), where b(n) = A079777(n) = (b(n-1)+b(n-2) mod n); b(0)=0, b(1)=1.
- A168361 (program): Period 2: repeat 2, -1.
- A168364 (program): a(n) = n^5*(n^2 + 1)/2.
- A168371 (program): a(n) = n^5*(n^3 + 1)/2.
- A168372 (program): a(n) = n^5*(n^4 + 1)/2.
- A168373 (program): a(n) = 7*n - a(n-1) - 6 with n>1, a(1)=4.
- A168374 (program): a(n) = 7 * floor(n/2).
- A168376 (program): a(n) = (14*n - 7*(-1)^n - 9)/4.
- A168377 (program): Riordan array (1/(1 + x), x*c(x)), where c(x) is the o.g.f. of Catalan numbers A000108.
- A168378 (program): a(n) = 3 + 8*floor(n/2).
- A168379 (program): a(n) = 4*n - 2*(-1)^n + 1.
- A168380 (program): Row sums of A168281.
- A168381 (program): a(n) = 4*n + 2*(-1)^n.
- A168384 (program): a(n) = 4*n - 2*(-1)^n.
- A168386 (program): Arithmetic derivative of the double factorial of n.
- A168388 (program): First number in the n-th row of A172002.
- A168389 (program): a(n) = PrimePi(A147819(n)).
- A168390 (program): a(n) = 1 + 8*floor(n/2).
- A168392 (program): a(n) = 5 + 8*floor((n-1)/2).
- A168393 (program): Moebius function of interprimes (A024675).
- A168394 (program): Moebius function of even interprimes (A072568).
- A168395 (program): Moebius function of odd interprimes (A072569).
- A168397 (program): a(n) = 8 * floor(n/2).
- A168398 (program): a(n) = 4 + 8*floor((n-1)/2).
- A168399 (program): a(n) = 3^n mod 13.
- A168400 (program): 3^n mod 15.
- A168401 (program): 4 + 9*floor(n/2).
- A168409 (program): a(n) = 8 + 9*floor((n-1)/2).
- A168410 (program): a(n) = 3 + 9*floor(n/2).
- A168411 (program): a(n) = 7 + 9*floor((n-1)/2).
- A168412 (program): a(n) = n^5*(n^6 + 1)/2.
- A168413 (program): a(n) = 9*n - a(n-1) - 5, with a(1)=2.
- A168414 (program): a(n) = (18*n - 9*(-1)^n - 3)/4.
- A168415 (program): a(n) = 2^n + 7.
- A168416 (program): a(n) = 1 + 9*floor(n/2).
- A168418 (program): a(n) = 9*n - a(n-1) - 8 with n>1, a(1)=5.
- A168419 (program): a(n) = 9*floor(n/2).
- A168420 (program): a(n) = 4 + 10*floor(n/2).
- A168427 (program): 3^n mod 30.
- A168428 (program): a(n) = 4^n mod 10.
- A168429 (program): a(n) = 4^n mod 11.
- A168430 (program): a(n) = 4^n mod 13.
- A168432 (program): a(n) = n^5*(n^7 + 1)/2.
- A168437 (program): a(n) = 3 + 10*floor(n/2).
- A168441 (program): Expansion of 1/(1-x/(1-2x/(1-4x/(1-6x/(1-8x/(1-…. (continued fraction).
- A168444 (program): Number of partitions of the set {1,2,…,n} such that no block is a sequence of consecutive integers (including 1-element blocks)
- A168455 (program): 3^n+n mod 7.
- A168456 (program): a(n) = (10*n - 5*(-1)^n + 1)/2.
- A168457 (program): a(n) = (10*n + 5*(-1)^n - 1)/2.
- A168458 (program): a(n) = 7 + 10*floor((n-1)/2).
- A168459 (program): a(n) = (10*n + 5*(-1)^n - 3)/2.
- A168460 (program): a(n) = 6 + 10*floor((n-1)/2).
- A168461 (program): a(n) = 10*floor(n/2).
- A168462 (program): a(n) = n^5*(n^8 + 1)/2.
- A168463 (program): a(n) = 5 + 11*floor(n/2).
- A168465 (program): Numbers that are congruent to 2 or 7 mod 11.
- A168471 (program): a(n) = n^5*(n^9 + 1)/2.
- A168472 (program): Partial sums of products of two distinct primes (A006881).
- A168480 (program): G.f.: Sum_{n>=0} 2^(n^2)*(1 + 2^n*x)^n*x^n.
- A168484 (program): Numbers that are congruent to {2, 3, 5, 7} mod 11.
- A168485 (program): A165342(3n)/3.
- A168486 (program): Numbers that are congruent to {2, 5} mod 11.
- A168489 (program): Numbers that are congruent to {7,11} mod 12.
- A168491 (program): a(n) = (-1)^n*Catalan(n).
- A168493 (program): a(n) = 3^floor(n^2/2).
- A168495 (program): a(n) = 3^floor(n^2/3).
- A168496 (program): The positions of non-single or nonisolated numbers in A001477.
- A168497 (program): The halfs of even single (or even isolated) numbers.
- A168504 (program): Hankel transform of A168503.
- A168505 (program): Expansion of 1/(1-x/(1+x/(1-x/(1-x/(1+x/(1-x/(1-x/(1+x/(1-… (continued fraction).
- A168506 (program): Number of rooted plane trees of total weight n whose nodes are themselves planted plane trees whose roots are distinguished as either red or blue, the weight of each such node being equal to the size of the corresponding planted tree.
- A168507 (program): a(n) = n^5*(n^10 + 1)/2.
- A168509 (program): Triangle read by rows, A051731 * A101688
- A168510 (program): Products across consecutive rows of the denominators of the Leibniz harmonic triangle (A003506).
- A168512 (program): Sum of divisors of n weighted by divisor multiplicity in n.
- A168517 (program): Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = -1, b = 1, and c = 1, read by rows.
- A168518 (program): Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = -4, b = 2, and c = 2, read by rows.
- A168520 (program): a(n) = 98*a(n-1) - a(n-2); a(1) = 0, a(2) = 10.
- A168522 (program): a(n) = 98*a(n-1) - 2*a(n-2); a(1) = 0, a(2) = 1.
- A168523 (program): Triangle of coefficients of g.f. a*(1+x)^n + b*(1-x)^(n+2)*polylog(-n-1, x)/x + 2^n*c*(1-x)^(n+1)*LerchPhi(x, -n, 1/2), with a = -1, b = 1, c = 1.
- A168524 (program): Triangle of coefficients of g.f. a*(1+x)^n + b*(1-x)^(n+2)*polylog(-n-1, x)/x + 2^n*c*(1-x)^(n+1)*LerchPhi(x, -n, 1/2), with a = -2, b = 2, c = 1.
- A168526 (program): a(n) = n^6*(n + 1)/2.
- A168527 (program): a(n) = n^6*(n^2 + 1)/2.
- A168538 (program): a(n) = (n+6)*(n+1)*(n^2 + 7*n + 16)/4.
- A168539 (program): Terms of A123239 which are prime in Z(i), Z(rho) and Z(sqrt(2)).
- A168543 (program): pi(n-th single or isolated number).
- A168547 (program): a(n) = 1 - 2*n^2 + 4*n*(1 + 2*n^2)/3.
- A168550 (program): Natural numbers k for which 1 + 2*k^3 is prime.
- A168551 (program): Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = 1, b = -1, and c = 1, read by rows.
- A168552 (program): Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = 3, b = -3, and c = 1, read by rows.
- A168553 (program): a(n) = 1 if it is possible to place n sets of n queens on an n X n chessboard with no two queens of the same set attacking each other.
- A168555 (program): a(n) = n^6*(n^3 + 1)/2.
- A168559 (program): a(n) = n^2 + a(n-1), with a(1)=0.
- A168561 (program): Riordan array (1/(1-x^2), x/(1-x^2)). Unsigned version of A049310.
- A168562 (program): Sum of squares of Eulerian numbers in row n of triangle A008292 with a(0)=1.
- A168563 (program): a(n) = (n-th prime > 3) minus (n-th composite number).
- A168564 (program): a(n) = n^6*(n^4 + 1)/2.
- A168565 (program): Let p = prime(n); then a(n) = p + (p-1)/2.
- A168566 (program): a(n) = (n-1)*(n+2)*(n^2 + n + 2)/4.
- A168569 (program): a(n) = 9*(3^n - 1)/2.
- A168570 (program): Exponent of 3 in 2^n - 1.
- A168571 (program): a(n) = 25*(5^n - 1)/4.
- A168572 (program): a(n) = Sum_{k=2..n}(7^k).
- A168574 (program): a(n) = (4*n + 3)*(1 + 2*n^2)/3.
- A168575 (program): a(n) = (10^n + 1)^3.
- A168577 (program): Pascal’s triangle, first two columns and diagonal removed.
- A168579 (program): G.f.: 1/(1-x-16*x^2).
- A168580 (program): a(n) = (n-th prime > 3) minus 3*n.
- A168582 (program): a(n) = (4*n^3 - 6*n^2 + 8*n + 9 + 3*(-1)^n)/12.
- A168583 (program): The number of ways of partitioning the multiset {1,1,2,3,…,n-1} into exactly three nonempty parts.
- A168584 (program): Number of ways of partitioning the multiset {1,1,2,3,…,n-1} into exactly four nonempty parts.
- A168585 (program): Number of ways of partitioning the multiset {1,1,2,3,…,n-1} into exactly five nonempty parts.
- A168587 (program): Smallest digit sum of an n-digit prime with only digits 0 add 1 (or 0, if no such prime exists).
- A168589 (program): a(n) = (2 - 3^n)*(-1)^n.
- A168592 (program): G.f.: exp( Sum_{n>=1} A082758(n)*x^n/n ), where A082758(n) = sum of the squares of the trinomial coefficients in row n of triangle A027907.
- A168595 (program): a(n) = Sum_{k=0..2n} C(2n,k)*A027907(n,k) where A027907 is the triangle of trinomial coefficients.
- A168596 (program): a(n) = 2*a(n-1) - 1 with a(0)=14.
- A168597 (program): Squares of the central trinomial coefficients (A002426).
- A168598 (program): G.f.: exp( Sum_{n>=1} A002426(n)^2*x^n/n ), where A002426(n) is the central trinomial coefficients.
- A168599 (program): G.f.: exp( Sum_{n>=1} A002426(n)^n * x^n/n ), where A002426(n) is the central trinomial coefficients.
- A168604 (program): a(n) = 2^(n-2) - 1.
- A168605 (program): Number of ways of partitioning the multiset {1,1,1,2,3,…,n-2} into exactly three nonempty parts.
- A168606 (program): The number of ways of partitioning the multiset {1,1,1,2,3,…,n-2} into exactly four nonempty parts.
- A168607 (program): a(n) = 3^n + 2.
- A168608 (program): Decimal expansion of average of two-digit primes.
- A168609 (program): a(n) = 3^n + 4.
- A168610 (program): a(n) = 3^n + 5.
- A168611 (program): a(n) = 3^n - 4.
- A168613 (program): a(n) = 3^n - 5.
- A168614 (program): a(n) = 2^n + 5.
- A168615 (program): Inverse binomial transform of A169609, or of A144437 preceded by 1.
- A168616 (program): a(n) = 2^n - 5.
- A168617 (program): a(n) = 7*2^(n-1) - 2*n - 5.
- A168618 (program): Numbers n such that 17*n-1, 17*n+1 are twin primes.
- A168619 (program): Triangle T(n,k) read by rows with the coefficient [x^k] of the polynomial (x+1)^n + (2*n-3) *( (x+1)^n -x^n -1 ) in column k, row n.
- A168620 (program): Table T(n,k) with the coefficient [x^k] of the polynomial 5*(x+1)^n - 4*(x^n+1) in column 0<=k<=n. T(0,0)=1.
- A168622 (program): Triangle T(n,k) with the coefficient [x^k] of the polynomial 7*(x+1)^n - 6*(x^n+1) in row n, column k. T(0,0)=1.
- A168623 (program): Table T(n,k) read by rows: Coefficients [x^k] of the polynomial 9*(x+1)^n -8*(x^n+1); T(0,0)=1.
- A168624 (program): a(n) = 1 - 10^n + 100^n.
- A168625 (program): Triangle T(n,k) = 8*binomial(n,k) - 7 with columns 0 <= k <= n.
- A168627 (program): a(n) = n^6*(n^5 + 1)/2.
- A168631 (program): a(n) = n^6*(n^7 + 1)/2.
- A168632 (program): a(n) = n^6*(n^8 + 1)/2.
- A168633 (program): a(n) = n^6*(n^9 + 1)/2.
- A168634 (program): a(n) = n^6*(n^10 + 1)/2.
- A168635 (program): a(n) = n^7*(n + 1)/2.
- A168636 (program): a(n) = n^7*(n^2 + 1)/2.
- A168637 (program): a(n) = a(n-1) + a(n-2) - a(n-4) starting a(0)=0, a(1)=1, a(2)=a(3)=3.
- A168638 (program): Number of distinct prime divisors of n is 2 or 3.
- A168639 (program): Expansion of x*(1 + x^2 - x^3) ) / ( (1-x)*(1-x-x^4) ).
- A168642 (program): a(n) = (8*2^n + (-1)^n)/3 for n > 0; a(0) = 1.
- A168645 (program): Numbers with 2 or 3 prime divisors (counted with multiplicity).
- A168647 (program): Reverse (palindrome) of A164844.
- A168648 (program): a(n) = (10*2^n + 2*(-1)^n)/3 for n > 0; a(0) = 1.
- A168649 (program): a(n) = (1/n)*Sum_{d|n} moebius(d)*2^(n^2/d).
- A168650 (program): Integers that can be generated with a C/C++ expression that is shorter than their decimal representation.
- A168651 (program): Integers that can be generated with a C/C++ expression that is two or more characters shorter than their decimal representation.
- A168652 (program): Integers that can be generated with a C/C++ expression that is three or more characters shorter than their decimal representation.
- A168658 (program): a(n) = ceiling(n^n/2).
- A168660 (program): a(n) = n^7*(n^3 + 1)/2.
- A168661 (program): a(n) = n^7*(n^4 + 1)/2.
- A168662 (program): a(n) = n^7*(n^5 + 1)/2.
- A168663 (program): a(n) = n^7*(n^6 + 1)/2.
- A168664 (program): a(n) = n^7*(n^7 + 1)/2.
- A168665 (program): a(n) = n^7*(n^8 + 1)/2.
- A168666 (program): a(n) = n^7*(n^9 + 1)/2.
- A168667 (program): a(n) = n^7*(n^10 + 1)/2.
- A168668 (program): a(n) = n*(2 + 5*n).
- A168669 (program): Numbers n such that sqrt(36*n+49) is prime.
- A168670 (program): Numbers that are congruent to {1, 8} mod 11.
- A168671 (program): Numbers that are congruent to {1, 10} mod 13.
- A168672 (program): Numbers that are congruent to {2,13} mod 17.
- A168673 (program): Binomial transform of A169609.
- A168674 (program): a(n) = 2*A001610(n).
- A168675 (program): a(n) = n^8*(n + 1)/2.
- A168676 (program): Coefficients of characteristic polynomials for a two diagonal Matrix type that has determinant equal to trace:M(n)=Table[If[ k == m && m < n, 1, If[k == m + 1, 1, If[k == 1 && m == n, (-1)^(n + 1)*(n - 1), 0]]], {k, n}, {m, n}]
- A168677 (program): Lexicographically earliest positive integer sequence such that no sum of consecutive terms is a positive power of 4.
- A168834 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168835 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168836 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168837 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168838 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168839 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168840 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168841 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168842 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168843 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168844 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168845 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168846 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168847 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168848 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168849 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168850 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168851 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168852 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168853 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168854 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168855 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168856 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168857 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168858 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168859 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168860 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168861 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168862 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168863 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168864 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168865 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168866 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168867 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168868 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168869 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168870 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168871 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
- A168876 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168877 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168878 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168879 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168880 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168882 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168883 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168884 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168885 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168886 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168887 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168888 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168889 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168890 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168891 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168892 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168893 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168894 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168895 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168896 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168897 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168898 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168899 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168900 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168901 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168902 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168903 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168904 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168905 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168906 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168907 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168908 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168909 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168910 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168911 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168912 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168913 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168914 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168915 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168916 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168917 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168918 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168919 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
- A168923 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168924 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168925 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168926 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168927 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168928 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168929 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168930 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168931 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168932 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168933 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168934 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168935 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168936 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168937 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168938 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168939 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168940 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168941 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168942 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168943 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168944 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168945 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168946 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168947 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168948 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168949 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168950 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168951 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168952 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168953 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
- A168954 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i