List of integer sequences with links to LODA programs.

  • A100005 (program): Bisection of A001414.
  • A100006 (program): Integer log of 2n: sum of primes dividing 2n (with repetition).
  • A100007 (program): Number of unitary divisors of 2n-1 (d such that d divides 2n-1, GCD(d,(2n-1)/d)=1). Bisection of A034444.
  • A100008 (program): Number of unitary divisors of 2n.
  • A100019 (program): a(n) = n^4 + n^3 + n^2.
  • A100029 (program): Bisection of A008472.
  • A100030 (program): Bisection of A008472.
  • A100033 (program): Bisection of A001700.
  • A100036 (program): a(n) = smallest m such that A100035(m) = n.
  • A100037 (program): Positions of occurrences of the natural numbers as a second subsequence in A100035.
  • A100038 (program): Positions of occurrences of the natural numbers as third subsequence in A100035.
  • A100039 (program): Positions of occurrences of the natural numbers as fourth subsequence in A100035.
  • A100040 (program): a(n) = 2*n^2 + n - 5.
  • A100041 (program): a(n) = 2*n^2 + n - 7.
  • A100042 (program): a(n) = prime(n)*2^prime(n).
  • A100043 (program): a(n) = (3*n-1)!.
  • A100047 (program): A Chebyshev transform of the Fibonacci numbers.
  • A100050 (program): A Chebyshev transform of n.
  • A100051 (program): A Chebyshev transform of 1,1,1,…
  • A100052 (program): A Chebyshev transform of the odd numbers.
  • A100057 (program): Sum of absolute differences of p(n) defined in A054065, oriented around a clock.
  • A100062 (program): Denominator of the probability that an integer n occurs in the cumulative sums of the decimal digits of a random real number between 0 and 1.
  • A100063 (program): A Chebyshev transform of Jacobsthal numbers.
  • A100066 (program): Expansion of x/((1-x)sqrt(1-4x^2)).
  • A100071 (program): a(n) = n * binomial(n-1, floor((n-1)/2)) = n * max_ i=0..n binomial(n-1, i).
  • A100088 (program): Expansion of (1-x^2)/((1-2x)(1+x^2)).
  • A100089 (program): a(n) = (3*n+1)!.
  • A100102 (program): 2^(2n)-(2n-1).
  • A100103 (program): a(n) = 2^(2n) - 2n.
  • A100104 (program): a(n) = n^3 - n^2 + 1.
  • A100105 (program): 2^prime(n)-prime(n).
  • A100109 (program): a(n) = n^3 - 2*n^2 + 2.
  • A100119 (program): a(n) = n-th centered n-gonal number.
  • A100131 (program): a(n) = Sum_ k=0..floor(n/4) binomial(n-2k, 2k)*2^(n-4k).
  • A100145 (program): Structured great rhombicosidodecahedral numbers.
  • A100146 (program): Structured great rhombicubeoctahedral numbers.
  • A100147 (program): Structured icosidodecahedral numbers.
  • A100148 (program): Structured small rhombicosidodecahedral numbers.
  • A100149 (program): Structured small rhombicubeoctahedral numbers.
  • A100150 (program): Structured snub cubic numbers.
  • A100151 (program): Structured snub dodecahedral numbers.
  • A100152 (program): Structured truncated cubic numbers.
  • A100153 (program): Structured truncated dodecahedral numbers.
  • A100154 (program): Structured truncated icosahedral numbers.
  • A100155 (program): Structured truncated octahedral numbers.
  • A100156 (program): Structured truncated tetrahedral numbers.
  • A100157 (program): Structured rhombic dodecahedral numbers (vertex structure 9).
  • A100158 (program): Structured disdyakis triacontahedral numbers (vertex structure 11).
  • A100159 (program): Structured disdyakis triacontahedral numbers (vertex structure 7).
  • A100160 (program): Structured disdyakis triacontahedral numbers (vertex structure 5).
  • A100161 (program): Structured disdyakis dodecahedral numbers (vertex structure 9).
  • A100162 (program): Structured disdyakis dodecahedral numbers (vertex structure 7).
  • A100163 (program): Structured disdyakis dodecahedral numbers (vertex structure 5).
  • A100164 (program): Structured rhombic triacontahedral numbers (vertex structure 11).
  • A100165 (program): Structured rhombic triacontahedral numbers (vertex structure 7).
  • A100166 (program): Structured deltoidal hexacontahedral numbers (vertex structure 9).
  • A100167 (program): Structured pentagonal icositetrahedral numbers (vertex structure 13).
  • A100168 (program): Structured pentagonal icositetrahedral numbers (vertex structure 10).
  • A100169 (program): Structured pentagonal hexacontahedral numbers (vertex structure 16).
  • A100170 (program): Structured pentagonal hexacontahedral numbers (vertex structure 10).
  • A100171 (program): Structured triakis octahedral numbers (vertex structure 4).
  • A100172 (program): Structured triakis icosahedral numbers (vertex structure 4).
  • A100173 (program): Structured pentakis dodecahedral numbers (vertex structure 6).
  • A100174 (program): Structured tetrakis hexahedral numbers (vertex structure 5).
  • A100175 (program): Structured triakis tetrahedral numbers (vertex structure 4).
  • A100176 (program): Structured octagonal prism numbers.
  • A100177 (program): Structured meta-prism numbers, the n-th number from a structured n-gonal prism number sequence.
  • A100178 (program): Structured hexagonal diamond numbers (vertex structure 5).
  • A100179 (program): Structured heptagonal diamond numbers (vertex structure 5).
  • A100182 (program): Structured tetragonal anti-prism numbers.
  • A100183 (program): Structured hexagonal anti-prism numbers.
  • A100184 (program): Structured octagonal anti-prism numbers.
  • A100185 (program): Structured meta-anti-prism numbers, the n-th number from a structured n-gonal anti-prism number sequence.
  • A100186 (program): Structured heptagonal anti-diamond numbers (vertex structure 7).
  • A100187 (program): Structured octagonal anti-diamond numbers (vertex structure 7).
  • A100188 (program): Polar structured meta-anti-diamond numbers, the n-th number from a polar structured n-gonal anti-diamond number sequence.
  • A100189 (program): Equatorial structured meta-anti-diamond numbers, the n-th number from an equatorial structured n-gonal anti-diamond number sequence.
  • A100190 (program): The (4,1)-entry in the 4 X 4 matrix M^n, where M = [1,0,0,0 / 3,3,0,0 / 3,6,3,0 / 1,3,3,1].
  • A100196 (program): Numbers of positive integer cubes <= n^2.
  • A100198 (program): Let f(0) = -1, f(n) = Moebius(n) = A008683(n) for n>0. Sequence gives partial sums a(n) = Sum_ 0 <= i <= n f(i).
  • A100201 (program): Primes of the form 23n+3.
  • A100206 (program): Row sums of Clark’s triangle A046902.
  • A100207 (program): a(n) = 4 + 8n + 10n^2 + 4*n^3.
  • A100214 (program): a(n) = 4*n^3 + 4.
  • A100219 (program): Expansion of (1-2x)/((1-x)(1-x+x^2)).
  • A100227 (program): Main diagonal of triangle A100226.
  • A100230 (program): Main diagonal of triangle A100229.
  • A100233 (program): a(n) = Lucas(3*n) - 1.
  • A100242 (program): a(n) = n^5 - n^2*(n^2 - 1)/2.
  • A100255 (program): Squares of pentagonal numbers: a(n) = (1/4)n^2(3*n-1)^2.
  • A100256 (program): Squares of second pentagonal numbers: (1/4) n^2(3n+1)^2.
  • A100284 (program): Expansion of (1-4x-x^2)/((1-x)(1-4x-5x^2)).
  • A100285 (program): Expansion of (1+5x^2)/(1-x+x^2-x^3).
  • A100286 (program): Expansion of (1+2x^2-2x^3+2x^4)/(1-x+x^2-x^3+x^4-x^5).
  • A100287 (program): First occurrence of n in A100002; the least k such that A100002(k) = n.
  • A100302 (program): Expansion of (1-x-6x^2)/((1-x)(1-x-8x^2)).
  • A100303 (program): Expansion of (1-x-4x^2)/(1-x-8x^2).
  • A100304 (program): Expansion of (1-x-6x^2)/(1-x-8x^2).
  • A100305 (program): Expansion of (1-x-4x^2)/(1-2x-7x^2+8x^3).
  • A100307 (program): Modulo 2 binomial transform of 3^n.
  • A100312 (program): Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1).
  • A100314 (program): Number of 2 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
  • A100315 (program): Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
  • A100316 (program): Number of 4 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
  • A100320 (program): A Catalan transform of (1 + 2x)/(1 - 2x).
  • A100335 (program): An inverse Catalan transform of J(2n).
  • A100336 (program): Arshon’s sequence with a different start: start from 2 and replace the letters in odd positions using 1 -> 123, 2 -> 231, 3 -> 312 and the letters in even positions using 1 -> 321, 2-> 132, 3 -> 213.
  • A100337 (program): Arshon’s sequence with a different start: start from 3 and replace the letters in odd positions using 1 -> 123, 2 -> 231, 3 -> 312 and the letters in even positions using 1 -> 321, 2-> 132, 3 -> 213.
  • A100345 (program): Triangle read by rows: T(n,k) = n*(n+k), 0<=k<=n.
  • A100371 (program): a(n) = 2^phi(n) - 1 = A066781(n) - 1.
  • A100374 (program): Largest power of 2 dividing prime(n+1)-prime(n), the n-th consecutive-prime-difference.
  • A100375 (program): a(n) = n-th consecutive-prime-difference divided by the largest power of 2 which divides it.
  • A100381 (program): a(n) = 2^n*binomial(n,2).
  • A100394 (program): a(n) is the subscript of the greatest prime factor of (2*prime(n) + 1).
  • A100399 (program): a(n) = Fibonacci(n)^n.
  • A100401 (program): Digital root of 3^n.
  • A100402 (program): Digital root of 4^n.
  • A100403 (program): Digital root of 6^n.
  • A100412 (program): a(n) = 8*10^n - 7.
  • A100413 (program): Numbers n such that n is reversal(n)-th even composite number (n is A004086(n)-th even composite number).
  • A100430 (program): Bisection of A002417.
  • A100431 (program): Bisection of A002417.
  • A100444 (program): Bisection of A000255.
  • A100449 (program): Number of ordered pairs (i,j) with i + j <= n and gcd(i,j) <= 1.
  • A100451 (program): a(n) = 0 for n <= 2; for n >= 3, a(n) = (n-2)*floor((n^2-2)/(n-2)).
  • A100455 (program): a(n) = 2^n + sin(n*Pi/2).
  • A100470 (program): n appears A055642(n) times (appearances equal number of decimal digits).
  • A100479 (program): Prime(2n-1) + prime(2n).
  • A100484 (program): Even semiprimes.
  • A100500 (program): a(n) = prime(3n-2) + prime(3n-1) + prime(3n).
  • A100503 (program): Bisection of A000125.
  • A100504 (program): a(n) = (4n^3 + 6n^2 + 8*n + 6)/3.
  • A100510 (program): Bisection of A005425.
  • A100511 (program): a(n) = Sum_ j=0..n Sum_ k=0..n binomial(n,j)binomial(n,k)max(j,k).
  • A100525 (program): Bisection of A048654.
  • A100530 (program): Numbers == 0,2,5,9 modulo 10.
  • A100531 (program): a(n) = a(n-1) + (2*n - 1) mod 8 + 1 with a(0)=1.
  • A100536 (program): a(n) = 3*n^2 - 2.
  • A100537 (program): Triangle read by rows: T(n,k) is the number of Dyck n-paths whose first descent has length k.
  • A100542 (program): Two-color Rado numbers R(0,n).
  • A100545 (program): Expansion of (7-2x) / (1-3x+x^2).
  • A100555 (program): Smallest square that is equal to the sum of n not-necessarily-distinct primes plus 1.
  • A100567 (program): Prime-indexed primes as n runs through the integers congruent to 0 or 1 mod 3.
  • A100571 (program): Cubes m^3 such that m^3 is the sum of m-1 consecutive primes plus a larger prime.
  • A100575 (program): Half the number of permutations of 0..n with exactly two maxima.
  • A100577 (program): Number of sets of divisors of n with an odd sum.
  • A100583 (program): Number of triangles in an n X n grid of squares with diagonals.
  • A100585 (program): a(n+1) = a(n)+floor(a(n)/3), a(1) = 3.
  • A100586 (program): Write down the numbers from 3 to infinity. Take next number, M say, that has not been crossed off. Counting through the numbers that have not yet been crossed off after that M, cross off every 5th term. Repeat, always crossing off every 5th term of those that remain. The numbers that are left form the sequence.
  • A100587 (program): Number of nonempty subsets of divisors of n.
  • A100606 (program): a(n) = n^4 + n^3 + n.
  • A100613 (program): Number of elements in the set (x,y): 1 <= x,y <= n, gcd(x,y) > 1 .
  • A100617 (program): There are n people in a room. The first half (i.e., floor(n/2)) of them leave, then 1/3 (i.e., floor of 1/3) of those remaining leave, then 1/4, then 1/5, etc.; sequence gives number who remain at the end.
  • A100626 (program): Numbers of the form 2^(2p+1) where p is prime.
  • A100627 (program): 3^(2p + 1) where p is prime.
  • A100628 (program): a(n) = 2^(3*prime(n) + 1).
  • A100634 (program): a(n) is the decimal equivalent of the binary number whose k-th least significant bit is 1 iff k is a prime number and k <= n.
  • A100637 (program): Trisection of A000720.
  • A100656 (program): a(n)=1 if a hexagonal number is a prime, otherwise 0.
  • A100659 (program): Floor of measure (in degrees) of the internal angles of a regular polygon with n sides.
  • A100661 (program): Quet transform of A006519 (see A101387 for definition). Also, least k such that n+k has at most k ones in its binary representation.
  • A100665 (program): a(n) = round(F(n)^(1/2)) where F(n) is the n-th Fibonacci number (A000045).
  • A100670 (program): Number of two-card Baccarat hands of point n.
  • A100672 (program): Second least-significant bit in the binary expansion of the n-th prime.
  • A100679 (program): Floor of cube root of tetrahedral numbers.
  • A100688 (program): a(n) = prime(n) * 3^prime(n) - 1.
  • A100689 (program): a(n) = prime(n) * 4^prime(n) - 1.
  • A100690 (program): a(n) = p * 5^p - 1 where p=prime(n).
  • A100691 (program): Number of self-avoiding paths with n steps on a triangular lattice in the strip Z x 0,1 .
  • A100701 (program): a(n) = a(n-1) + a(n-2) + a(n-1)*a(n-2) for n>=2; a(0)=2, a(1)=3.
  • A100702 (program): Number of layers of dough separated by butter in successive foldings of croissant dough.
  • A100705 (program): a(n) = n^3 + (n+1)^2.
  • A100706 (program): Bisection of A002275.
  • A100710 (program): Characterized by a(n) XOR (a(n) + 1) = a(n) - n.
  • A100714 (program): Number of runs in binary expansion of A000040(n) (the n-th prime number) for n>0.
  • A100726 (program): Prime numbers whose binary representations are split into a maximum of 7 runs.
  • A100732 (program): a(n) = (3*n)!.
  • A100747 (program): A modular recurrence.
  • A100764 (program): a(1) = 1, a(2) = 2, a(3) = 3, a(n) = least number not the sum of three or fewer previous terms.
  • A100768 (program): a(n) = p * (n^p) - 1 where p = prime(n).
  • A100774 (program): a(n) = 2*(3^n - 1).
  • A100775 (program): a(n) = 97*n + 101.
  • A100776 (program): a(n) = 997 * n + 1009.
  • A100795 (program): n occurs n times, as early as possible subject to the constraint that no two successive terms are identical.
  • A100803 (program): A100802(m) where A100802(m) > A100802(m-1).
  • A100810 (program): a(n) = 0 if prime(n) + 2 = prime(n+1), otherwise 1.
  • A100817 (program): Product of the digits of n, each doubled.
  • A100820 (program): Number of odd numbers between prime(n) and prime(n+1).
  • A100821 (program): a(n) = 1 if prime(n) + 2 = prime(n+1), otherwise 0.
  • A100828 (program): Expansion of (1+2x-2x^3-3x^2)/((x-1)(x+1)(x^2+2x-1)).
  • A100832 (program): Amenable numbers: n such that there exists a multiset of integers (s(1), …, s(n)) whose size, sum and product are all n.
  • A100833 (program): Smallest positive palindrome-free and squarefree sequence.
  • A100855 (program): n*(n^3-n^2+n+1)/2.
  • A100876 (program): Least number of squares that sum to prime(n).
  • A100879 (program): a(n) = n^sigma(n).
  • A100886 (program): Expansion of x(1+3x+2x^2)/((1+x+x^2)(1-x-x^2)).
  • A100892 (program): a(n) = (2n-1) XOR (2n+1), bitwise.
  • A100990 (program): a(n) = n^21 mod 100.
  • A100994 (program): If n is a prime power p^m, m >= 1, then n, otherwise 1.
  • A100995 (program): If n is a prime power p^m, m >= 1, then m, otherwise 0.
  • A101000 (program): Periodic sequence with period 3.
  • A101037 (program): Triangle read by rows: T(n,1) = T(n,n) = n and for 1<k<n: T(n,k) = floor((T(n-1,k-1)+T(n-1,k))/2).
  • A101040 (program): If n has one or two prime-factors then 1 else 0.
  • A101041 (program): Number of numbers not greater than n having no more than two prime factors.
  • A101052 (program): Number of preferential arrangements of n labeled elements when only k<=3 ranks are allowed.
  • A101089 (program): Second partial sums of fourth powers (A000583).
  • A101090 (program): Third partial sums of fourth powers (A000583).
  • A101091 (program): Fourth partial sums of fourth powers (A000583).
  • A101092 (program): Second partial sums of fifth powers (A000584).
  • A101093 (program): Second partial sums of sixth powers (A001014).
  • A101094 (program): a(n) = n(n+1)(n+2)(n+3)(1+3*n+n^2)/120.
  • A101095 (program): Fourth difference of fifth powers (A000584).
  • A101096 (program): Third differences of fifth powers (A000584).
  • A101097 (program): a(n) = n(n+1)(n+2)(n+3)(n+4)(2 + 4n + n^2)/840.
  • A101098 (program): a(1)=1; thereafter, a(n+1) = 20n^3 + 10n.
  • A101099 (program): Third partial sums of fifth powers (A000584).
  • A101100 (program): The first summation of row 5 of Euler’s triangle - a row that will recursively accumulate to the power of 5.
  • A101101 (program): a(1)=1, a(2)=5, and a(n)=6 for n>=3.
  • A101102 (program): Fifth partial sums of cubes (A000578).
  • A101103 (program): Partial sums of A101104. First differences of A005914.
  • A101104 (program): a(1)=1, a(2)=12, a(3)=23, and a(n)=24 for n>=4.
  • A101107 (program): Sorted and uniqued list of class numbers (number of conjugacy classes) of all non-Abelian simple groups.
  • A101123 (program): Numbers n for which 7*n + 11 is prime.
  • A101156 (program): a(n) = 2Fibonacci(n) + 8Fibonacci(n-5).
  • A101165 (program): a(n) = (7n^3 + 6n^2 + 5*n) / 6.
  • A101184 (program): a(n) = n + pi(n) + pi(pi(n)) + pi(pi(pi(n))) + pi(pi(pi(pi(n)))) + …
  • A101202 (program): Multiples of 142857.
  • A101203 (program): a(n) = sum of nonprimes <= n.
  • A101213 (program): a(n) = n * (n+1)^2 * (n+2)^3.
  • A101243 (program): Slowest increasing sequence where the absolute difference between the last digit of a(n) and the first digit of a(n+1) equals 9.
  • A101256 (program): Sum of composites <= n.
  • A101264 (program): a(n) = 1 if 2*n + 1 is prime, otherwise a(n) = 0.
  • A101265 (program): a(1) = 1, a(2) = 2, a(3) = 6; a(n) = 5a(n-1) - 5a(n-2) + a(n-3) for n>3.
  • A101266 (program): First differences of A101402.
  • A101272 (program): a(n)=n, n <=6; a(n)=6, n > 6.
  • A101279 (program): a(1) = 1; a(2k) = a(k), a(2k+1) = k.
  • A101291 (program): Sum of all numbers with n digits.
  • A101292 (program): a(n) = n! + Sum_ i=1..n i.
  • A101297 (program): Bisection of A001622 (decimal expansion of the golden ratio).
  • A101300 (program): Second-smallest prime larger than n.
  • A101301 (program): The sum of the first n primes, minus n.
  • A101304 (program): a(n) = 2^(prime(n) + 1) + 1.
  • A101306 (program): a(n) = Sum_ i=1..n last digit of prime(i) .
  • A101322 (program): a(n) = n - (least divisor of n greater than the square root of n) + (greatest divisor of n less than the square root of n) = n + A033676(n) - A033677(n).
  • A101328 (program): Recurring numbers in the count of consecutive composite numbers between balanced primes and their lower or upper prime neighbors.
  • A101334 (program): a(n) = n^n - (n+1)^(n-1).
  • A101338 (program): Antidiagonal sums in A101321.
  • A101344 (program): Number of primes between prime(n) and 3prime(n).
  • A101345 (program): a(n) = Knuth’s Fibonacci (or circle) product “2 o n”.
  • A101346 (program): a(n) = binomial(2^n, n-1).
  • A101349 (program): Numbers of cubes between prime(n) and prime(n+1).
  • A101351 (program): a(n) = 2^n-1 + Fibonacci(n).
  • A101352 (program): Partial sums of A101351.
  • A101353 (program): a(n) = Sum_ k=0..n (2^k + Fibonacci(k)).
  • A101357 (program): Partial sums of A060354.
  • A101361 (program): a(1) = a(2) = 1; for n > 2, a(n) = Knuth’s Fibonacci (or circle) product “a(n-1) o a(n-2)”.
  • A101362 (program): a(n) = (n+1)*n^4.
  • A101368 (program): The sequence solves the following problem: find all the pairs (i,j) such that i divides 1+j+j^2 and j divides 1+i+i^2. In fact, the pairs (a(n),a(n+1)), n>0, are all the solutions.
  • A101374 (program): a(n) = n*(n^3 - n + 2)/2.
  • A101375 (program): a(n) = n(n+1)(n^2-2*n+2)/2.
  • A101376 (program): a(n) = n^2*(n^3 - n^2 + n + 1)/2.
  • A101377 (program): a(n) = n^2*(n^3-n+2)/2.
  • A101378 (program): a(n) = n^2*(n^3+1)/2.
  • A101383 (program): a(n) = n(n+1)(2*n^3 - n^2 + 2)/6.
  • A101384 (program): a(n) = n(n-1)^3(n^2-n-1)/2.
  • A101386 (program): Expansion of g.f.: (5 - 3x)/(1 - 6x + x^2).
  • A101399 (program): a(0) = 1, a(1) = 2, a(2) = 5; for n >= 3, a(n) = a(n-1) + 2*a(n-2) + a(n-3).
  • A101402 (program): a(0)=0, a(1)=1; for n>=2, let k = smallest power of 2 that is >= n, then a(n) = a(k/2) + a(n-1-k/2).
  • A101405 (program): a(n) = n^(pi(n-1)).
  • A101423 (program): Number of different cuboids with volume p^3 * q^n, where p,q are distinct prime numbers.
  • A101424 (program): Number of different cuboids with volume p^4 * q^n, where p,q are distinct prime numbers.
  • A101425 (program): Number of different cuboids with volume p^5 X q^n, where p,q are distinct prime numbers.
  • A101426 (program): Number of different cuboids with volume p^6 * q^n, where p,q are distinct prime numbers.
  • A101432 (program): Each term is the number of letters in the Spanish name of the previous term.
  • A101433 (program): Partial sums of A101402.
  • A101441 (program): n^prime(n+1).
  • A101442 (program): a(n) = 9973*n + 10007.
  • A101443 (program): Continued fraction expansion of (I_0(1/2)/I_1(1/2)-1)/2 = 1.56185896… (where I_n is the modified Bessel function of the first kind).
  • A101448 (program): Nonnegative numbers k such that 2k + 11 is prime.
  • A101455 (program): a(n) = 0 for even n, a(n) = (-1)^((n-1)/2) for odd n. Periodic sequence 1,0,-1,0,…
  • A101465 (program): Decimal expansion of 2-sqrt(2), square of the edge length of a regular octagon with circumradius 1.
  • A101485 (program): a(n) = (4n)! / ( 4^n * (2n)! ).
  • A101503 (program): Numbers n such that 11*n + 101 is prime.
  • A101553 (program): A modular recurrence.
  • A101566 (program): Binary partition sequence matrix.
  • A101605 (program): a(n) = 1 if n is a product of exactly 3 (not necessarily distinct) primes, otherwise 0.
  • A101621 (program): Initial decimal digit of n^11.
  • A101622 (program): A Horadam-Jacobsthal sequence.
  • A101626 (program): Initial decimal digit of n^12.
  • A101634 (program): Subtract 1, multiply by 1, subtract 2, multiply by 2, etc.
  • A101637 (program): a(n) = 1 if n is a 4-almost prime, that is a product of exactly four (not necessarily distinct) primes, 0 otherwise.
  • A101642 (program): a(n) = Knuth’s Fibonacci (or circle) product “3 o n”.
  • A101651 (program): a(n)=Product k=0..n, 1+0^A010060(k) /2.
  • A101653 (program): a(n)=Product k=0..n, 1+3^A010060(k) /2.
  • A101660 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 12.
  • A101663 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 22.
  • A101671 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 10.
  • A101673 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 20.
  • A101675 (program): Expansion of (1 - x - x^2)/(1 + x^2 + x^4).
  • A101676 (program): a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) with initial terms 1,0,-2,-1,0.
  • A101677 (program): a(n) = a(n-1) - 2a(n-2) + 2a(n-3) - 2a(n-4) + 2a(n-5) - a(n-6).
  • A101686 (program): a(n) = Product_ i=1..n (i^2 + 1).
  • A101688 (program): Once 1, once 0, repeat, twice 1, twice 0, repeat, thrice 1, thrice 0… and so on.
  • A101741 (program): 4th row of A101646.
  • A101776 (program): Smallest k such that k^2 is equal to the sum of n not-necessarily-distinct primes plus 1.
  • A101803 (program): Nearest integer to n*(phi-1), where phi is golden ratio 1.618033988749895… (A001622).
  • A101808 (program): Number of primes between two consecutive even numbers.
  • A101810 (program): Number of compositions (ordered partitions) of the n-th prime into n nonnegative integers.
  • A101825 (program): G.f.: x*(1+x)^2/(1-x^3).
  • A101853 (program): a(n) = n(20+15n+n^2)/6.
  • A101854 (program): a(n) = n(n+1)(n^2+21*n+50)/24.
  • A101855 (program): a(n) = n(n+1)(n+2)(n+4)(n+23)/120.
  • A101859 (program): a(n) = 11 + (23*n)/2 + n^2/2.
  • A101860 (program): a(n) = (3+n)(2 + 33n + n^2)/6.
  • A101861 (program): n(n+5)(50+45*n+n^2)/24.
  • A101862 (program): a(n) = n(n+1)(n+7)(122+57n+n^2)/120.
  • A101863 (program): Main diagonal of A101858.
  • A101864 (program): Wythoff BB numbers.
  • A101865 (program): Third row of A101858.
  • A101868 (program): a(n) = n + 2*ceiling(phi n), where phi = (1 + sqrt(5))/2. Row 1 of A101866.
  • A101869 (program): Row 2 of A101866.
  • A101870 (program): Row 3 of A101866.
  • A101871 (program): Number of Abelian groups of order 2n+1.
  • A101875 (program): Number of Abelian groups of order 4n+2.
  • A101879 (program): a(0) = 1, a(1) = 1, a(2) = 2; for n > 2, a(n) = 5a(n-1) - 5a(n-2) + a(n-3).
  • A101881 (program): Write two numbers, skip one, write two, skip two, write two, skip three … and so on.
  • A101882 (program): Write three numbers, skip one, write three, skip two, write three, skip three… and so on.
  • A101883 (program): Write four numbers, skip one, write four, skip two, write four, skip three… and so on.
  • A101909 (program): Number of primes between 2n and 4n.
  • A101921 (program): a(2n) = a(n) + 2n - 1, a(2n+1) = 4n.
  • A101925 (program): a(n) = A005187(n) + 1.
  • A101926 (program): a(n) = 2^A101925(n).
  • A101945 (program): a(n) = 6*2^n - n - 5.
  • A101946 (program): 62^n - 3n - 5.
  • A101979 (program): Antidiagonal sums of A101309, which is the matrix logarithm of A047999 (Pascal’s triangle mod 2).
  • A101986 (program): Maximum sum of products of successive pairs in a permutation of order n+1.
  • A101987 (program): Product of nonzero digits of n-th prime.
  • A102039 (program): a(n) = a(n-1) + last digit of a(n-1), starting at 1.
  • A102040 (program): a(n) = a(n-1) + last digit of a(n-1), starting at 3.
  • A102041 (program): a(n) = a(n-1) + last digit of a(n-1), starting at 7.
  • A102042 (program): a(n) = a(n-1) + last digit of a(n-1), starting at 9.
  • A102047 (program): Decimal expansion of -1/4 + log(2)/2.
  • A102066 (program): Sum of the first n primes, mod 6.
  • A102068 (program): a(n) = P(n)!, where P(n) is the largest prime factor of n (with a(1) = 1).
  • A102083 (program): a(n) = 8n^2 + 4n + 1.
  • A102091 (program): Number of perfect matchings in the C_ 2n X P_3 graph (C_ 2n is the cycle graph on 2n vertices and P_3 is the path graph on 3 vertices).
  • A102094 (program): a(n) = (2n-1)(2*n+1)^2.
  • A102126 (program): Minimum number of pieces needed to dissect a square into n smaller squares (not necessarily of the same size).
  • A102147 (program): Second Eulerian transform of 1, 2, 3, 4, 5, … (A000027).
  • A102206 (program): a(0) = 3, a(1) = 8, a(n+2) = 4*a(n+1) - a(n) - 2.
  • A102207 (program): a(n) = 5a(n-1) - 5a(n-2) + a(n-3) with a(0) = 4, a(1) = 17, a(2) = 65.
  • A102214 (program): Expansion of (1 + 4x + 4x^2)/((1+x)*(1-x)^3).
  • A102239 (program): a(n) = (Sum_ i=0..n 5^i) + 1 - (Sum_ i=0..n 5^i) mod 2.
  • A102283 (program): Period 3: repeat [0, 1, -1].
  • A102285 (program): G.f. (1-x)/(7x^2-6x+1).
  • A102296 (program): a(n) = (1/6)(n+1)(10n^2 + 17n + 12).
  • A102301 (program): a(n) = ((3n + 1)2^(n+3) + 9 + (-1)^n)/18.
  • A102302 (program): Largest number < n/2 coprime to n.
  • A102303 (program): a(n) = (1/6) * (7^(n+1) - 3*(-1)^n + 2).
  • A102305 (program): a(n) = n^2 + 2*n + 3.
  • A102307 (program): a(n) = Fibonacci(2n+1) * binomial(2n,n).
  • A102310 (program): Square array read by antidiagonals: Fibonacci(k*n).
  • A102312 (program): a(n) = Fibonacci(5*n).
  • A102338 (program): Numbers n such that 10n+3 is prime.
  • A102342 (program): Numbers k such that 10k + 7 is prime.
  • A102344 (program): Numbers n such that the Diophantine equation (x+2)^3-x^3=2*n^2 has solutions.
  • A102345 (program): a(n) = 3^n + (-1)^n.
  • A102348 (program): Decimated primes: every 10th prime has been omitted.
  • A102352 (program): Numbers n such that n^3 can be partitioned into n primes such that n-1 are consecutive primes and the remaining prime is larger than the sum of the n-1 consecutive primes.
  • A102363 (program): Triangle read by rows, constructed by a Pascal-like rule with left edge = 2^k, right edge = 2^(k+1)-1 (k >= 0).
  • A102366 (program): Number of subsets of 1,2,…,n in which exactly half of the elements are less than or equal to sqrt(n).
  • A102376 (program): a(n) = 4^A000120(n).
  • A102377 (program): Gould’s sequence A001316 in binary.
  • A102378 (program): a(n) = a(n-1) + a([n/2]) + 1, a(1) = 1.
  • A102379 (program): a(n) = minimal number of nodes in a binary tree of height n.
  • A102389 (program): An evil count.
  • A102390 (program): An odious count.
  • A102391 (program): Evil numbers in evil places.
  • A102392 (program): Odious numbers in odious places.
  • A102393 (program): A wicked evil sequence.
  • A102394 (program): A wicked odious sequence.
  • A102395 (program): A mod 2 related Jacobsthal sequence.
  • A102396 (program): A mod 2 related Jacobsthal sequence.
  • A102428 (program): Central column of triangle A102427.
  • A102438 (program): a(n) = 100*n + 44.
  • A102439 (program): a(n) = 100*n + 4.
  • A102446 (program): a(n) = a(n-1) + 4*a(n-2) for n>1, a(0) = a(1) = 2.
  • A102485 (program): a(n) = 53^n - 42^n.
  • A102486 (program): a(n) = 4a(n-1) - 5a(n-2).
  • A102511 (program): Sum(A008683(A102510(k)): k<=n).
  • A102515 (program): a(n) = floor(1 + sqrt(2n + 1)).
  • A102518 (program): a(n) = Sum_ k=0..n binomial(n, k) * Sum_ j=0..k binomial(3k, 3j).
  • A102557 (program): Denominator of the probability that 2n-dimensional Gaussian random triangle has an obtuse angle.
  • A102560 (program): Expansion of (1-x^3)/(1-x^4).
  • A102561 (program): a(n) = 2^floor(n/2)*((-1)^floor(n/2) + (-1)^n)/2.
  • A102566 (program): a(n) = minimal k such that f^k(prime(n)) = 1 where f(m) = (m+1)/2^r, 2^r is the highest power of two dividing m+1.
  • A102572 (program): a(n) = floor(log_4(n)).
  • A102591 (program): a(n) = Sum_ k=0..n binomial(2n+1, 2k)*3^(n-k).
  • A102592 (program): a(n) = Sum_ k=0..n binomial(2n+1, 2k)*5^(n-k).
  • A102603 (program): 24n + 21.
  • A102615 (program): Nonprime numbers of order 2.
  • A102616 (program): Nonprime numbers of order 3.
  • A102620 (program): Number of legal Go positions on a 1 X n board (for which 3^n is a trivial upper bound).
  • A102631 (program): a(n) = n^2 / (squarefree kernel of n).
  • A102650 (program): a(n) = 4 * floor(28*2^n/15).
  • A102651 (program): a(n) = 4 * floor(23*2^n/15).
  • A102652 (program): a(n) = 4 * floor(242^n/15) = 4A077854(n).
  • A102653 (program): a(n) = 4 * floor(27*2^n/15).
  • A102656 (program): Numbers n such that 11*n + 1 is prime.
  • A102669 (program): Number of digits >= 2 in decimal representation of n.
  • A102670 (program): Number of digits >= 2 in the decimal representations of all integers from 0 to n.
  • A102671 (program): Number of digits >= 3 in decimal representation of n.
  • A102672 (program): Number of digits >= 3 in the decimal representations of all integers from 0 to n.
  • A102673 (program): Number of digits >= 4 in decimal representation of n.
  • A102674 (program): Number of digits >= 4 in the decimal representations of all integers from 0 to n.
  • A102675 (program): Number of digits >= 5 in decimal representation of n.
  • A102676 (program): Number of digits >= 5 in the decimal representations of all integers from 0 to n.
  • A102677 (program): Number of digits >= 6 in decimal representation of n.
  • A102678 (program): Number of digits >= 6 in the decimal representations of all integers from 0 to n.
  • A102679 (program): Number of digits >= 7 in decimal representation of n.
  • A102680 (program): Number of digits >= 7 in the decimal representations of all integers from 0 to n.
  • A102681 (program): Number of digits >= 8 in decimal representation of n.
  • A102682 (program): Number of digits >= 8 in the decimal representations of all integers from 0 to n.
  • A102683 (program): Number of digits 9 in decimal representation of n.
  • A102684 (program): Number of times the digit 9 appears in the decimal representations of all integers from 0 to n.
  • A102685 (program): Partial sums of A055640.
  • A102686 (program): Numbers k such that 11*k + 3 is prime.
  • A102689 (program): a(n) = 10000*n + 2468.
  • A102690 (program): Number of n-expodigital numbers (i.e., numbers m such that m^n has exactly n decimal digits).
  • A102691 (program): Least n-expodigital number (i.e., numbers m such that m^n has exactly n decimal digits).
  • A102693 (program): a(n) is the number of digraphs (not allowing loops) with vertices 1,2,…,n that have a unique Eulerian tour (up to cyclic shift).
  • A102700 (program): Numbers k such that 10*k + 9 is prime.
  • A102711 (program): Numbers k such that 11*k + 7 is prime.
  • A102714 (program): Expansion of (x+2) / ((x+1)(x^2-3x+1)).
  • A102715 (program): Triangle read by rows: T(n,k) is phi(binomial(n,k)), where phi is Euler’s totient function (0 <= k <= n).
  • A102716 (program): Triangle read by rows: T(n,k) = sigma(binomial(n,k)) (0 <= k <= n), where sigma(m) is the sum of the positive divisors of m.
  • A102721 (program): Numbers n such that 11*n + 13 is prime.
  • A102731 (program): Numbers k such that 11*k + 23 is prime.
  • A102732 (program): Primes of the form 13n+5.
  • A102733 (program): Numbers n such that 2*n + 101 is prime.
  • A102734 (program): Primes of the form 23n+5.
  • A102741 (program): a(n) = 3^4 * binomial(n+3, 4).
  • A102757 (program): a(n) = Sum_ i=0..n C(n,i)^2 * i! * 3^i.
  • A102762 (program): Curvatures of (largest) kissing circles along the circumference, starting with curvature = -1 and 2.
  • A102768 (program): Numbers k such that 23*k + 11 is prime.
  • A102770 (program): (p*q - 1)/2 where p and q are consecutive odd primes.
  • A102773 (program): a(n) = Sum_ i=0..n binomial(n,i)^2i!4^i.
  • A102781 (program): Number of positive even numbers less than the n-th prime.
  • A102807 (program): a(n) is the square of one plus the number consisting of n 3’s.
  • A102815 (program): “False so far” sequence.
  • A102845 (program): Number of prime factors of the sum of the first n odd primes.
  • A102846 (program): a(0)=1, a(1)=1, a(n) = a(n-1)*a(n-2) + 2.
  • A102853 (program): Number of prime factors (with multiplicity) of number of points on surface of square pyramid.
  • A102860 (program): Number of ways to change three non-identical letters in the word aabbccdd…, where there are n types of letters.
  • A102862 (program): Numbers of prime factors of the sum of the first n primes.
  • A102863 (program): a(n)=1 if at least one of the first n primes is a divisor of the sum of the first n primes; otherwise a(n)=0.
  • A102865 (program): Base-4 digits are, in order, the first n terms of the sequence (1, 3, 21, 203, 2021, 20203, 202021, 2020203, 20202021, 202020203, … ).
  • A102871 (program): a(n) = a(n-3) - 5a(n-2) + 5a(n-1), a(0) = 1, a(1) = 3, a(2) = 10.
  • A102899 (program): a(n) = ceiling(n/3)^2 - floor(n/3)^2.
  • A102900 (program): a(n) = 3a(n-1) + 4a(n-2), a(0)=a(1)=1.
  • A102901 (program): a(n) = a(n-1) + 6a(n-2), a(0)=1, a(1)=0.
  • A102902 (program): a(n) = 9a(n-1) - 16a(n-2).
  • A102909 (program): a(n) = Sum_ j=0..8 n^j.
  • A103115 (program): a(n) = 6n(n-1)-1.
  • A103116 (program): a(n) = Sum_ i=1..n (n-i+1)*phi(i).
  • A103127 (program): Numbers congruent to -1, 1, 3, 5 mod 16.
  • A103128 (program): a(n) = floor(sqrt(2n-1)).
  • A103134 (program): a(n) = Fibonacci(6n+4).
  • A103145 (program): a(n) = (1/6)(n^3 + 21n^2 + 74*n + 18).
  • A103154 (program): Each letter appears an even number of times in the English names for 1 through n taken together (names without “and”).
  • A103157 (program): Number of ways to choose 4 distinct points from an (n+1) X (n+1) X (n+1) lattice cube.
  • A103164 (program): Integers but with the primes squared.
  • A103168 (program): a(n) = remainder when (n written backwards) is divided by n.
  • A103177 (program): (7*3^n + 2n + 5)/4.
  • A103192 (program): Trajectory of 1 under repeated application of the function n -> A102370(n).
  • A103194 (program): LAH transform of squares.
  • A103196 (program): a(n) = (1/9)(2^(n+3)-(-1)^n(3n-1)).
  • A103202 (program): A102370 sorted.
  • A103204 (program): a(1) = 2, a(2) = 4; a(n) = 2*a(n-1) - 1.
  • A103214 (program): a(n) = 24*n + 1.
  • A103217 (program): Hexagonal numbers triangle read by rows: T(n,k)=(n+1-k)(2(n+1-k)-1).
  • A103220 (program): a(n) = n(n+1)(3*n^2+n-1)/6.
  • A103221 (program): Number of partitions of n into parts 2 and 3.
  • A103271 (program): a(n) = (prime(n)+prime(n+1)) mod 4.
  • A103290 (program): n(n-1)(n^2-n+4)/6.
  • A103303 (program): Complete list of digits used in the counting numbers (in base 10). Also known as the “Arabic numerals”.
  • A103312 (program): A transform of the Jacobsthal numbers.
  • A103325 (program): Fifth powers of Lucas numbers.
  • A103326 (program): a(n) = Fibonacci(5n)/Fibonacci(n).
  • A103327 (program): Triangle read by rows: T(n,k) = binomial(2n+1, 2k+1).
  • A103328 (program): Triangle T(n, k) read by rows: binomial(2n, 2k+1).
  • A103333 (program): Number of closed walks on the graph of the (7,4) Hamming code.
  • A103334 (program): Number of closed walks of length 2n at any of the nodes of degree 1 on the graph of the (7,4) Hamming code.
  • A103354 (program): a(n) = floor(x), where x is the solution to x = 2^(n-x).
  • A103355 (program): a(n) = n - floor( sqrt(prime(n) ).
  • A103368 (program): Period 6: repeat [1, 1, -1, -1, 0, 0].
  • A103390 (program): Natural numbers but with nonprimes squared.
  • A103391 (program): ‘Even’ fractal sequence for the natural numbers: Deleting every even-index term results in the same sequence.
  • A103416 (program): a(n) = n - ceiling(sqrt(prime(n))).
  • A103424 (program): E.g.f.: 1 + sinh(2*x).
  • A103425 (program): a(n) = 3a(n-1) + a(n-2) - 3a(n-3).
  • A103433 (program): a(n) = Sum_ i=1..n Fibonacci(2i-1)^2.
  • A103434 (program): a(n) = Sum_ i=1..n Fibonacci(2i)^2.
  • A103435 (program): a(n) = 2^n * Fibonacci(n).
  • A103439 (program): a(n) = Sum_ i=0..n-1 Sum_ j=0..i (i-j+1)^j.
  • A103444 (program): Triangle read by rows: T(n,k) is number of unitary divisors of C(n,k), 0<=k<=n.
  • A103447 (program): Triangle read by rows: T(n,k) = Moebius(binomial(n,k)) (0 <= k <= n).
  • A103451 (program): Triangular array T read by rows: T(n, 0) = T(n, n) = 1, T(n, k) = 0 for 0 <= k <= n.
  • A103452 (program): Inverse of number triangle A103451.
  • A103453 (program): a(n) = 0^n + 3^n - 1.
  • A103454 (program): a(n) = 0^n + 4^n - 1.
  • A103455 (program): a(n) = 0^n + 5^n - 1.
  • A103456 (program): a(n) = 0^n + 10^n - 1.
  • A103457 (program): a(n) = 3^n + 1 - 0^n.
  • A103458 (program): a(n) = 7^n + 1 - 0^n.
  • A103459 (program): a(n) = 8^n + 1 - 0^n.
  • A103460 (program): a(n) = 9^n + 1 - 0^n.
  • A103461 (program): a(n) = (-10)^n + 1 - 0^n.
  • A103469 (program): Number of polyominoes without holes consisting of 3 regular unit n-gons.
  • A103480 (program): Row sums of A103462.
  • A103486 (program): a(0)=7, a(1)=11, a(2)=13, a(3)=17; then a(n) = a(n-1)+a(n-3)-a(n-4).
  • A103488 (program): a(n) = 2^(n^2-1).
  • A103505 (program): Denominator in expansion of (1-x)*log(1-x).
  • A103516 (program): Triangle read by rows: count in a vee.
  • A103517 (program): Expansion of (1+2*x-x^2)/(1-x)^2.
  • A103519 (program): a(1) = 1, a(n) = sum of n successive numbers starting with a(n-1) + 1.
  • A103532 (program): Number of divisors of 240^n.
  • A103566 (program): Sum of the primes > 5 modulo 3.
  • A103568 (program): Sum of the (primes > 5 modulo 7).
  • A103569 (program): Sum of the (primes > 5 modulo 11).
  • A103570 (program): Sum of the (primes > 5 modulo 13).
  • A103571 (program): Sum of the (primes > 5 modulo 17).
  • A103572 (program): Sum of the (primes > 5 modulo 19).
  • A103586 (program): a(0)=1, for n > 0: n-th run consists of 2^n-1 copies of n+1.
  • A103604 (program): a(n) = C(n+6,6) * C(n+10,6).
  • A103609 (program): Fibonacci numbers repeated (cf. A000045).
  • A103623 (program): n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.
  • A103627 (program): Let S(n) = n,1,n ; sequence gives concatenation S(0), S(1), S(2), …
  • A103636 (program): Sum[d n, d==0 mod 3, d^2].
  • A103637 (program): Sum[d n, d==1 mod 3, d^2].
  • A103638 (program): Sum[d n, d==2 mod 3, d^2].
  • A103639 (program): a(n) = Product_ i=1..2n 2*i+1.
  • A103644 (program): Expansion of g.f. (3x+1)/(1+2x-6x^2-27x^3).
  • A103645 (program): G.f.: (108x^2+27x+1)/(1+2x-6x^2-27x^3).
  • A103646 (program): G.f.: 9*(3x+1)/(1+2x-6x^2-27x^3).
  • A103675 (program): a(n) = 1 if the binary representation of n! contains 7! (bit string “1001110110000”), otherwise a(n) = 0.
  • A103681 (program): Numbers m such that in binary representation m! doesn’t contain 7!.
  • A103685 (program): Consider the morphism 1-> 1,2 , 2-> 1,3 , 3-> 1 ; a(n) is the total number of ‘3’ after n substitutions.
  • A103701 (program): Add 2 to each of the preceding digits, beginning with 1.
  • A103704 (program): Add 5 to each of the preceding digits, beginning with 1.
  • A103729 (program): Column k=2 sequence of array A103728.
  • A103730 (program): Negative of column k=3 sequence of array A103728.
  • A103736 (program): Fibonacci numbers with nonprime indices.
  • A103747 (program): Trajectory of 2 under repeated application of the map n -> A102370(n).
  • A103754 (program): Number of contiguous digits i in the counting numbers, for i=0.
  • A103772 (program): Larger of two sides in a (k,k,k-1)-integer-sided triangle with integer area.
  • A103775 (program): Number of ways to write n! as product of distinct squarefree numbers.
  • A103815 (program): a(n) = -1 + Product_ k=1..n Fibonacci(k).
  • A103819 (program): Whitney transform of Jacobsthal numbers.
  • A103820 (program): Whitney transform of 3^n.
  • A103831 (program): For even n, a(n) = n(n+1), for odd n, a(n) = 2n + 1.
  • A103832 (program): For even n, a(n)=2n+1, for odd n, a(n)=n(n+1)
  • A103838 (program): Complement of A001671.
  • A103889 (program): Odd and even positive integers swapped.
  • A103897 (program): a(n) = 32^(n-1)(2^n-1).
  • A103904 (program): Number of perfect matchings of an n X (n+1) Aztec rectangle with the third vertex in the topmost row removed.
  • A103947 (program): a(n) is the number of distinct n-th powers of functions 1, 2 -> 1, 2 .
  • A103969 (program): Positions n such that A005941(n) = A005940(n).
  • A103974 (program): Smaller sides (a) in (a,a,a+1)-integer triangle with integer area.
  • A103975 (program): Smaller side in (a,a+1,a+1)-integer triangle with integer area.
  • A103976 (program): Partial sums of A040976 (= primes-2).
  • A103991 (program): Reduced denominators of the hypercube line-picking integrand sqrt(Pi)*I(n,0).
  • A104039 (program): Number of primitive roots modulo prime(n)^2, where prime(n) is n-th prime.
  • A104099 (program): n * (10n^2 - 6n + 1), or n*A087348(n).
  • A104103 (program): a(n) = ceiling(sqrt(prime(n))).
  • A104104 (program): a(1) = 1, if A(k) = sequence of first 2^(k-1) terms and if B(k) is A(k) with 0’s and 1’s exchanged, then A(k+1) = A(k)A(k) if a(k) = 0, A(k+1) = A(k)B(k) if a(k) = 1.
  • A104105 (program): a(1) = 1, if A(k) = sequence of first 2^k -1 terms and if B(k) is A(k) with 0’s and 1’s exchanged, then A(k+1) = A(k),1,B(k) if a(k) = 0, A(k+1) = A(k),0,B(k) if a(k) = 1.
  • A104106 (program): a(1) = 1; thereafter, if A(k) = sequence of first 2^k -1 terms, then A(k+1) = A(k),1,A(k) if a(k) = 0, and A(k+1) = A(k),0,A(k) if a(k) = 1.
  • A104117 (program): For n=2^k, a(n) = k+1, else 0.
  • A104120 (program): (Prime(n + 1) - Prime(n))/2 (mod 2).
  • A104121 (program): a(n)=1 if there is a partition of n^3 into n primes such that n-1 are consecutive primes and the remaining prime is larger than the sum of the n-1 consecutive primes, otherwise a(0)=0 if no such partition exists.
  • A104147 (program): Number of cubes <= n-th prime.
  • A104150 (program): Shifted factorial numbers: a(0)=0, a(n) = (n-1)!.
  • A104155 (program): The 64 codons of the genetic code, giving the value 1 to thymine (T), 3 to adenine (A), 2 to cytosine (C) and 4 to guanine (G).
  • A104161 (program): G.f.: x*(1 - x + x^2)/((1-x)^2 * (1 - x - x^2)).
  • A104162 (program): Indicator sequence for the Fibonacci numbers.
  • A104188 (program): a(n) = 4n*(4n - 1).
  • A104199 (program): Lower bound on a straddle prime pair.
  • A104200 (program): Upper bound on a straddle prime pair.
  • A104218 (program): Sum of opposite numbers on a clock, starting at 12.
  • A104220 (program): a(n) = Fibonacci[n]+1-Mod[Fibonacci[n],2]
  • A104221 (program): a(n) = Fibonacci(n) - (Fibonacci(n) mod 2).
  • A104249 (program): a(n) = (3*n^2 + n + 2)/2.
  • A104270 (program): a(n) = 2^(n-2)*(C(n,2)+2).
  • A104293 (program): a(n) = prime((prime(n)-1)/2).
  • A104294 (program): a(n) = prime((prime(n)+1)/2).
  • A104295 (program): a(n) = A104294(n) - A104293(n).
  • A104344 (program): a(n) = Sum_ k=1..n k!^2.
  • A104356 (program): Smallest m such that A104350(m) has exactly n trailing zeros in decimal representation.
  • A104376 (program): a(n) = Sum_ j=0..13 n^j.
  • A104401 (program): a(n) = A104235(n)/4.
  • A104406 (program): Number of numbers <= n having no 2 in ternary representation.
  • A104407 (program): Number of Hamiltonian groups of order <= n.
  • A104435 (program): Number of ways to split 1, 2, 3, …, 2n into 2 arithmetic progressions each with n terms.
  • A104436 (program): Number of ways to split 1, 2, 3, …, 3n into 3 arithmetic progressions each with n terms.
  • A104449 (program): Fibonacci sequence with initial values a(0) = 3 and a(1) = 1.
  • A104457 (program): Decimal expansion of 1 + phi = phi^2 = (3 + sqrt(5))/2.
  • A104462 (program): Convert the binary strings in A101305 to decimal.
  • A104473 (program): a(n) = binomial(n+2,2)*binomial(n+6,2).
  • A104474 (program): a(n) = binomial(n+3,3)*binomial(n+7,3).
  • A104475 (program): a(n) = binomial(n+4,4) * binomial(n+8,4).
  • A104478 (program): a(n) = binomial(n+8,8)*binomial(n+12,8).
  • A104492 (program): Cube excess of the n-th prime.
  • A104514 (program): a(n) = least number k > 1 of consecutive integers which sum to 2*n; or a(n) = 0 if n is a power of 2.
  • A104521 (program): Fixed point of the morphism 0-> 1 , 1-> 1,0,1 .
  • A104522 (program): Expansion of (-1+x+3x^2-x^3)/((x+1)(3x-1)(x-1)^2).
  • A104538 (program): Expansion of (1 + 2x) / (1 + 2x + 4*x^2).
  • A104551 (program): Expansion of x/((1-x)sqrt(1+4x^2)).
  • A104563 (program): A floretion-generated sequence relating to centered square numbers.
  • A104566 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product H*R of the infinite lower triangular matrices H = [1; 1,2; 1,2,1; 1 2,1,2; …] and R = [1; 1,1; 1,1,1; 1,1,1,1; …].
  • A104568 (program): Triangle of numbers that are 0 or 1 mod 3.
  • A104571 (program): Triangle T(n,k) = A042948(n-k+1) read by rows, 0<=k<=n.
  • A104572 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product A*B of the infinite lower triangular matrices A = [1; 3, 1; 5, 3, 1; 7, 5, 3, 1; …] and B=[1; 2,1; 1,2,1; 2,1,2,1; …].
  • A104581 (program): Expansion of 1/(1 + x + x^3 + x^4).
  • A104582 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product of the lower triangular matrix (Fibonacci(i-j+1)) and of the lower triangular matrix all of whose entries are equal to 1 (for j <= i).
  • A104584 (program): a(n) = (1/2) * ( 3n^2 + n(-1)^n ).
  • A104585 (program): a(n) = (1/2) * ( 3n^2 - n(-1)^n ).
  • A104594 (program): A129760/2.
  • A104626 (program): Numbers having three 1’s in their base-phi representation.
  • A104635 (program): Odd n such that 2*n+1 is prime.
  • A104636 (program): Even n such that 2n+1 is prime.
  • A104638 (program): Number of odd digits in n-th prime.
  • A104640 (program): Number of odd digits in n^3.
  • A104643 (program): Number of arrangements that can be formed by taking n distinct things out of 25.
  • A104670 (program): a(n) = binomial(n+2, 2)*binomial(n+7, n).
  • A104671 (program): C(n+3,3)*C(n+8,n+0).
  • A104672 (program): C(n+4,4)*C(n+9,n+0)
  • A104673 (program): C(n+5,5)*C(n+10,n+0).
  • A104674 (program): a(n) = binomial(n+6, 6) * binomial(n+11, n).
  • A104675 (program): a(n) = C(n+1,n) * C(n+6,1).
  • A104676 (program): a(n) = binomial(n+2,2) * binomial(n+7,2).
  • A104677 (program): a(n) = binomial(n+3,3)*binomial(n+8,3).
  • A104679 (program): a(n) = C(n+5,5)*C(n+10,5).
  • A104682 (program): a(n) = Sum_ j=0..14 n^j.
  • A104686 (program): n*(n+1)/2 (mod 6).
  • A104706 (program): First terms in the rearrangements of integer numbers (see comments).
  • A104720 (program): Expansion of 1/((1-x)(1-x^2)(1-10x)).
  • A104721 (program): Expansion of (1+x)^2/(1-4*x^2).
  • A104738 (program): Positions of records in A104706.
  • A104739 (program): Positions of records in A104717.
  • A104743 (program): Numbers m = n + 3^n such that the equation x = 3^(m-x) has solution x = 3^n.
  • A104745 (program): a(n) = 5^n + n.
  • A104747 (program): a(n) = (n-3)2^n + n(n+3)/2 + 3.
  • A104762 (program): Triangle read by rows: row n contains first n nonzero Fibonacci numbers in decreasing order.
  • A104763 (program): Triangle read by rows: Fibonacci(1), Fibonacci(2), …, Fibonacci(n) in row n.
  • A104764 (program): Triangle T(n,k) = Lucas(n-k+1) read by rows, 1<=k<=n.
  • A104765 (program): Triangle T(n,k) read by rows: row n contains the first n Lucas numbers A000204.
  • A104767 (program): a(n)=n for n <= 3, a(n) = 2a(n-1) - 2a(n-2) + 2a(n-3) for n >= 4.
  • A104777 (program): Integer squares congruent to 1 mod 6.
  • A104792 (program): Triangle T(n,k) = A000330(n-k), n>=1, 0<=k<n, read by rows.
  • A104793 (program): Triangle T(n,k) = A023537(n-k), n >= 1, 0 <= k < n, read by rows.
  • A104859 (program): Partial sums of A001764.
  • A104861 (program): Number of compositions (ordered partitions) of the n-th prime into n positive integers.
  • A104879 (program): Row sums of a sum-of-powers triangle.
  • A104887 (program): Triangle T(n,k) = (n-k+1)th prime, read by rows.
  • A104891 (program): a(0) = 0; a(n) = 5*a(n-1) + 5.
  • A104896 (program): a(0) = 0; a(n) = 7*a(n-1) + 7.
  • A104934 (program): Expansion of (1-x)/(1 - 3x - 2x^2).
  • A104974 (program): A Fredholm-Rueppel triangle.
  • A105038 (program): Nonnegative n such that 6n^2 + 6n + 1 is a square.
  • A105042 (program): Numbers n such that 10n - 1 is prime.
  • A105058 (program): G.f. (1+8x-x^2)/((x+1)(x^2-6x+1)).
  • A105060 (program): Triangle read by rows in which the n-th row consists of the first n nonzero terms of A033312.
  • A105062 (program): Triangle read by rows, based on the morphism f: 1->2, 2->3, 3->4, 4->5, 5->6, 6-> 6,6,10,7 , 7->8, 8->9, 9->10, 10->11, 11->12, 12-> 12,12,5,1 . First row is 1. If current row is a,b,c,…, then the next row is a,b,c,…,f(a),f(b),f(c),…
  • A105067 (program): a(n) = Sum_ j=0..11 n^j.
  • A105073 (program): Define a(1)=0, a(2)=2 then a(n) = 3a(n-1) - a(n-2), a(n+1) = 3a(n)-a(n-1) and a(n+2) = 3*a(n+1) - a(n) + 2.
  • A105081 (program): a(n) = 1 + A003188(n - 1), n>=1.
  • A105082 (program): Expansion of (5+4x)/(1-2x-x^2).
  • A105086 (program): Sum of the divisors of n minus the least nontrivial proper divisor of n.
  • A105088 (program): Sum of the sides of ordered 2 X 2 prime squares.
  • A105092 (program): Sum of the sides of ordered 2 prime sided prime triangles.
  • A105100 (program): Sum of ordered 3 prime sided prime triangles.
  • A105125 (program): Triangle read by rows: T(n,k) = n^3 + k^3, n >= 0, 0 <= k <= n.
  • A105126 (program): Primes of the form 16n+9.
  • A105127 (program): Primes of the form 32n+17.
  • A105133 (program): Numbers n such that 8n + 5 is prime.
  • A105134 (program): Numbers n such that 16n+9 is prime.
  • A105135 (program): Numbers n such that 32n+17 is prime.
  • A105150 (program): Approximation to leading digit of n-th Fibonacci number.
  • A105161 (program): Difference between n and the second-smallest prime larger than n.
  • A105163 (program): a(n) = (n^3 - 7*n + 12)/6.
  • A105198 (program): a(n) = n(n+1)/2 mod 4.
  • A105202 (program): Irregular triangle read by rows: row n gives the word f(f(f(…(1)))) [with n applications of f], where f is the morphism 1-> 1,2,1 , 2-> 2,3,2 , 3-> 3,1,3 .
  • A105203 (program): Trajectory of 1 under the morphism f: 1-> 1,2,1 , 2-> 2,3,2 , 3-> 3,1,3 .
  • A105206 (program): Number of edges in a pancyclic graph on n+2 vertices with the fewest possible edges.
  • A105209 (program): Nearest integer to the cube root of n.
  • A105218 (program): a(n) = Sum_ k=0..n C(n,k)^2(n-k)!k^3.
  • A105220 (program): Trajectory of 1 under the morphism 1-> 1,2,1 , 2-> 2,2,2 .
  • A105221 (program): a(n) = the sum of n’s distinct prime factors below n.
  • A105225 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = -1, a(2) = -2.
  • A105234 (program): Central column of a Moebius-binomial triangle.
  • A105235 (program): Partial sums of the central column of a Moebius-binomial triangle.
  • A105249 (program): a(n) = binomial(n+2,n)*binomial(n+6,n).
  • A105250 (program): a(n) = binomial(n+3,n)*binomial(n+7,n).
  • A105251 (program): a(n) = binomial(n+4,n)*binomial(n+8,n).
  • A105252 (program): a(n) = binomial(n+5,n)*binomial(n+9,n).
  • A105253 (program): a(n) = binomial(n+6,n)*binomial(n+10,n).
  • A105254 (program): a(n) = binomial(n+7,n)*binomial(n+11,n).
  • A105266 (program): a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that no three terms x,y,z of the sequence, with x<y<z, satisfy z-y=y-x+1.
  • A105279 (program): a(0)=0; a(n) = 10*a(n-1) + 10.
  • A105280 (program): a(0)=0; a(n) = 11*a(n-1) + 11.
  • A105281 (program): a(0)=0; a(n)=6*a(n-1)+6.
  • A105283 (program): (2n)-th prime mod n.
  • A105312 (program): a(n) = Sum_ j=0..15 n^j.
  • A105314 (program): Write the natural numbers as an infinite sequence of digits, starting at the left; a(n) is the subset (i.e., the position in this sequence of the “counting digits”) of the first digit of the n-th square.
  • A105321 (program): Convolution of binomial(1,n) and Gould’s sequence A001316.
  • A105332 (program): a(n) = n*(n+1)/2 mod 8.
  • A105333 (program): a(n) = n*(n+1)/2 mod 16.
  • A105334 (program): a(n) = n*(n+1)/2 mod 32.
  • A105335 (program): a(n) = n*(n+1)/2 mod 64.
  • A105336 (program): a(n) = n*(n+1)/2 mod 128.
  • A105337 (program): a(n) = n*(n+1)/2 mod 256.
  • A105338 (program): a(n) = n*(n+1)/2 mod 512.
  • A105339 (program): a(n) = n*(n+1)/2 mod 1024.
  • A105340 (program): a(n) = n*(n+1)/2 mod 2048.
  • A105343 (program): Elements of even index in the sequence gives A005893, points on surface of tetrahedron: 2n^2 + 2 for n > 1.
  • A105348 (program): An indicator sequence for the Jacobsthal numbers.
  • A105349 (program): Characteristic sequence for the Pell numbers.
  • A105367 (program): Expansion of (1-x^3)/(1-x^5).
  • A105368 (program): Expansion of (1-x-x^3+x^4)/(1-x^5).
  • A105374 (program): a(n) = 4n^3 + 4n.
  • A105384 (program): Expansion of x/(1 + x + x^2 + x^3 + x^4).
  • A105385 (program): Expansion of (1-x^2)/(1-x^5).
  • A105392 (program): Frobenius number of the subsemigroup of the natural numbers generated by successive pairs of Lucas numbers.
  • A105395 (program): A simple “Fractal Jump Sequence” (FJS).
  • A105396 (program): A simple “Fractal Jump Sequence” (FJS).
  • A105397 (program): Periodic with period 2: repeat [4,2].
  • A105398 (program): A simple “Fractal Jump Sequence” (FJS).
  • A105426 (program): a(0)=1, a(1)=5, a(n)=8*a(n-1)-a(n-2).
  • A105427 (program): Numbers n such that the near-repdigit number consisting of a 1 followed by n 3’s (i.e., of form 1333…33) is composite.
  • A105452 (program): Numerator of (7 n -1)/3.
  • A105470 (program): a(n)=1 if there is number of the form 6k+3 with prime(n) <= 6k+3 <= prime(n+1), otherwise 0.
  • A105471 (program): a(n) = Fibonacci(n) mod 100.
  • A105472 (program): Next-to-last digit of n-th Fibonacci number in decimal representation, a(n) = 0 for n <= 6.
  • A105476 (program): Number of compositions of n when each even part can be of two kinds.
  • A105498 (program): Trajectory of 1 under the morphism 1-> 1,2 , 2-> 1,4 , 3-> 3,4 , 4-> 3,4 .
  • A105500 (program): Trajectory of 1 under the morphism 1-> 1,2 , 2-> 3,2 , 3-> 3,4 , 4-> 1,4 .
  • A105531 (program): Decimal expansion of arctan 1/3.
  • A105555 (program): Let d = number of divisors of n; a(n) = d-th prime.
  • A105560 (program): a(1) = 1, and for n >= 2, a(n) = prime(bigomega(n)), where prime(n) = A000040(n) and bigomega(n) = A001222(n).
  • A105561 (program): a(n) is the m-th prime, where m is the number of distinct prime factors of n (A001221), a(1) = 1.
  • A105562 (program): a(n) is the prime whose index is the greatest prime factor of n, for n >1; a(1)=2.
  • A105563 (program): a(n) = if (exactly 4 Fibonacci numbers exist with exactly n digits) then 1, otherwise 0.
  • A105564 (program): Number of blocks of exactly 4 Fibonacci numbers having equal length <= n.
  • A105566 (program): Number of blocks of exactly 5 Fibonacci numbers having equal length <= n.
  • A105570 (program): Nonsquarefree numbers in place: a(n) = n if n is not squarefree, 0 otherwise.
  • A105574 (program): a(1) = 2; for n > 1, a(n) is the prime whose index is the least prime factor of n.
  • A105576 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 3, a(1) = 4, a(2) = 0.
  • A105577 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2*a(n); a(0) = 1, a(1) = 5, a(2) = 6.
  • A105578 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 1, a(2) = 0.
  • A105579 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 3, a(2) = 4.
  • A105635 (program): a(n) = (2*Pell(n+1) - (1+(-1)^n))/4.
  • A105636 (program): Transform of n^3 by the Riordan array (1/(1-x^2), x).
  • A105637 (program): a(n) = a(n-2)+a(n-3)-a(n-5).
  • A105638 (program): Maximum number of intersections in self-intersecting n-gon.
  • A105644 (program): a(n) = floor((Pi+e)*n).
  • A105661 (program): a(n)=1 if n is a prime, 2 if n is an even semiprime, otherwise 0.
  • A105670 (program): a(1)=1 then bracketing n by powers of 2 as f(t)=2^t for f(t) < n <= f(t+1), a(n) = f(t+1) - a(n-f(t)).
  • A105674 (program): Highest minimal distance of any Type I (strictly) singly-even binary self-dual code of length 2n.
  • A105676 (program): Highest minimal Hamming distance of any Type 3 ternary self-dual code of length 4n.
  • A105686 (program): Number of inequivalent codes attaining highest minimal Hamming distance of any Type 4^H Hermitian linear self-dual code over GF(4) of length 2n.
  • A105693 (program): a(n) = Fibonacci(2n+2)-2^n.
  • A105694 (program): 10^n-10^(n-2).
  • A105700 (program): a(n)=1 if n is a prime, 2 if n is a semiprime, otherwise 0.
  • A105723 (program): a(n) = 3^n - (-1)^n.
  • A105734 (program): For n>2, a(n) > 0 is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, with a(1)=1, a(2)=1.
  • A105748 (program): Number of ways to use the elements of 1,..,k , 0<=k<=2n, once each to form a collection of n (possibly empty) sets, each with at most 2 elements.
  • A105752 (program): Expansion of e.g.f. cos(i*log(1 + x)), i = sqrt(-1).
  • A105760 (program): Nonnegative numbers k such that 2k+7 is prime.
  • A105770 (program): Expansion of (x^2-x+1)(4x^2+x+1) / ((1+x+x^2)(1-x)^3).
  • A105772 (program): Numbers k such that 7*k + 2 is prime.
  • A105773 (program): Numbers n such that 11*n + 97 is prime.
  • A105800 (program): Greatest Fibonacci number that is a proper divisor of the n-th Fibonacci number; a(1) = a(2) = 1.
  • A105811 (program): Expansion of (1+x-x^2)/(1+x)^2.
  • A105812 (program): Expansion of (1+x-x^2)/(1+x).
  • A105814 (program): a(n) = n^2 + (n concatenated with n).
  • A105824 (program): a(n) = sigma(n) mod 4.
  • A105825 (program): a(n) = sigma(n) (mod 5).
  • A105826 (program): a(n) = sigma(n) (mod 7).
  • A105827 (program): a(n) = sigma(n) (mod 8).
  • A105852 (program): sigma(n) mod 9.
  • A105853 (program): a(n) = sigma(n) (mod 10), i.e., unit’s digit of sigma(n).
  • A105870 (program): Fibonacci sequence (mod 7).
  • A105899 (program): Period 6: repeat [1, 1, 2, 2, 3, 3].
  • A105931 (program): a(1) = 1 then a(n) = a(n-1) - (-1)^ceiling(n/2)*a(floor(n/2)).
  • A105938 (program): a(n) = binomial(n+2,2)*binomial(n+5,2).
  • A105939 (program): a(n) = binomial(n+3,3)*binomial(n+6,3).
  • A105940 (program): a(n) = binomial(n+5, n)*binomial(n+8, 5).
  • A105942 (program): C(n+6,n)*C(n+9,6)
  • A105944 (program): C(n+8,n)*C(n+11,8)
  • A105946 (program): C(n+5,n)*C(n+3,3).
  • A105947 (program): C(n+6,n)*C(n+4,4)
  • A105948 (program): C(n+7,n)*C(n+5,5).
  • A105955 (program): a(n) = Fibonacci(n) mod 11.
  • A105963 (program): Expansion of (1+4x)/(1-x-3x^2).
  • A105968 (program): a(n) = 4a(n-1) - a(n-2) - 2(-1)^n, a(0) = 1, a(1) = 4.
  • A105994 (program): Fibonacci sequence (mod 13).
  • A105995 (program): Fibonacci sequence (mod 14).
  • A106002 (program): a(n)=1 if there is a number of the form 6k+3 such that prime(n) < 6k+3 < prime(n+1), otherwise 0.
  • A106005 (program): Fibonacci sequence (mod 15).
  • A106006 (program): [n/2] + [n/3] + [n/5].
  • A106035 (program): The “Octanacci” sequence: Trajectory of 1 under the morphism 1-> 1,2,1 , 2-> 1 .
  • A106040 (program): First 9-free digit in the fractional part of the decimal expansion of (1/10^n)^(1/10^n).
  • A106043 (program): First digit other than 9 in the fractional part of the decimal expansion of (1/1000^n)^(1/1000^n).
  • A106044 (program): Difference between n-th prime and next larger perfect square.
  • A106058 (program): 4th diagonal of triangle in A059317.
  • A106147 (program): A Levy dragon -Heighway’s dragon two state 4-symbol substitution : q=1 state Levy dragon : q=0 state Heighway’s dragon: Characteristic Polynomial:x^4-4x^3+6x^2-4*x.
  • A106149 (program): Number of prime factors with multiplicity of the difference between consecutive primes.
  • A106154 (program): Generation 5 of the substitution 1-> 2, 1, 2 , 2-> 3, 2, 3 , 3-> 4, 3, 4 , 4-> 5, 4, 5 , 5-> 6, 5, 6 , 6-> 1, 6, 1 , starting with 1.
  • A106157 (program): G.f. (1-x-x^3+x^4-2x^2)/((1-2x)(x-1)^2(x+1)^2).
  • A106160 (program): Highest minimal Hamming distance of Hermitian Type IV self-dual codes over GF(2) X GF(2) and length 2n.
  • A106187 (program): Sequence array for central binomial numbers A000984.
  • A106188 (program): Expansion of 1/((1-x^2)sqrt(1-4x)).
  • A106191 (program): Expansion of sqrt(1-4x)/(1-x).
  • A106197 (program): Analog of A094091 for S=4.
  • A106229 (program): Least j > 1 for n > 0 such that j^2 = (n^2 + 1)(k^2) + (n^2 + 1)k + 1 where k sequence = A106230.
  • A106230 (program): Least k > 0 for n > 0 such that (n^2 + 1)(k^2) + (n^2 + 1)k + 1 = j^2 where j sequence = A106229.
  • A106231 (program): Least j > 1 such that j^2 = (4n^2 + 2)(k^2) + (4n^2 + 2)k + 1.
  • A106232 (program): Least k > 0 such that (4n^2 + 2)(k^2) + (4n^2 + 2)k + 1 = j^2.
  • A106247 (program): Expansion of (1+2x-x^2-2x^3+x^4) / (1-x^2)^3.
  • A106249 (program): Expansion of (1-x+x^2+x^3)/(1-x-x^4+x^5).
  • A106250 (program): Expansion of (1-x+x^2+x^3)/(1-x-x^5+x^6).
  • A106251 (program): Expansion of (1-x+x^2+x^3+x^5)/(1-x-x^6+x^7).
  • A106252 (program): Number of positive integer triples (x,y,z), with x<=y<=z<=n, such that each of x,y and z divides the sum of the other two.
  • A106253 (program): First difference of A106252.
  • A106255 (program): Triangle composed of triangular numbers, row sums = A006918.
  • A106256 (program): Numbers n such that 12*n^2 + 13 is a square.
  • A106268 (program): Number triangle T(n,k) = binomial(k-n, n-k)(-1)^(n-k) = (0^(n-k) + binomial(2(n-k), n-k))/2 if k <= n, 0 otherwise; Riordan array (1/(2-C(x)), x) where C(x) is g.f. for Catalan numbers A000108.
  • A106269 (program): Expansion of 1/((1 - x^2)*(2 - c(x))), where c(x) is the g.f. of A000108.
  • A106271 (program): Row sums of number triangle A106270.
  • A106314 (program): Triangle T(n,k) composed of the squares min(n,k)^2.
  • A106318 (program): Bhaskara twins: n such that 2n^2 = X^3 and 2n^3 = Y^2.
  • A106328 (program): Numbers j such that 8*(j^2) + 9 = k^2 for some positive number k.
  • A106329 (program): Numbers k such that k^2 = 8*j^2 + 9.
  • A106344 (program): Triangle read by rows: T(n,k) = binomial(k,n-k) mod 2.
  • A106348 (program): Partial sums of a generalized Fredholm-Rueppel sequence.
  • A106352 (program): Number of compositions of n into 3 parts such that no two adjacent parts are equal.
  • A106370 (program): Smallest b>1 such that n contains no zeros in its base b representation.
  • A106387 (program): Numbers j such that 6j^2 + 6j + 1 = 11k.
  • A106388 (program): Numbers k such that 11k = 6j^2 + 6j + 1.
  • A106389 (program): Numbers j such that 6j^2 + 6j + 1 = 13k.
  • A106390 (program): Numbers k such that 13k = 6j^2 + 6j + 1.
  • A106392 (program): Expansion of 1/(1 - 6x + 10x^2).
  • A106400 (program): Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 1 and for k >= 0, A_ k+1 = A_k B_k, where B_k is obtained from A_k by interchanging 1’s and -1’s.
  • A106404 (program): Number of even semiprimes dividing n.
  • A106409 (program): n XOR (greatest proper divisor of n).
  • A106434 (program): The (1,1)-entry of the matrix A^n, where A = [0,1;2,3].
  • A106435 (program): a(n) = 3a(n-1) + 3a(n-2), a(0)=0, a(1)=3.
  • A106440 (program): a(n) = binomial(2n+4,n)*binomial(n+4,4).
  • A106459 (program): Expansion of f(-x, -x^3) in powers of x where f(,) is Ramanujan’s general theta function.
  • A106465 (program): A number triangle of GCDs mod 2.
  • A106466 (program): Interleave 1,2,3,.. with 1,1,2,2,3,3,…
  • A106469 (program): Expansion of (1+x^2)(1+2x)/(1-x^2).
  • A106472 (program): Expansion of (1 - x)^2(1 + x) / (1 - 2x)^2.
  • A106474 (program): A006579(4n+4)/4.
  • A106476 (program): Sequence array of Euler phi function.
  • A106477 (program): Diagonal sums of Euler phi function sequence array.
  • A106481 (program): An Euler phi transform of 1/(1-x^2).
  • A106487 (program): Number of leaves in combinatorial game trees.
  • A106505 (program): Ordered and uniqued length of side common to the two angles, one being the double of the other, of a primitive integer-sided triangle.
  • A106510 (program): Expansion of (1+x)^2/(1+x+x^2).
  • A106514 (program): Expansion of (1-x)/((1-2x)(1-2*x-x^2)).
  • A106524 (program): Interleave A038573(n+1) and 2*A038573(n+1).
  • A106539 (program): a(1)=1, a(2)=1, a(n) = (n-1)a(n-1) - (n-2)a(n-2) - … - a(1) for n>=3.
  • A106540 (program): a(n) = a(n-1) - 2a(n-2) - 3a(n-3) - … - (n-1)*a(1), with a(1) = a(2) = 1, a(3) = -1.
  • A106541 (program): a(n) = a(n-1) - 2a(n-2) - 3a(n-3) - … - (n-1)*a(1), with a(1) = a(2) = 2, a(3) = -2.
  • A106542 (program): a(n) = a(n-1) - 2a(n-2) - 3a(n-3) - … - (n-1)*a(1), a(1) = a(2) = 3, a(3) = -3.
  • A106546 (program): a(n) = n^2 if n^2 is the difference of two primes, otherwise a(n) = 0.
  • A106549 (program): a(n) = -1 if 2n+1 is a prime, 1 if 2n+1 is a prime squared, or 0 otherwise.
  • A106565 (program): a(n) = 5a(n-1) + 5a(n-2) with a(0) = 0, a(1) = 5.
  • A106567 (program): a(n) = 5a(n-1) + 4a(n-2), with a(0) = 4, a(1) = 4.
  • A106568 (program): Expansion of 4x/(1 - 4x - 4*x^2).
  • A106569 (program): a(n) = 5a(n-1) + 3a(n-2), where a(0) = 0, a(1) = 3.
  • A106570 (program): a(n) = 4a(n-1) + 3a(n-2), with a(0)=0, a(1)=3.
  • A106576 (program): Period 20. Sequence gives last digit of A106157, starting from the first positive term.
  • A106586 (program): Digit next to last in squares ending in 6.
  • A106587 (program): Sum of n-th prime squared and n-th perfect square.
  • A106588 (program): Difference between n-th prime squared and n-th perfect square.
  • A106607 (program): Expansion of (1+t^3)^2/((1-t)(1-t^2)^2(1-t^4)).
  • A106608 (program): a(n) = numerator of n/(n+7).
  • A106609 (program): Numerator of n/(n+8).
  • A106610 (program): Numerator of n/(n+9).
  • A106611 (program): a(n) = numerator of n/(n+10).
  • A106612 (program): a(n) = numerator of n/(n+11).
  • A106614 (program): a(n) = numerator of n/(n+13).
  • A106615 (program): a(n) = numerator of n/(n+14).
  • A106616 (program): Numerator of n/(n+15).
  • A106617 (program): Numerator of n/(n+16).
  • A106618 (program): a(n) = numerator of n/(n+17).
  • A106619 (program): a(n) = numerator of n/(n+18).
  • A106620 (program): a(n) = numerator of n/(n+19).
  • A106621 (program): a(n) = numerator of n/(n+20).
  • A106624 (program): Expansion of g.f.: (1 - x^2 + x^3)/((1-x^2)(1-2x^2)).
  • A106633 (program): Number of ways to express n as k+l*m, with k, l, m all in the range [0..n].
  • A106637 (program): Accumulation of permutation sequence on three symbols such that the a[n+2]-2*a[n+1]-a[n]=0 overall.
  • A106638 (program): 3-symbol substitution that gives a dragon fractal.
  • A106648 (program): a(n) = 3n^2 + 6n + 8.
  • A106649 (program): Replace each digit d (except the leading one) of n with 9-d.
  • A106665 (program): Alternate paper-folding (or alternate dragon curve) sequence.
  • A106666 (program): Expansion of g.f. (1-4x^2+2x^3)/((1-x)(1-2x-2x^2+2x^3)).
  • A106690 (program): Numbers k such that 11*k - 97 is prime.
  • A106701 (program): a(n) = next-to-most-significant binary digit of n-th composite positive integer.
  • A106707 (program): First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,-1],[1,4]] and v is the column vector [0,1].
  • A106709 (program): Expansion of g.f. -2x/(1 - 5x + 2*x^2).
  • A106710 (program): Number of words with n letters from an alphabet of size 26 with at least two equal consecutive letters.
  • A106729 (program): Sum of two consecutive squares of Lucas numbers (A001254).
  • A106731 (program): Expansion of -2x/(1 - 4x + 2*x^2).
  • A106732 (program): Expansion of -3x/(1 - 5x + 3*x^2).
  • A106734 (program): a(n) = n^3 - 7*n + 7.
  • A106742 (program): a(n) = a(a(a(a(a(n - a(n-1)))))) + a(n - a(n-2)) with a(1) = a(2) = 1.
  • A106743 (program): a(n) = -1 iff n is prime, a(n) = 1 iff n is not squarefree, otherwise (n is nonprime and squarefree) a(n) = 0.
  • A106744 (program): Given n shoelaces, each with two aglets; sequence gives number of aglet pairs that must be picked up to guarantee that the probability that no shoelace is left behind is > 1/2.
  • A106753 (program): Discriminants, negated, of definite binary quadratic forms.
  • A106793 (program): Number of words (over an alphabet of size 26) of length n with all different letters.
  • A106803 (program): Expansion of x(1-x)/(1-2x-x^2+x^3).
  • A106805 (program): Expansion of g.f.: 1/(1 - 2*x - x^2 + x^3).
  • A106825 (program): Trajectory of 1 under the morphism 1->1222, 2->2111.
  • A106826 (program): Trajectory of 1 under the morphism 1-> 2,1 , 2-> 2,3 , 3-> 4,3 , 4-> 4,1 .
  • A106832 (program): 4n-2 and 6n alternatively.
  • A106833 (program): 3n and 2n, alternating.
  • A106839 (program): Numbers congruent to 11 mod 16.
  • A106842 (program): (1 + n + n^2)^n.
  • A106845 (program): n^2 * (n^3 + 2n^2 + 7n - 2) / 8.
  • A106852 (program): Expansion of 1/(1-x(1-3x)).
  • A106853 (program): Expansion of 1/(1 - x + 4*x^2).
  • A106854 (program): Expansion of 1/(1-x(1-5x)).
  • A107003 (program): Primes of the form 24n + 5.
  • A107006 (program): Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative.
  • A107008 (program): Primes of the form x^2 + 24*y^2.
  • A107017 (program): Second largest term in Zeckendorf representation of n, a(n)=0 if n itself is a Fibonacci number.
  • A107044 (program): A symmetric factorial triangle, read by rows: T(n,k) = min(n,k)!.
  • A107058 (program): a(n) = smallest number m>0 such that prime(n)*prime(n+1)-m is a prime.
  • A107075 (program): Centered square numbers that are also centered pentagonal numbers.
  • A107078 (program): Whether n has non-unitary prime divisors.
  • A107079 (program): Minimal number of squared primes in a squarefree gap of length n.
  • A107105 (program): Triangle, read by rows, where T(n,k) = C(n,k)*(C(n,k) + 1)/2, n>=k>=0.
  • A107118 (program): Numbers that are both centered triangular numbers (A005448) and centered hexagonal numbers (A003215).
  • A107181 (program): Primes of the form 8x^2 + 9y^2.
  • A107231 (program): a(n) = C(n+2,2)*C(n,floor(n/2)).
  • A107239 (program): Sum of squares of tribonacci numbers (A000073).
  • A107240 (program): Sum of squares of first n tribonacci numbers (A000213).
  • A107253 (program): a(n) = n^4 - 15*n + 15.
  • A107255 (program): a(n) = n^5 - 31n + 31, with na(n) + n( n - 1 )31 = n^6.
  • A107256 (program): a(n) = n^6 - 63n + 63, with na(n) + n(n-1)63 = n^7.
  • A107279 (program): a(n) = 1 if n is an odd prime, a(n) = 2 if n is a nonzero even number, otherwise a(n) = 0.
  • A107283 (program): E.g.f. exp(x)*(x^2+x+2)/(1-x).
  • A107285 (program): 5401(10^n + 1).
  • A107286 (program): a(0) = 0; for n>0, minimal prime factor of n, or 1 if n is 1 or a prime.
  • A107303 (program): Numbers k such that (3*k - 5) is prime.
  • A107304 (program): Numbers k such that 5k - 7 is prime.
  • A107305 (program): Numbers k such that 11*k - 13 is prime.
  • A107306 (program): Numbers k such that (17*k - 19) is prime.
  • A107316 (program): Floor(exp(n)/n).
  • A107319 (program): C(n+8,8)*C(n+6,6)
  • A107323 (program): If n-th prime is 6m-1, then a(n) = 6m+1. If n-th prime is 6m+1, then a(n) = 6m-1.
  • A107324 (program): Floor(A063655(n)/2).
  • A107325 (program): a(n) = ceiling(A063655(n)/2).
  • A107347 (program): Number of even semiprimes strictly between prime(n) and 2*prime(n).
  • A107351 (program): Expansion of (1+x^3)/((1-x)^3(1-x^2)^3(1-x^3)).
  • A107386 (program): a(n) = 2a(n-1) - 2a(n-3) + a(n-4), n>6.
  • A107387 (program): Expansion of x(1-2x-x^2)/( (1-x)(1+x)(1-3*x+x^2)).
  • A107392 (program): Number of (inequivalent) fuzzy subgroups of the direct sum of group of integers modulo p^n and group of integers modulo 2 for a prime p with (p,2) = 1. Z_ p^n + Z_2.
  • A107393 (program): a(n) = -1 if n is a prime, else a(n) = 1 if n is the sum of three odd primes, else a(n) = 2 if n is the sum of two primes, else a(n) = 0.
  • A107395 (program): C(n+4,4)*C(n+6,4).
  • A107397 (program): a(n) = binomial(n+6, 6) * binomial(n+8, 6).
  • A107399 (program): C(n+8,8)*C(n+10,8).
  • A107409 (program): Each term is sum of three previous terms mod 10.
  • A107410 (program): Each term is sum of three previous terms mod 9.
  • A107417 (program): C(n+2,2)*C(n+5,5).
  • A107418 (program): a(n) = C(n+3,3)*C(n+6,6).
  • A107419 (program): a(n) = C(n+4,4)*C(n+7,7).
  • A107420 (program): a(n) = C(n+5,5)*C(n+8,8).
  • A107421 (program): C(n+6,6)*C(n+9,9).
  • A107422 (program): a(n) = binomial(n+7,7) * binomial(n+10,10).
  • A107427 (program): Maximal number of simple triangular regions that can be formed by drawing n line segments in the Euclidean plane.
  • A107430 (program): Triangle read by rows: row n is row n of Pascal’s triangle (A007318) sorted into increasing order.
  • A107436 (program): a(n) = (a^5)(n-1) + a(n-a(n-1)) = a(a(a(a(a(n-1))))) + a(n-a(n-1)), a(1) = a(2) = 1.
  • A107443 (program): G.f. (3x^2+1)/((1-x)(2x^2+x+1)(2*x^2-x+1)).
  • A107444 (program): a(n) = C(n^3, n).
  • A107446 (program): a(n) = binomial(n^4, n).
  • A107453 (program): 1 followed by repetitions of the period-4 sequence 1,1,1,2.
  • A107454 (program): Number of nonisomorphic generalized Petersen graphs P(n,k) with girth 5 on 2n vertices for 1<=k<=Floor[(n-1)/2].
  • A107458 (program): Expansion of g.f.: (1-x^2-x^3)/( (1+x)*(1-x-x^3) ).
  • A107459 (program): Number of nonisomorphic bipartite generalized Petersen graphs P(2n,k) with girth 6 on 4n vertices for 1<=k<n.
  • A107464 (program): Number of fuzzy subgroups of rank 3 cyclic group of order (p^n)qr where p, q and r are three distinct prime.
  • A107493 (program): Coefficients of a certain theta series.
  • A107495 (program): Coefficients of a certain theta series.
  • A107496 (program): Coefficients of a certain theta series.
  • A107583 (program): a(n) = 3^n - 3*n.
  • A107584 (program): a(n) = 4^n - 4*n.
  • A107585 (program): a(n) = 5^n - 5*n.
  • A107620 (program): Primes multiplied alternately by 3 and 2.
  • A107621 (program): Primes multiplied alternately by 2 and 3.
  • A107622 (program): Primes plus alternately 2 and 3.
  • A107623 (program): Primes plus alternately 3 and 2.
  • A107659 (program): a(n) = Sum_ k=0..n 2^max(k, n-k).
  • A107660 (program): Sum 3^max(k,n-k),k=0..n.
  • A107680 (program): Repeating k-th ternary repunit (A003462) 2^k times, k >= 0.
  • A107684 (program): Union of sequences 2^k-1, 2^k and 2^k+1.
  • A107731 (program): Row 7 of the array in A107735.
  • A107732 (program): Column 1 of the array in A107735.
  • A107744 (program): Smallest prime factor of 6*n+1.
  • A107745 (program): Smallest prime factor of 6*n-1.
  • A107750 (program): If n=0 then 0, else smallest number greater than its predecessor and having either more or fewer zeros in its binary representation.
  • A107751 (program): a(n) = A107750(n+1) - A107750(n).
  • A107755 (program): Numbers k such that Sum_ j=1..k Catalan(j) == 0 (mod 3).
  • A107757 (program): Numbers k such that Sum_ j=1..k Catalan(j) == 2 (mod 3).
  • A107767 (program): a(n) = (1 + 3^n - 23^(n/2))/4 if n is even, (1 + 3^n - 43^((n-1)/2))/4 if n odd.
  • A107782 (program): In binary representation of n: (number of zeros) minus (number of blocks of contiguous zeros).
  • A107818 (program): Slowest increasing sequence where (product of 2 consecutive integers)-1 is prime.
  • A107819 (program): Slowest increasing sequence where a(n)+n is prime.
  • A107820 (program): a(1)=3, a(2)=5; thereafter a(n) = n+5.
  • A107839 (program): a(n) = 5a(n-1) - 2a(n-2); a(0)=1, a(1)=5.
  • A107843 (program): Number of iterations of McCarthy 91 Function until it terminates.
  • A107857 (program): a(n) = floor[(phi + n mod 2)*a(n-1)], a(1)=1.
  • A107858 (program): a(n) = b(k), where b(k) = Fibonacci(n-1) and k = floor( n*(1+sqrt(5))/2 ).
  • A107863 (program): Column 1 of triangle A107862; a(n) = C( n*(n+1)/2 + n, n).
  • A107868 (program): Column 0 of triangle A107867; a(n) = C( n*(n-1)/2 + n + 1, n).
  • A107869 (program): Column 1 of triangle A107867; a(n) = binomial( n*(n+1)/2 + n+1, n).
  • A107871 (program): Column 0 of triangle A107870; a(n) = C( n*(n-1)/2 + n+2, n).
  • A107872 (program): Column 1 of triangle A107870; a(n) = C(n*(n+1)/2 + n+2, n).
  • A107874 (program): Column 0 of triangle A107873; a(n) = C( n*(n-1)/2 + n+3, n).
  • A107875 (program): Column 1 of triangle A107873; a(n) = C( n*(n+1)/2 + n+3, n).
  • A107891 (program): a(n) = (n+1)(n+2)^2(n+3)^2(n+4)(3n^2 + 15n + 20)/2880.
  • A107903 (program): Generalized NSW numbers.
  • A107904 (program): Expansion of (1+6x)/(1-12x^2).
  • A107905 (program): Decimal expansion of (5+sqrt(21))/2.
  • A107906 (program): Expansion of (1+8x)/(1-16x^2).
  • A107907 (program): Numbers having consecutive zeros or consecutive ones in binary representation.
  • A107920 (program): Lucas and Lehmer numbers with parameters (1+-sqrt(-7))/2.
  • A107929 (program): Smallest list of integers from 1 to n such that sum of any two adjacent terms is a square.
  • A107942 (program): a(n) = (n+1)(n+2)^3(n+3)^3(n+4)(2n+5)/4320.
  • A107959 (program): a(n) = (n+1)(n+2)^2(n+3)^2(n+4)(n^2 + 5n + 5)/720.
  • A107960 (program): Numbers n such that 11*n - 1 is prime.
  • A107963 (program): a(n) = (n+1)(n+2)(n+3)(n+4)(5n^2 + 19n + 15)/360.
  • A107973 (program): Numbers of the form a^2 + b for a= 21 to 40 and b= 20 to 1 step -1.
  • A107979 (program): a(n) = 4a(n-1) + 2a(n-2) for n>1, with a(0)=2, a(1)=9.
  • A107991 (program): Complexity (number of maximal spanning trees) in an unoriented simple graph with nodes 1,2,…,n and edges i,j if i + j > n.
  • A107992 (program): Numbers n such that 11*n - 3 is prime.
  • A107994 (program): Numbers n such that 11*n - 2 is prime.
  • A108019 (program): a(n) = (8^n - 1)*4/7.
  • A108020 (program): Numbers n whose binary representation is 1100, n times.
  • A108021 (program): Numbers n whose binary representation is the first Fibonacci(n) binary digits of the pattern 1010101010101010…
  • A108035 (program): Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n times.
  • A108037 (program): Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.
  • A108044 (program): Triangle read by rows: right half of Pascal’s triangle (A007318) interspersed with 0’s.
  • A108051 (program): a(n+1) = 4*(a(n)+a(n-1)) for n>1, a(1)=1, a(2)=6.
  • A108099 (program): a(n) = 8n^2 + 8n + 4.
  • A108100 (program): (2n-1)^2+(2n+1)^2.
  • A108103 (program): Fixed point of the square of the morphism: 1->3, 2->1, 3->121, starting with 1.
  • A108104 (program): Sequence A000930 with terms repeated.
  • A108105 (program): 2^floor(n/5).
  • A108118 (program): Integers not divisible by 3 or 4.
  • A108120 (program): Floor[n*1/Sin[1]], or Beatty sequence for 1/sin(1).
  • A108122 (program): G.f.: (1-2x^2)/(1-x-2x^2-x^3).
  • A108137 (program): Primes p such that p + 6^k is composite for all k >= 0.
  • A108151 (program): a(n) = n^2 + 3*n + 1 if prime or 0 if composite.
  • A108154 (program): a(n) = n^2 - n + 1 if prime else 0.
  • A108161 (program): Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.
  • A108165 (program): a(n)=a(n-1) +A108173(n+1) -A108173(n).
  • A108171 (program): Tribonacci version of A076662 using beta positive real Pisot root of x^3 - x^2 - x - 1.
  • A108173 (program): Let beta = A058265. Sequence gives a(n) = 1 + ceiling((n-1)*beta^2).
  • A108187 (program): Numbers n such that 11*n - 5 is prime.
  • A108195 (program): a(n) = n^2 + 5*n - 1.
  • A108211 (program): a(n) = 16*n^2 + 1.
  • A108213 (program): a(0)=44; if n odd, a(n) = a(n-1)/2, otherwise a(n) = 4*a(n-1).
  • A108214 (program): Denominator of the O(x^2) term in the Maclaurin series of the square of the Jacobi polynomial P^ a,b _n(z) about z=1-x for real positive x.
  • A108217 (program): a(0) = 1, a(1) = 1, a(n) = n! + (n-2)! for n >= 2.
  • A108225 (program): a(0) = 0, a(1) = 2; for n >= 2, a(n) = (a(n-1) + a(n-2))*(a(n-1) - a(n-2) + 1)/2.
  • A108228 (program): (A003961(n) - 1)/2, a permutation of the nonnegative integers.
  • A108229 (program): n occurs Lucas number L(n) times (A000204).
  • A108232 (program): Numbers n such that 11*n - 7 is prime.
  • A108233 (program): Numbers n such that 11*n + 5 is prime.
  • A108245 (program): If n-th prime is 4m - 1, then a(n) = 4m + 1. If n-th prime is 4m + 1, then a(n) = 4m - 1.
  • A108261 (program): 2nd order recursive series having the property that the product of any two adjacent terms is a triangular number, T(b) = b(b+1)/2 where b equals term a(n) of related series A108262.
  • A108262 (program): Second order recursive series having the property that the product of any two adjacent terms equals 4 times a triangular number. That is a(n)a(n+1)= 4T(c) = 2c(c+1), where c = the term a(n+1) of related series A108261.
  • A108281 (program): Numbers that are both triangular and pentagonal of the second kind.
  • A108288 (program): Main diagonal of table A060543; a(n) = C((n+1)^2-1, n*(n+1)).
  • A108300 (program): a(n+2) = 3*a(n+1) + a(n), with a(0) = 1, a(1) = 5.
  • A108306 (program): Expansion of (3x+1)/(1-3x-3*x^2).
  • A108321 (program): a(n) = n^2 if n^2 is not the difference of two primes; otherwise a(n) = 0.
  • A108340 (program): A083952 read mod 2.
  • A108351 (program): Diagonal sums of symmetric triangle A108350.
  • A108354 (program): Expansion of 1/((1-x)^2(1+x^2)^2) in powers of x.
  • A108356 (program): Count, repeating multiples of 3 four times, all other numbers twice.
  • A108357 (program): Expansion of (1+x^2+x^4)/(1-x^8).
  • A108396 (program): Triangle read by rows: T(n,k) = n*(1+n^k)/2, 0<=k<=n.
  • A108397 (program): Sums of rows of the triangle in A108396.
  • A108398 (program): a(n) = n*(1 + n^n)/2.
  • A108400 (program): a(n) = Product_ k = 0..n k!*2^k.
  • A108411 (program): a(n) = 3^floor(n/2). Powers of 3 repeated.
  • A108412 (program): Expansion of (1 + x + x^2)/(1 - 4x^2 + x^4).
  • A108474 (program): Expansion of 1/((1-2x)*(1+4x^2)).
  • A108475 (program): Expansion of (1-3x) / (1-5x-5*x^2+x^3).
  • A108479 (program): Diagonal sums of number triangle A086645.
  • A108495 (program): a(n) = (n^7 - n)/6.
  • A108514 (program): If n is a power of 2, a(n)=n; otherwise a(n) = (p-1)*n/p where p = smallest odd prime divisor of n.
  • A108568 (program): a(n) = prime(n) + prime(n+1) - 2n - 1.
  • A108576 (program): Number of 3 X 3 magic squares (with distinct positive entries) having all entries < n.
  • A108577 (program): Number of symmetry classes of 3 X 3 magic squares (with distinct positive entries) having all entries < n.
  • A108578 (program): Number of 3 X 3 magic squares with magic sum 3n.
  • A108579 (program): Number of symmetry classes of 3 X 3 magic squares (with distinct positive entries) having magic sum 3n.
  • A108581 (program): Positive triangular numbers repeated their own number of times.
  • A108582 (program): n appears n^3 times.
  • A108584 (program): Numbers k such that 10*k - 97 is prime.
  • A108587 (program): Floor(n/(1-sin(1))).
  • A108588 (program): Numbers n such that 10*n + 97 is prime.
  • A108594 (program): Numbers n such that 10*n + 101 is prime.
  • A108595 (program): Numbers n such that 10*n + 103 is prime.
  • A108598 (program): Floor(n*((5+sqrt(5))/4)).
  • A108601 (program): Numbers n such that 7*n - 911 is prime.
  • A108612 (program): Beatty-2 (or nested Beatty) sequence for 1/sin(1).
  • A108613 (program): Excess of Beatty-2 function of 1/sin(1) over n^2.
  • A108647 (program): a(n) = (n+1)^2(n+2)^2(n+3)^2*(n+4)/144.
  • A108648 (program): a(n) = (n+1)^2(n+2)^3(n+3)/24.
  • A108650 (program): a(n) = (n+1)^2(n+2)(n+3)(3n+4)/24.
  • A108674 (program): a(n) = (n+1)^2 * (n+2)^2 * (2*n+3) / 12.
  • A108676 (program): a(n) = (n+1)^2(n+2)(5n^2 + 15n + 12)/24.
  • A108678 (program): a(n) = (n+1)^2*(n+2)(2n+3)/6.
  • A108679 (program): a(n) = (n+1)(n+2)^2(n+3)^2(n+4)^2(n+5)^2*(n+6)/86400.
  • A108680 (program): Kekulé numbers for certain benzenoids.
  • A108681 (program): a(n) = (n+1)(n+2)^2(n+3)(n+4)(n+5)(2n+3)/720.
  • A108689 (program): Smallest integer q >= 1 such that difference between q*Pi and the nearest integer is <= 1/n.
  • A108696 (program): Generated by a sieve: see comments.
  • A108719 (program): Primes which can be partitioned into a sum of distinct primes in more than one way.
  • A108724 (program): Numbers n such that 11*n + 17 is prime.
  • A108725 (program): Numbers n such that 11*n + 19 is prime.
  • A108726 (program): Numbers n such that 11*n + 29 is prime.
  • A108727 (program): Numbers n such that 11*n + 31 is prime.
  • A108732 (program): a(0)=22; if n odd, a(n) = a(n-1)/2, otherwise a(n) = 4*a(n-1).
  • A108738 (program): a(n) = n/(smallest odd prime divisor of n), if any.
  • A108741 (program): Member r=100 of the family of Chebyshev sequences S_r(n) defined in A092184.
  • A108744 (program): Decimal expansion of B = Sum_ n > 0 1/A007559(n).
  • A108751 (program): Numbers n such that 11*n - 911 is prime.
  • A108752 (program): Numbers k such that 12 divides k*(k+1).
  • A108754 (program): Difference between partial sum of the first n primes and n^2.
  • A108765 (program): G.f. (1 - x + x^2)/((1-3x)(x-1)^2).
  • A108766 (program): a(n) = A007290(n+2) - 1 = 2*C(n+2,3) - 1.
  • A108775 (program): a(n) = floor(sigma(n)/n).
  • A108782 (program): Difference between n and the largest number with the same digit set as n.
  • A108784 (program): Difference between A107757 and A107755.
  • A108812 (program): 11^n mod 50.
  • A108850 (program): Number of 1’s in the binary expansion of the repunits.
  • A108852 (program): Number of Fibonacci numbers <= n.
  • A108854 (program): Numbers n such that 10*n - 127 is prime.
  • A108855 (program): Numbers n such that 10*n + 127 is prime.
  • A108856 (program): Numbers n such that 10*n - 131 is prime.
  • A108857 (program): Numbers n such that 10*n + 131 is prime.
  • A108869 (program): E.g.f. : exp(6x)/(1-x).
  • A108872 (program): Sums of ordinal references for a triangular table read by columns, top to bottom.
  • A108882 (program): Period doubling sequence starting with ‘1 0 1’.
  • A108895 (program): Partial sums of quadruple factorial numbers n!!!! (A007662).
  • A108896 (program): Numbers such that the outer 2 digits are 9 and the inner digits are 4.
  • A108898 (program): a(n+3) = 3a(n+2) - 2a(n), a(0) = -1, a(1) = 1, a(2) = 3.
  • A108903 (program): Numbers such that the outer 2 digits are 9 and the inner digits are 5.
  • A108904 (program): Numbers such that the outer two digits are 9’s and the inner digits are 7’s.
  • A108911 (program): Difference between n and the sum of the factorials of its digits.
  • A108920 (program): Number of positive integers k>n such that n+k divides n^2+k^2.
  • A108922 (program): Expansion of 1/((x^8+1)*(x-1)^2).
  • A108923 (program): Expansion of 1/((x^8+1)*(1-x)^3).
  • A108924 (program): J(n)^2+J(n+1)^2, with J(n) the Jacobsthal number A001045(n).
  • A108928 (program): a(n) = 8*n^2 - 3.
  • A108936 (program): Numbers n such that 11*n + 911 is prime.
  • A108942 (program): Degrees of irreducible representations of SL(2,7).
  • A108954 (program): a(n) = pi(2*n) - pi(n). Number of primes in the interval (n,2n].
  • A108955 (program): Floor(Li(2n) - Li(n)).
  • A108956 (program): Floor(R(2n) - R(n)).
  • A108958 (program): Number of unordered pairs of distinct length-n binary words having the same number of 1’s.
  • A108976 (program): Numbers n such that 17*n + 19 is prime.
  • A108977 (program): Numbers n such that 19*n + 17 is prime.
  • A108981 (program): a(n) = 3a(n-1) + 4a(n-2), a(0) = 1, a(1) = 5.
  • A108982 (program): Inverse binomial of A003949.
  • A108983 (program): Inverse binomial transform of A003950.
  • A108984 (program): Inverse binomial transform of A003951.
  • A109002 (program): Maximal difference between two n-digit numbers.
  • A109004 (program): Table of gcd(n,m) read by antidiagonals, n >= 0, m >= 0.
  • A109007 (program): a(n) = gcd(n,3).
  • A109008 (program): a(n) = gcd(n,4).
  • A109009 (program): a(n) = gcd(n,5).
  • A109010 (program): a(n) = gcd(n,7).
  • A109011 (program): a(n) = gcd(n,8).
  • A109012 (program): a(n) = gcd(n,9).
  • A109013 (program): a(n) = gcd(n,10).
  • A109014 (program): a(n) = gcd(n,11).
  • A109015 (program): a(n) = gcd(n,12).
  • A109021 (program): (27^n - 63^n + 4)/6.
  • A109043 (program): a(n) = lcm(n,2).
  • A109044 (program): a(n) = lcm(n,3).
  • A109045 (program): a(n) = lcm(n,4).
  • A109046 (program): a(n) = lcm(n, 5).
  • A109047 (program): a(n) = lcm(n, 6).
  • A109048 (program): a(n) = lcm(n, 7).
  • A109049 (program): a(n) = lcm(n, 8).
  • A109050 (program): a(n) = lcm(n, 9).
  • A109051 (program): a(n) = lcm(n,10).
  • A109052 (program): a(n) = lcm(n,11).
  • A109053 (program): a(n) = lcm(n,12).
  • A109065 (program): Numerator of the fraction due in month n of the total interest for a one-year installment loan based on the Rule of 78s (each denominator is 78).
  • A109094 (program): Length of the longest path (repeated edges not allowed) between two arbitrary, distinct nodes in K_n, the complete graph on n vertices.
  • A109105 (program): a(n) = (8sqrt(5)/25)((sqrt(5) + 2)((15 + 5sqrt(5))/2)^n + (sqrt(5) - 2)((15 - 5*sqrt(5))/2)^n.
  • A109106 (program): a(n) = (1/sqrt(5))((sqrt(5) + 1)((15 + 5sqrt(5))/2)^(n-1) + (sqrt(5) - 1)((15 - 5*sqrt(5))/2)^(n-1)).
  • A109110 (program): a(n) = 2a(n-1) + a(n-2) - a(n-3); a(0)=4, a(1)=9, a(2)=20.
  • A109112 (program): a(n) = 6a(n-1) - 3a(n-2), a(0)=2, a(1)=13.
  • A109114 (program): a(n) = 5a(n-1) - 3a(n-2), a(0)=1, a(1)=6.
  • A109116 (program): a(n) = (n+1)^3(n+2)^2(n+5).
  • A109117 (program): a(n) = (n+1)^3*(2n+1)(5n+1).
  • A109118 (program): a(n) = 2(n^2 + 3n + 1)^3.
  • A109119 (program): a(n) = 2(5n^2 + 5n + 1)^3.
  • A109123 (program): a(n) = 4(n+1)^2(n+3)^2(5n^2 + 20n + 12).
  • A109128 (program): Triangle read by rows: T(n,k) = T(n-1,k-1) + T(n-1,k) + 1 for 0<k<n, T(n,0) = T(n,n) = 1.
  • A109130 (program): Magic constant of smallest order-n perfect magic cube.
  • A109134 (program): Decimal expansion of Phi, the real root of the equation 1/x = (x-1)^2.
  • A109161 (program): Triangle read by rows: T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.
  • A109164 (program): a(n) = 4a(n-1) - 4a(n-2) + a(n-3), n >= 3; a(0)=1, a(1)=6, a(2)=20.
  • A109168 (program): Continued fraction expansion of the constant x (A109169) such that the continued fraction of 2*x yields the continued fraction of x interleaved with the positive even numbers.
  • A109222 (program): Row sums of a triangle related to the Fibonacci polynomials.
  • A109231 (program): a(n) = floor(n*cosh(1)).
  • A109232 (program): a(n) = floor(n*(e^2+1)/(e-1)^2).
  • A109234 (program): a(n) = floor(n*sinh(1)).
  • A109235 (program): a(n) = floor(n(e^2-1)/(e^2-2e-1)).
  • A109237 (program): a(n) = floor(n*coth(1)).
  • A109238 (program): a(n) = floor(n*(e^2+1)/2).
  • A109241 (program): Expansion of 1/((1-10x)(1-100*x)).
  • A109242 (program): Expansion of 1/((1-x)(1-10x)(1-100x)).
  • A109255 (program): a(n) = (p^2 - 1) / 12, where p is the n-th prime of the form 4*k+1.
  • A109256 (program): a(n) = n^6 - 11n^4 + 36n^2 - 36.
  • A109265 (program): Row sums of Riordan array (1-x-x^2,x(1-x)).
  • A109338 (program): Triangle read by rows: T(n,k) = number of inequivalent binary sequences of length n and weight k, where two sequences are said to be equivalent if they have the same set of phrases in their Ziv-Lempel encodings (the phrases can appear in a different order in the two sequences).
  • A109340 (program): Expansion of x^2(1+x+4x^2)/((1+x+x^2)*(1-x)^3).
  • A109341 (program): Take a deck of 52 cards face-down, split it in half and flip one deck and reinsert it into the other deck such that the cards are alternatingly face up and face down. This sequence is the number of face-up cards after repeating this process n times.
  • A109344 (program): a(n) consists of n 4’s, n-1 8’s and a single 9 (in that order).
  • A109345 (program): a(n) = 5^((n^2 - n)/2).
  • A109354 (program): a(n) = 6^((n^2 - n)/2).
  • A109362 (program): Period 6: repeat [0, 0, 1, 2, 0, 3].
  • A109363 (program): a(n) = 42^n - 3n - 5.
  • A109375 (program): Bisection of A093411.
  • A109377 (program): Expansion of ( 2+x+2x^2 ) / ( 1-2x+x^2-x^3 ).
  • A109391 (program): a(n) = (n^(n+1))(n + 1)/2 = A000217(n)A000312(n).
  • A109392 (program): Partial sums of A109391.
  • A109395 (program): Denominator of phi(n)/n = Product_ p n (1 - 1/p); phi(n)=A000010(n), the Euler totient function.
  • A109398 (program): a(n) = (1/n!)*Sum_ k=0..n (n+k)!.
  • A109415 (program): a(n) equals the (n(n+1)/2)-th partial sum of the self-convolution 4th power of A010054, which has the g.f.: Sum_ k>=0 x^(k(k+1)/2).
  • A109437 (program): a(-1) = a(0) = 0, a(1) = 1; a(n) = 5a(n-1) - 5a(n-2) + a(n-3) + 2*(-1)^(n+1), alternatively a(n) = 3a(n-1) + 3a(n-2) - a(n-3).
  • A109438 (program): a(n) = 5a(n-1) - 5a(n-2) + a(n-3) + 2*(-1)^(n+1), alternatively a(n) = 3a(n-1) + 3a(n-2) - a(n-3).
  • A109442 (program): Cumulative sum of smallest prime power >= n.
  • A109443 (program): Cumulative sum of largest prime power <= n.
  • A109446 (program): Binomial coefficients C(n,k) with n-k even, read by rows.
  • A109447 (program): Binomial coefficients C(n,k) with n-k odd, read by rows.
  • A109451 (program): a(1)=1; a(n) = smallest positive integer not already present such that a(n-1) and a(n) have a different number of 1’s in their binary expansions.
  • A109453 (program): Cumulative sum of initial digits of n.
  • A109470 (program): Sum of first n noncubes.
  • A109474 (program): a(1)=1, a(2)=3; thereafter, a(n) = least positive integer > a(n-1) and not equal to a(i)+a(j)+a(k) for 1<=i<=j<=k<=n-1.
  • A109493 (program): a(n) = 7^((n^2 - n)/2).
  • A109499 (program): Number of closed walks of length n on the complete graph on 5 nodes from a given node.
  • A109500 (program): Number of closed walks of length n on the complete graph on 6 nodes from a given node.
  • A109501 (program): Number of closed walks of length n on the complete graph on 7 nodes from a given node.
  • A109522 (program): a(n) = the (1,2)-entry in the matrix P^n + F^n, where the 2 X 2 matrices P and F are defined by P=[0,1;1,0] and F=[0,1;1,1].
  • A109534 (program): a(0)=1, a(n)=n+a(n-1) if n mod 2=0, a(n)=3n-a(n-1) if n mod 2 = 1.
  • A109540 (program): a(n) = a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+2*a(n-7)+a(n-8).
  • A109541 (program): a(n) = a(n-2)+a(n-3)+a(n-4)+a(n-5)+2*a(n-6)+a(n-7).
  • A109546 (program): (4^(n+1)-(-1)^n 9 )/5.
  • A109588 (program): n followed by n^2 followed by n^3.
  • A109592 (program): Sequence and first differences include all even numbers exactly once and no odd numbers.
  • A109595 (program): n^3 followed by n^2 followed by n.
  • A109606 (program): Number of numbers k with 1 < k < n which are relatively prime to n.
  • A109607 (program): Sum of coprimes of n greater than 1.
  • A109610 (program): Expansion of (1+3x^4-2x^7+x^10-x^12)/((x+1)(x^2+1)(x^2+x+1)(x^2-x+1)(x^4-x^2+1)*(x-1)^2).
  • A109613 (program): Odd numbers repeated.
  • A109614 (program): n^3 followed by n followed by n^2.
  • A109620 (program): a(n) = (1/3)n^3 - n^2 - (1/3)n - 1.
  • A109622 (program): Number of different isotemporal classes of diasters with n peripheral edges.
  • A109630 (program): The winning position when playing the “eeny meeny miny moe” game with n players and eliminating every 8th player.
  • A109632 (program): In the game of bridge, a(n) is the penalty for going down n tricks in a vulnerable, doubled contract.
  • A109633 (program): In the game of bridge, a(n) is the penalty for going down n tricks in a non-vulnerable, doubled contract.
  • A109634 (program): Number of 1’s that appear among all ternary strings of length n that contain no consecutive 1’s.
  • A109652 (program): Prime(A000201(n)).
  • A109664 (program): a(1) = 1; for n>1, a(n) = Sum_ i=1..n-1 a(i)*prime(i).
  • A109674 (program): a(n)^(n/a(n)) = A092975(n) and a(n) is a prime.
  • A109678 (program): Sequence and first differences include all square numbers exactly once.
  • A109680 (program): a(n) = 2^(4n-2) - A104403(n).
  • A109718 (program): Periodic sequence with period 0,1,0,3 , or n^3 mod 4.
  • A109720 (program): Periodic sequence 0,1,1,1,1,1,1 or n^6 mod 7.
  • A109722 (program): Sum of first 2n primes.
  • A109723 (program): Sum of the first 2n+1 primes.
  • A109753 (program): n^3 mod 8; the periodic sequence 0,1,0,3,0,5,0,7 .
  • A109763 (program): Primes repeated.
  • A109764 (program): Sum of the first n^2 squares.
  • A109765 (program): Expansion of x/((4x-1)(2x-1)(x+1)).
  • A109768 (program): a(n) = gcd(3^n-2,2^n-3).
  • A109774 (program): a(n) = (3^(n-1) - 1) * (3^n - 1)/2.
  • A109786 (program): Expansion of -(x+2x^2+3x^3-1+5x^4)/((x+1)(x^2-3x+1)(1+x^2)).
  • A109794 (program): a(2n) = A001906(n+1), a(2n+1) = A002878(n).
  • A109795 (program): a(n)= n*(1+floor(n/10)).
  • A109804 (program): Cumulative sum of initial digits of (n base 6).
  • A109808 (program): a(n) = 2*7^(n-1).
  • A109815 (program): n^2 followed by n^3 followed by n.
  • A109857 (program): Next 2n-1 odd numbers in decreasing order followed by next 2n even numbers in decreasing order.
  • A109866 (program): 9’s complement of the digits of the golden ratio phi (A001622): 9.999999999999… - 1.6180339887… = 8.3819660112501051517954131656334…
  • A109883 (program): Start subtracting from n its divisors beginning from 1 until one reaches a number smaller than the last divisor subtracted or reaches the last nontrivial divisor < n. Define this to be the perfect deficiency of n. Then a(n) = perfect deficiency of n.
  • A109900 (program): The (n,r)-th term of the following triangle is T(n)-T(r) for r = 0 to n. The n-th row contains n+1 terms. T(n) = the n-th triangular number = n(n+1)/2. Sequence contains the sum of terms at a 45-degree angle.
  • A109901 (program): a(n) = binomial(n^2, n*(n+1)/2).
  • A109916 (program): a(n) = n-th digit after decimal point in e^n.
  • A109921 (program): a(2n) = prime(n). a(2n+1) = sum of composite numbers between prime(n) and prime(n+1). We define a(1) = 1.
  • A109952 (program): Degrees Centigrade for which Fahrenheit is a prime.
  • A109961 (program): Expansion of (1-x)^3/(1-4x+5x^2-4x^3+x^4).
  • A109964 (program): a(n) = floor(sqrt(Sum_ i<n a(i))), with a(0)=1.
  • A109965 (program): Sum_i i<n floor(sqrt(a(i))) with a(0) = 1.
  • A109966 (program): a(n) = 8^((n^2-n)/2).
  • A109975 (program): Second differences of A045623, prefixed by an initial 1.
  • A110013 (program): Squares of the form 4p + 5, where p is a prime.
  • A110035 (program): Row sums of an unsigned characteristic triangle for the Fibonacci numbers.
  • A110090 (program): Numerators of sequence of rationals defined by r(n) = n for n<=1 and for n>1: r(n) = (sum of denominators of r(n-1) and r(n-2))/(sum of numerators of r(n-1) and r(n-2)).
  • A110091 (program): Denominators of sequence of rationals defined by r(n) = n for n<=1 and for n>1: r(n) = (sum of denominators of r(n-1) and r(n-2))/(sum of numerators of r(n-1) and r(n-2)).
  • A110132 (program): a(n) = floor(n/2)^ceiling(n/2).
  • A110138 (program): a(n) = ceiling(n/2)^floor(n/2).
  • A110139 (program): Floor(n/2)^floor(n/2).
  • A110146 (program): n^(n+1) mod n+2.
  • A110147 (program): 10^((n^2-n)/2).
  • A110157 (program): a(n) = a(rad(n) - 1) + 1, where rad(n) is the squarefree kernel of n, rad=A007947.
  • A110158 (program): Expansion of x^4 / ((x+1)(2x^3-2x^2-2x+1)*(x-1)^2).
  • A110159 (program): a(n) = (n+1)(n+2)(n+3)(9n^2 + 26n + 20)/120.
  • A110161 (program): Expansion of x(1-x^2)/(1-x^2+x^4).
  • A110164 (program): Expansion of (1-x^2)/(1+2x).
  • A110185 (program): Coefficients of x in the partial quotients of the continued fraction expansion exp(1/x) = [1, x - 1/2, 12x, 5x, 28x, 9x, 44x, 13x, …]. The partial quotients all have the form a(n)*x except the constant term of 1 and the initial partial quotient which equals (x - 1/2).
  • A110195 (program): a(n) = 11^((n^2-n)/2).
  • A110199 (program): a(n) = Sum_ k=0..floor(n/2) Catalan(k).
  • A110206 (program): Row sums of triangle A110205, where A110205(n,k) equals the sum of cubes of numbers < 2^n having exactly k ones in their binary expansion.
  • A110254 (program): Square-indexed values of A110243.
  • A110258 (program): Denominators in the coefficients that form the odd-indexed partial quotients of the continued fraction representation of the inverse tangent of 1/x.
  • A110269 (program): n mod 2 + n mod 3.
  • A110270 (program): a(n) = (n mod 2)*(n mod 3).
  • A110272 (program): a(n) = Pell(n)^3.
  • A110286 (program): a(n) = 15*2^n.
  • A110287 (program): 17*2^n.
  • A110288 (program): 19*2^n.
  • A110293 (program): a(2n) = A001570(n), a(2n+1) = A011943(n+1).
  • A110295 (program): a(n) = prime(n)*2^(n-1).
  • A110303 (program): Alternators.
  • A110315 (program): Diagonal sums of the Fibonacci related number triangle A110314.
  • A110316 (program): a(n) is the number of different shapes of balanced binary trees with n nodes. The tree is balanced if the total number of nodes in the left and right branch of every node differ by at most one.
  • A110325 (program): Row sums of number triangle related to the Jacobsthal numbers.
  • A110326 (program): Diagonal sums of triangle A110324.
  • A110331 (program): Row sums of a number triangle related to the Pell numbers.
  • A110332 (program): Diagonal sums of number a triangle related to the Pell numbers.
  • A110344 (program): a(n) = sum( n+k, k=0..n-1 ) = n(3n-1)/2 if n is even; a(n) = sum( n-k, k=0..n-1 ) = n(n+1)/2 if n is odd.
  • A110345 (program): a(n) = n +(n+1) +(n+2)… n terms if n is odd, else a(n) = n + (n-1) + (n-2) … n terms = n(n+1)/2 = n-th triangular number if n is even.
  • A110349 (program): a(n) = n + (n+1) + (n-1) + (n+2) + (n-2) … n terms.
  • A110350 (program): Least sum (n+1) + (n+2) + …+(n+k) >= (n(n+1)/2), the n-th triangular number.
  • A110356 (program): Array read by antidiagonals: T(n,k) (n>=3, k>=3) = minimal number of polygonal pieces in a dissection of a regular n-gon to a regular k-gon (conjectured).
  • A110369 (program): (Digit 1 repeated n times) + n.
  • A110371 (program): a(n)=[(n+1)(n+2)(n+3)…(2n)]/(1+2+3+…+n).
  • A110388 (program): a(n) = F(n)*F(n+1) mod 9, where F(n) = n-th Fibonacci number.
  • A110391 (program): a(n) = L(3*n)/L(n), where L(n) = Lucas number.
  • A110426 (program): The r-th term of the n-th row of the following array contains the sum of r successively decreasing integers beginning from n. 0<r<=n. e.g. the row corresponding to 4 contains 4, (3+2), (1) +(0)+(-1) , (-2)+(-3)+(-4)+(-5) —-> 4,5,0,-14 1 2 1 3 3 -3 4 5 0 -14 5 7 3 -10 -35 6 9 6 -6 -30 -69 … Sequence contains the row sums.
  • A110427 (program): The r-th term of the n-th row of the following array contains the sum of r successively decreasing integers beginning from n. 0 < r <= n. E.g., the row corresponding to 4 contains 4, (3+2), (1) +(0)+(-1) , (-2)+(-3)+(-4)+(-5) —-> 4,5,0,-14 1 2 1 3 3 -3 4 5 0 -14 5 7 3 -10 -35 6 9 6 -6 -30 -69 … Sequence contains the leading diagonal.
  • A110430 (program): Arithmetic mean of all n-digit positive even numbers.
  • A110431 (program): Average of positive multiples of 3 with n decimal digits, rounded down.
  • A110450 (program): a(n) = n(n+1)(n^2+n+1)/2.
  • A110451 (program): a(n) = n(4n^2 + 2*n + 1).
  • A110468 (program): a(n) = (2*n + 1)!/(n + 1).
  • A110475 (program): Number of symbols ‘*’ and ‘^’ to write the canonical prime factorization of n.
  • A110491 (program): Expansion of e.g.f.: sqrt(1+2x)/sqrt(1-2x).
  • A110494 (program): Least k such that prime(n)^2 divides binomial(2k,k).
  • A110496 (program): Least k such that prime(n)^3 divides binomial(2k,k).
  • A110507 (program): Number of nodes in the smallest cubic graph with crossing number n.
  • A110512 (program): Expansion of (1 + x)/(1 + x + 2x^2).
  • A110514 (program): Expansion of (1 - x + x^2 + x^3)/(1 - x^2 - x^4 + x^6).
  • A110515 (program): Sequence array for (1 - x + x^2 + x^3)/(1 - x^4).
  • A110516 (program): Expansion of (1-x+x^2+x^3)/(1+x-x^4-x^5).
  • A110526 (program): a(n+3) = 3a(n+2) + 5a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 3.
  • A110528 (program): a(n+3) = 3a(n+2) + 5a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37.
  • A110532 (program): a(n) = floor(n/2) + floor(n/5).
  • A110533 (program): a(n) = floor(n/2) * floor(n/5).
  • A110548 (program): One of the three ordered sets of positive integers that solves the minimal magic die puzzle.
  • A110549 (program): Period 8: repeat [1, 2, 4, 3, 3, 4, 2, 1].
  • A110550 (program): Periodic 1,3,2,4,4,2,3,1 .
  • A110551 (program): Period 6: repeat [1, 3, 5, 5, 3, 1].
  • A110555 (program): Triangle of partial sums of alternating binomial coefficients: T(n,k) = Sum_ k=0..n binomial(n,k)*(-1)^k.
  • A110556 (program): a(n) = binomial(2n-1,n)(-1)^n for n>0; a(0) = 1.
  • A110560 (program): Numerators of T(n+1)/n! reduced to lowest terms, where T(n) are the triangular numbers A000217.
  • A110567 (program): a(n) = n^(n+1) + 1.
  • A110568 (program): Period 6: repeat [1, 0, 2, 2, 0, 1].
  • A110569 (program): Period 6: repeat [2, 1, 3, 3, 1, 2].
  • A110591 (program): Number of digits in base-4 representation of n.
  • A110592 (program): Number of digits in base-5 representation of n. String length of A007091.
  • A110593 (program): a(1) = 3, a(n+1) = 2*(3^n).
  • A110594 (program): a(1) = 4, a(2) = 12, for n>1: a(n) = 3*4^(n-1).
  • A110595 (program): a(1)=5. For n > 1, a(n) = 4*5^(n-1) = A005054(n).
  • A110609 (program): a(n) = n * C(2*n,n-1).
  • A110610 (program): Maximal value of sum(p(i)p(i+1),i=1..n), where p(n+1)=p(1), as p ranges over all permutations of 1,2,…,n .
  • A110611 (program): Minimal value of sum(p(i)p(i+1),i=1..n), where p(n+1)=p(1), as p ranges over all permutations of 1,2,…,n .
  • A110613 (program): a(n+3) = 5a(n+2) - 2a(n+1) - 8*a(n), a(0) = 1, a(1) = 0, a(2) = 3.
  • A110614 (program): a(n+3) = 5a(n+2) - 2a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15.
  • A110654 (program): a(n) = ceiling(n/2), or: a(2k) = k, a(2k+1) = k+1.
  • A110655 (program): a(n) = A110654(A110654(n)).
  • A110656 (program): a(n) = A110654(A110654(A110654(n))).
  • A110657 (program): a(n) = A028242(A028242(n)).
  • A110658 (program): a(n) = A028242(A028242(A028242(n))).
  • A110659 (program): a(n) = A028242(A110654(n)).
  • A110660 (program): Pronic numbers repeated.
  • A110665 (program): Sequence is a(0,n) , where a(m,0)=0, a(m,n) = a(m-1,n)+a(m,n-1) and a(0,n) is such that a(n,n) = n for all n.
  • A110666 (program): Sequence is a(1,n) , where a(m,n) is defined at sequence A110665.
  • A110667 (program): Sequence is a(2,n) , where a(m,n) is defined at sequence A110665.
  • A110668 (program): Sequence is a(3,n) , where a(m,n) is defined at sequence A110665.
  • A110669 (program): Sequence is a(4,n) , where a(m,n) is defined at sequence A110665.
  • A110678 (program): a(n) = -n^2 - n + 72.
  • A110679 (program): a(n+3) = 3a(n+2) + 5a(n+1) + a(n), a(0) = 1, a(1) = 2, a(2) = 11.
  • A110749 (program): Triangle read by rows with the n-th row containing the first n multiples of n with digits reversed.
  • A110766 (program): Fractalization of Pi.
  • A110771 (program): The r-th term of the n-th row of the following triangle is C[ T(n)-T(r-1) ,r] where T(n) is the n-th triangular number. 1 3 1 6 10 1 10 36 35 1 … Sequence contains the row sums.
  • A110779 (program): Fractalization of e.
  • A110800 (program): n-th digit after decimal point in decimal expansion of n/(n+1).
  • A110801 (program): Numbers n such that 12n + 1 is prime.
  • A110803 (program): n times the number of digits in the decimal expansion of n.
  • A110805 (program): Sum of digits of n times number of digits of n.
  • A110807 (program): n times largest n-digit number.
  • A110831 (program): a(n) = 3n^2 + 27n + 1.
  • A110833 (program): a(n) = (prime(n)+1)^2.
  • A110847 (program): Weight enumerator of [32,31,2] Reed-Muller code RM(4,5).
  • A110851 (program): Weight enumerator of [64,63,2] Reed-Muller code RM(5,6).
  • A110862 (program): Highest minimal distance of odd formally self-dual binary codes of length 2n.
  • A110867 (program): Highest minimal distance of Type I but not Type II additive Hermitian self-dual codes of length n over GF(4).
  • A110870 (program): Highest minimal distance of Type II additive Hermitian self-dual codes of length n over GF(4).
  • A110882 (program): a(n) is the least integer x such that x^n < 2 * (x-1)^n.
  • A110892 (program): Sum of the squares of digits of n^2.
  • A110895 (program): Number of integers between a(n) and a(n+1) equals the n-th prime.
  • A110907 (program): Number of points in the standard root system version of the D_3 (or f.c.c.) lattice having L_infinity norm n.
  • A110923 (program): Final two digits of prime(n), with leading zero omitted.
  • A110953 (program): Starting a priori with the fraction 1/1, the denominators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 9 times the bottom to get the new top.
  • A110962 (program): Fractalization of Kimberling’s sequence beginning with 0.
  • A110963 (program): Fractalization of Kimberling’s sequence beginning with 1.
  • A111007 (program): Triangle T(n,m) which contains in row n the rounded ordinate value at abscissa m along the upper rim of the circle with diameter n centered at (n/2, 1).
  • A111033 (program): Sum of squares of first n digits of Pi.
  • A111034 (program): Sum of squares of digits of e.
  • A111043 (program): Partial sums of squares of digits of golden ratio phi (A001622).
  • A111063 (program): a(0) = 1; a(n) = (n-1)*a(n-1) + n.
  • A111072 (program): Write the digit string 0123456789, repeated infinitely many times. Then, starting from the first “0” digit at the left end, move to the right by one digit (to the “1”), then two digits (to the “3”), then three digits (to the “6”), four digits (“0”), five digits (“5”), and so on. Partial sums of the digits thus reached are 0, 1, 4, 10, 10, 15, …
  • A111074 (program): Let t(n) denote the triangular numbers (A000217). Sequence mixes t(n+2) and t(n).
  • A111080 (program): Sum of numbers under a triangle on a spiral staircase of width 10.
  • A111089 (program): Largest prime factor of 2n.
  • A111093 (program): Like sequence A111072 but moving right by the squares of the sequence of positive integers.
  • A111094 (program): Numbers k such that 18*k + 1 is prime.
  • A111097 (program): Maximum likelihood estimate of the number of distinguishable marbles in an urn if repeated random sampling of one marble with replacement yields n different marbles before the first repeated marble.
  • A111113 (program): a(2^m) = 1, a(2^m+1) = -1 (m>0), otherwise a(n) = 0.
  • A111132 (program): a(n+1) = a(n) + (a(n) - a(n-1) + a(n) mod 10) mod 10 with a(0)=0 and a(1)=1.
  • A111136 (program): a(n) = Sum_ k=1..n Fibonacci(prime(k)).
  • A111138 (program): Let b(n) denote the number of nontriangular numbers less than or equal to n. Then a(n) = b(n-1) + a(b(n-1)), with a(1) = a(2) = 0, a(3) = 1.
  • A111144 (program): a(n) = n(n+13)(n+14)/6.
  • A111150 (program): a(n) is the number of integers of the form (n+k)/ (n-k) for k>0.
  • A111174 (program): Numbers k such that 24*k + 1 is prime.
  • A111175 (program): Numbers n such that 30*n + 1 is prime.
  • A111179 (program): a(n) = Sum_ k=1..n prime(k)!, where prime(k) is k-th prime.
  • A111181 (program): Prime(n) - Pi(n).
  • A111199 (program): Numbers n such that 4k + 9 is prime.
  • A111208 (program): Number of primes <= n-th triangular number.
  • A111209 (program): Difference between the powers of two and the primes.
  • A111215 (program): Numbers k such that 4k + 5 is prime.
  • A111216 (program): a(n) = 31*a(n-1)-a(n-2).
  • A111223 (program): Numbers n such that 5*n + 2 is prime.
  • A111224 (program): Numbers n such that 5*n + 7 is prime.
  • A111225 (program): Numbers n such that 5*n + 8 is prime.
  • A111226 (program): Numbers n such that 5*n + 12 is prime.
  • A111230 (program): Numbers n such that 5*n + 14 is prime.
  • A111234 (program): a(1)=2; thereafter a(n) = (largest proper divisor of n) + (smallest prime divisor of n).
  • A111249 (program): Numbers n such that 7*n + 8 is prime.
  • A111250 (program): Numbers n such that 7*n + 10 is prime.
  • A111251 (program): Numbers k such that 3k^2 + 3k + 1 is prime.
  • A111254 (program): a(n) = Prime[n+2]+Prime[n]+1.
  • A111277 (program): Number of permutations avoiding the patterns 2413,4213,2431,4231,4321 ; also number of permutations avoiding the patterns 3142,3412,3421,4312,4321 ; number of weak sorting class based on 2413 or 3142.
  • A111282 (program): Number of permutations avoiding the patterns 1432,2431,3412,3421,4132,4231,4312,4321 ; number of strong sorting class based on 1432.
  • A111284 (program): Number of permutations of [n] avoiding the patterns 2143, 2341, 2413, 2431, 3142, 3241, 3412, 3421, 4123, 4213, 4231, 4321, 4132, 4312 ; number of strong sorting classes based on 2143.
  • A111285 (program): Number of permutations avoiding the patterns 2431, 3421, 4231, 4321, 24513, 42513, 34512, 43512 ; number of strong sorting class based on 2431.
  • A111286 (program): Number of permutations avoiding the patterns 1342, 1432, 2341, 2431, 3142, 3241, 3412, 3421, 4132, 4231, 4312, 4321 ; number of strong sorting class based on 1342.
  • A111297 (program): First differences of A109975.
  • A111312 (program): Numbers n such that 11*n + 2 is prime.
  • A111314 (program): a(n) = a(n-1) + a(n-2) + 2 where a(0) = a(1) = 1.
  • A111333 (program): Number of odd numbers <= n-th prime.
  • A111365 (program): a(n) = 5a(n-1) + 3a(n-2) where a(0) = a(1) = 1.
  • A111367 (program): Numbers k such that 7*k + 5 is prime.
  • A111368 (program): The number of maximal determinant -1,1 matrices of order n.
  • A111369 (program): Numbers k such that 13*k + 11 is prime.
  • A111384 (program): a(n) = binomial(n,3) - binomial(floor(n/2),3) - binomial(ceiling(n/2),3).
  • A111386 (program): a(1) = 1, a(2) = 3; for n >= 3, take a(n) to be the smallest odd number not occurring earlier such that a(n-1) divides the concatenation a(n-2)a(n).
  • A111393 (program): Number of digits in n^3.
  • A111394 (program): a(n) = product of first n integers not divisible by 3.
  • A111395 (program): First digit of powers of 5 (n>=1).
  • A111396 (program): a(n) = n(n+7)(n+8)/6.
  • A111397 (program): Composite numbers (modulo 3).
  • A111406 (program): a(n) = f(f(n+1)) - f(f(n)), where f(m) = pi(m) = A000720(m), with f(0) = 0.
  • A111424 (program): Sum_ i=1..n (2i)!/i!.
  • A111425 (program): a(n) = tribonacci(Fibonacci(n)).
  • A111426 (program): Difference between largest and smallest prime factor of the n-th composite number.
  • A111431 (program): a(n) = Fibonacci(tribonacci(n)).
  • A111454 (program): a(n) = (n-4)^(n-3) - (n-3)^(n-4) + 1.
  • A111490 (program): Antidiagonal sums of the numerical array defined by M(n,k) = 1 + (k-1) mod n.
  • A111495 (program): Floor of 10^n/Li(10^n) - 1.
  • A111500 (program): Number of squares in an n X n grid of squares with diagonals.
  • A111517 (program): Numbers n such that (7*n + 1)/2 is prime.
  • A111566 (program): a(n) = ((1+sqrt(8))(2+sqrt(2))^n + (1-sqrt(8))(2-sqrt(2))^n)/2.
  • A111567 (program): Binomial transform of A048654: generalized Pellian with second term equal to 4.
  • A111575 (program): Powers of 3 repeated four times.
  • A111587 (program): a(n) = 2a(n-1) + 2a(n-3) + a(n-4), a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 20.
  • A111601 (program): Exponential (binomial) convolution of A001818 (with interspersed zeros) and A000142 (factorials).
  • A111607 (program): Fourth column of A109626.
  • A111648 (program): a(n) = A001541(n)^2 + A001653(n)^2 + A002315(n)^2.
  • A111650 (program): 2n appears n times (n>0).
  • A111651 (program): n appears 3n times.
  • A111652 (program): 3n appears n times.
  • A111653 (program): n-th composite number appears n times.
  • A111654 (program): n appears n-th composite number times.
  • A111657 (program): n-th composite number appears n-th prime times.
  • A111665 (program): Expansion of (-1+x+2x^2+5x^4+3x^3) / ((x-1)(x+1)(x^2-3x+1)*(1+x^2)).
  • A111684 (program): Least k such that the product of n consecutive integers beginning with k exceeds n^n.
  • A111685 (program): n + n(n+1) + n(n+1)(n+2) + …, with n terms.
  • A111686 (program): (n+1) + (n+1)(n+2) + …, with n terms.
  • A111688 (program): Primes and composite numbers alternately in increasing order.
  • A111693 (program): The number system may be represented by linearly stringing together all the square domains. The number of the domain is given by r. It is noted that this has the same value as the circuit number in the Ellerstein square spiral. One below each odd square is a zero-centered octagonal number, which is divisible by 8. The value of this is eight times a triangular number. It may be seen that there are r octads in each square domain. The sequence is the first prime number in the first octad of each square domain.
  • A111694 (program): a(1) = 1+2-3 = 0, a(2) = 4+5+6-7 = 8, a(3) = 8+9+10+11-12 = 26, a(4) = 13+14+15+16+17-18 = 57, …
  • A111700 (program): Number of integers between p(n) and p(n+1) which are coprime to (p(n+1)-p(n)), where p(n) is the n-th prime.
  • A111701 (program): Least integer obtained when n is divided by prime(1), then by prime(2), then by prime(3), …, stopping as soon as one of the primes does not divide it. In particular, a(2n-1) = 2n-1.
  • A111706 (program): a(n) = concatenation of k times the k-th digit of n.
  • A111708 (program): a(n) = n concatenated with 9’s complement of n.
  • A111710 (program): Consider the triangle shown below in which the n-th row contains the n smallest numbers greater than those in the previous row such that the arithmetic mean is an integer. Sequence contains the leading diagonal.
  • A111711 (program): Leading column of triangle mentioned in A111710.
  • A111712 (program): Arithmetic mean of the n-th row of triangle mentioned in A111710.
  • A111721 (program): a(n) = a(n-1) + a(n-2) + 5 where a(0) = a(1) = 1.
  • A111733 (program): a(n) = a(n-1) + a(n-2) + 7 where a(0) = a(1) = 1.
  • A111735 (program): Distance between k*(n-th prime) and next prime, k=3 case.
  • A111736 (program): Distance between k*(n-th prime) and next prime, k=4 case.
  • A111737 (program): Distance between k*(n-th prime) and next prime, k=5 case.
  • A111738 (program): Distance between k*(n-th prime) and next prime, k=6 case.
  • A111739 (program): Distance between k*(n-th prime) and next prime, k=7 case.
  • A111740 (program): Distance between k*(n-th prime) and next prime, k=8 case.
  • A111746 (program): Number of squares in the interior of the square with vertices (n,0), (0,n), (-n,0) and (0,-n) in a square (x,y)-grid.
  • A111748 (program): a(n) = 1 if n-th composite number is squarefree, otherwise a(n) = 0.
  • A111775 (program): Number of ways n can be written as a sum of at least three consecutive integers.
  • A111802 (program): n^2-n-1 for n>3; a(1)=1; a(2)=2; a(3)=3.
  • A111859 (program): Number of numbers m <= n such that 9 equals the first digit after decimal point of square root of n in decimal representation.
  • A111862 (program): Second digit after decimal point of square root of n in decimal representation.
  • A111863 (program): Smallest prime factor of 6*n-1 that is congruent to 5 modulo 6.
  • A111868 (program): The work performed by a function f: 1,…,n -> 1,…,n is defined to be work(f) = sum( i-f(i) , i=1…n); a(n) is equal to sum(work(f)) where the sum is over all functions f: 1,…,n -> 1,…,n .
  • A111873 (program): The work performed by a partial function f: 1,…,n -> 1,…,n is defined to be work(f)=sum( i-f(i) ,i in dom(f)); a(n) is equal to sum(work(f)) where the sum is over all partial functions f: 1,…,n -> 1,…,n .
  • A111883 (program): Unsigned row sums of triangle A111595 (normalized rescaled squared Hermite polynomials).
  • A111889 (program): A repeated permutation of 0,…,8 .
  • A111903 (program): The work performed by a partial function f: 1,…,n -> 1,…,n is defined to be work(f)=sum( i-f(i) ,i in dom(f)); a(n) is equal to sum(work(f)) where the sum is over all order-preserving partial functions f: 1,…,n -> 1,…,n .
  • A111926 (program): Expansion of x^4/((1-2x)(x^2-x+1)*(x-1)^2).
  • A111927 (program): Expansion of x^3 / ((x-1)(2x-1)*(x^2-x+1)).
  • A111946 (program): Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Fibonacci(k)), 1 <= k <= n.
  • A111951 (program): Period 8: repeat [0,3,1,2,2,1,3,0].
  • A111952 (program): a(n) = 3*n mod 7.
  • A111954 (program): a(n) = A000129(n) + (-1)^n.
  • A111955 (program): a(n) = A078343(n) + (-1)^n.
  • A111958 (program): Lucas numbers (A000032) mod 8.
  • A111972 (program): a(n) = Max(omega(k): 1<=k<=n), where omega(n) = A001221(n), the number of distinct prime factors of n.
  • A111982 (program): Row sums of abs(A111967).
  • A112030 (program): a(n) = (2 + (-1)^n) * (-1)^floor(n/2).
  • A112031 (program): Numerator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 + ….
  • A112032 (program): Denominator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 …
  • A112033 (program): a(n) = 3 * 2^(floor(n/2) + 1 + (-1)^n).
  • A112039 (program): Let b(0)=1/2, b(n) = b(n-1) + Prime[n]/2; a(n)=b(2*n).
  • A112044 (program): Let b(0)=1/2, b(n) = (b(n-1)+Prime[n])/2; sequence gives 2^(n+1)*b(n).
  • A112045 (program): Positions of primes (A000040) among nonsquares A000037.
  • A112051 (program): a(1)=1, a(n) = first index i (> a(n-1)), where A112046(i) gets a value distinct from any values A112046(1)..A112046(a(n-1)).
  • A112052 (program): a(n) = 2*A112051(n)+1.
  • A112062 (program): Positive integers i for which A112049(i) == 2.
  • A112063 (program): Positive integers i for which A112049(i) == 3.
  • A112072 (program): Odd numbers n for which 3 is the smallest i (>= 1) with Jacobi symbol J(i,n) getting either a value 0 or -1.
  • A112073 (program): Odd numbers n for which 5 is the smallest i (>= 1) with Jacobi symbol J(i,n) getting either a value 0 or -1.
  • A112087 (program): 4*(n^2 - n + 1).
  • A112088 (program): Number of leaf nodes in a binary tree.
  • A112091 (program): Number of idempotent order-preserving partial transformations (of an n-element chain).
  • A112132 (program): Period 4: repeat [1, 3, 1, 7].
  • A112133 (program): First differences of A112063.
  • A112231 (program): Repeat each prime in the sequence of natural numbers.
  • A112232 (program): Repeat each composite number in the sequence of natural numbers.
  • A112248 (program): a(n) = n mod floor(log_2(n)).
  • A112282 (program): a(n) = (-1)^n(2n+1) (mod 9).
  • A112293 (program): Row sums of number triangle A112292.
  • A112300 (program): Expansion of x * (1 - x)^2 * (1 - x^2) / (1 - x^6) in powers of x.
  • A112310 (program): Number of terms in lazy Fibonacci representation of n.
  • A112335 (program): Row sums of number triangle A112334.
  • A112347 (program): Kronecker symbol (-1, n) except a(0) = 0.
  • A112355 (program): Triangular numbers that are the sum of three positive triangular numbers.
  • A112367 (program): a(n) = A000217(n-k), where k is the largest triangular number less than n.
  • A112368 (program): a(n) = Sum_ i=0..n 2^i*i!.
  • A112369 (program): -1 + Sum_ i=0..n 2^i*i!.
  • A112370 (program): Sum_ i=0..n 3^i*i!.
  • A112385 (program): a(n) = 6binomial(4n-1,n-1)/(4*n-1).
  • A112387 (program): a(1)=1, a(2)=2, a(n)= 2^(n/2) if even and a(n-1)-a(n-2) if odd.
  • A112414 (program): 3n+7.
  • A112415 (program): a(n) = C(1+n,1) * C(2+n,1) * C(4+n,2).
  • A112416 (program): Next-to-most-significant binary digit of the n-th prime.
  • A112421 (program): Number of 6 element subsets of 1,2,3,…,n for which the sum-set has 12 elements.
  • A112440 (program): Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 9.
  • A112447 (program): a(2n) = A001045(n+2); a(2n+1) = A001045(n+1).
  • A112456 (program): Least triangular number divisible by n-th prime.
  • A112459 (program): Absolute value of coefficient of term [x^(n-3)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 3. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112460 (program): Absolute value of coefficient of term [x^(n-4)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 4. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112461 (program): Absolute value of coefficient of term [x^(n-5)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 5. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112462 (program): Absolute value of coefficient of term [x^(n-6)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 6. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112469 (program): Partial sums of (-1)^n*F(n-1).
  • A112508 (program): Counts the objects described in A047969 and A089246 when grouped by minimum part. (Row sums give A047970).
  • A112524 (program): a(1)=1; a(n) = a(n-1) + 2*n^2.
  • A112526 (program): Characteristic function for powerful numbers.
  • A112532 (program): First differences of [0, A047970].
  • A112539 (program): Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.
  • A112556 (program): Sums of squared terms in rows of triangle A112555.
  • A112557 (program): Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire which make use of (2*n-1)-th hole for n>=1; a bisection of A002491.
  • A112558 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 4 multiples of n-1, n-2, …, 1, for n>=1.
  • A112560 (program): Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 2 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
  • A112561 (program): Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 3 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
  • A112562 (program): Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 4 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
  • A112563 (program): Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 5 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
  • A112566 (program): a(n) = (A112565(n) - 1)/n for n>=1.
  • A112568 (program): Secondary diagonal of square table A112564 of generalized Flavius Josephus sieves.
  • A112591 (program): a(n) = prime(n) XOR prime(n + 1).
  • A112594 (program): Natural function used for generating x^2 and sqrt(x) only using iteration and Q(x) (the characteristic function of sqrt).
  • A112604 (program): Number of representations of n as a sum of three times a square and two times a triangular number.
  • A112605 (program): Number of representations of n as a sum of a square and six times a triangular number.
  • A112606 (program): Number of representations of n as a sum of six times a square and a triangular number.
  • A112607 (program): Number of representations of n as a sum of a triangular number and twelve times a triangular number.
  • A112608 (program): Number of representations of n as a sum of a twice a square and three times a triangular number.
  • A112609 (program): Number of representations of n as a sum of three times a triangular number and four times a triangular number.
  • A112610 (program): Number of representations of n as a sum of two squares and two triangular numbers.
  • A112624 (program): If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = Product_ p n b(p,n)!.
  • A112627 (program): Decimal equivalent of number defined by last k bits of the infinite binary string …0011001100110011 (numbers with leading zeros omitted).
  • A112632 (program): Excess of 3k - 1 primes over 3k + 1 primes, beginning with 2.
  • A112651 (program): Numbers k such that k^2 == k (mod 11).
  • A112652 (program): a(n) squared is congruent to a(n) (mod 12).
  • A112653 (program): a(n) squared is congruent to a(n) (mod 13).
  • A112654 (program): Numbers k such that k^3 == k (mod 11).
  • A112655 (program): a(n) cubed is congruent to a(n) (mod 13).
  • A112658 (program): Dean’s Word: Omega 2,1: the trajectory of 0 -> 01, 1 -> 21, 2 -> 03, 3 -> 23.
  • A112689 (program): A modified Chebyshev transform of the Jacobsthal numbers.
  • A112690 (program): Expansion of 1/(1+x^2-x^3-x^5).
  • A112695 (program): Number of steps needed to reach 4,2,1 in Collatz’ 3*n+1 conjecture.
  • A112696 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 2.
  • A112698 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 4.
  • A112700 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 6.
  • A112702 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 8.
  • A112704 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 10.
  • A112712 (program): Expansion of x/(1 - x + 2x^2 - 2x^3 + 2*x^4 - x^5 + x^6).
  • A112713 (program): Expansion of x/(1 - x + x^5 - x^6).
  • A112714 (program): Numbers of the form k*2^m-1 with k<2^m and k odd.
  • A112742 (program): a(n) = n^2*(n^2-1)/3.
  • A112751 (program): Number of numbers less than or equal to n of the form 3^i*5^j.
  • A112765 (program): Exponent of highest power of 5 dividing n. Or, 5-adic valuation of n.
  • A112772 (program): Semiprimes of the form 6n+2.
  • A112773 (program): 3 together with primes multiplied by 3.
  • A112774 (program): Semiprimes of the form 6n+4.
  • A112821 (program): Numbers n such that lcm(1,2,3,…,n)/19 equals the denominator of the n-th harmonic number H(n).
  • A112831 (program): Number of non-intersecting cycle systems in a particular directed graph.
  • A112832 (program): Number of non-intersecting cycle systems in a particular directed graph.
  • A112849 (program): Number of congruence classes (epimorphisms/vertex partitionings induced by graph endomorphisms) of undirected cycles of even length: C(C_ 2*n ) .
  • A112851 (program): a(n) = (n-1)n(n+1)(n+2)(2*n+1)/40.
  • A112865 (program): a(n) = (-1)^(n + floor(n/4) + floor(n/4^2) + …).
  • A112873 (program): Partial sums of A032378.
  • A112884 (program): Number of bits required to represent binomial(2^n, 2^(n-1)).
  • A112926 (program): Smallest squarefree integer > the n-th prime.
  • A112929 (program): Number of squarefree integers less than the n-th prime.
  • A112930 (program): a(n) = order of n-th term of A112926 among squarefree integers.
  • A112953 (program): a(1) = 0; a(n) = pi(n)^pi(n) for n>1, where pi is the prime counting function (A000720).
  • A112959 (program): a(1) = a(2) = a(3) = a(4) = a(5) = 1; for n>1: a(n+5) = (a(n))^2 + (a(n+1))^2 + (a(n+2))^2 + (a(n+3))^2 + (a(n+4))^2.
  • A112983 (program): 2^(n+1) mod n.
  • A112986 (program): Crossing number of K_ 4,n on the real projective plane.
  • A112988 (program): Position of n-th prime in A089088.
  • A112997 (program): Sum of first n primes minus sum of their indices.
  • A113009 (program): Sum of the digits of n raised to the power number of digits of n .
  • A113010 (program): Number of digits of n raised to the power of the sum of the digits of n .
  • A113011 (program): Decimal expansion of 1/(e^(1/2)-1).
  • A113014 (program): Decimal expansion of value of the continued fraction 1/(2+3/(4+5/(6+7/….
  • A113022 (program): a(n) = size of union of 2^k (mod 10^n), 0 < k <= 5^n.
  • A113023 (program): Number of terms in A095810 which have n digits.
  • A113047 (program): a(n) = C(3n,n)/(2n+1) mod 3.
  • A113048 (program): Binomial(4n,n)/(3n+1) mod 4.
  • A113052 (program): Binomial(5n,n)/(4n+1) mod 5.
  • A113067 (program): Expansion of -x/((x^2+x+1)(x^2+3x+1)); Invert transform gives signed version of Tetrahedral numbers A000292.
  • A113070 (program): Expansion of ((1+x)/(1-2x))^2.
  • A113071 (program): Expansion of ((1+x)/(1-3*x))^2.
  • A113119 (program): Total number of digits in all n-digit nonnegative integers.
  • A113125 (program): A simple tridiagonal matrix.
  • A113127 (program): Expansion of (1 + x + x^2 + x^3)/(1-x)^2.
  • A113184 (program): Absolute difference between sum of odd divisors of n and sum of even divisors of n.
  • A113215 (program): Repeat A006218(n) 2n+1 times.
  • A113217 (program): Parity of decimal digital root of n.
  • A113224 (program): a(2n) = A002315(n), a(2n+1) = A082639(n+1).
  • A113225 (program): a(2n) = A011900(n), a(2n+1) = A001109(n+1).
  • A113240 (program): Expansion of (1/(1-x))*sum(k>=2,x^k/(1-2x^k)).
  • A113241 (program): Sum k=1..n, tau(2k)-1 .
  • A113296 (program): Cumulative product of double factorial A006882.
  • A113300 (program): Sum of even-indexed terms of tribonacci numbers.
  • A113301 (program): Sum of odd-indexed terms of tribonacci numbers.
  • A113311 (program): Expansion of (1+x)^2/(1-x).
  • A113312 (program): Expansion of (1+x)^2/(1-2x^2+x^3).
  • A113335 (program): a(n) = 3^5 * binomial(n+4, 5).
  • A113338 (program): Positive integers of the form (18*m^2+1)/11.
  • A113402 (program): Algebraic degree of cos(Pi/n) for constructible n-gons (A003401).
  • A113405 (program): Expansion of x^3/(1 - 2x + x^3 - 2x^4) = x^3/( (1-2x)(1+x)*(1-x+x^2) ).
  • A113407 (program): Expansion of psi(x) * phi(x^2) in powers of x where psi(), phi() are Ramanujan theta functions.
  • A113415 (program): Expansion of Sum_ k>0 x^k/(1-x^(2k))^2.
  • A113422 (program): a(n) = floor((5*n^2+1)/3).
  • A113424 (program): a(n) = (6n)!/((3n)!(2n)!n!).
  • A113452 (program): a(n) is the n-th smallest permanental minor of any H_m (m >= n), where H_m is the square matrix of order m with 1’s on or below the super diagonal and 0’s elsewhere.
  • A113453 (program): Triangle giving maximal permanent P(n,k) of an n X n lower Hessenberg (0,1)-matrix with exactly k 1’s for 2 <= n <= k <= 2n, read by rows.
  • A113459 (program): Least number that begins an arithmetic progression of n numbers with the same prime signature.
  • A113473 (program): n repeated 2^(n-1) times.
  • A113474 (program): a(n) = a(floor(n/2)) + floor(n/2) with a(1) = 1.
  • A113479 (program): Starting with the fraction 4/1 as the first term, a(n) is the numerator of the reduced fraction of the n-th term according to the rule: if n is even, multiply the previous term by n/(n+1); otherwise multiply the previous term by (n+1)/n.
  • A113497 (program): Ascending descending base exponent transform of sequence A000034(n) = 1 + n mod 2.
  • A113523 (program): a(n) = largest composite nonnegative integer <= n.
  • A113531 (program): a(n) = 1 + 2n + 3n^2 + 4n^3 + 5n^4 + 6*n^5.
  • A113532 (program): a(n) = 1 + 2n + 3n^2 + 4n^3 + 5n^4 + 6n^5 + 7n^6.
  • A113541 (program): Numbers n such that 18n^2+1 is multiple of 19.
  • A113551 (program): a(n) = product of next n even numbers beginning with n if n is even, otherwise product of next n odd numbers beginning with n.
  • A113553 (program): Numbers k such that A113552(k) is odd.
  • A113618 (program): a(n) = 1 + 2n + 3n^2 + 4n^3 + 5n^4 + 6n^5 + 7n^6 + 8*n^7.
  • A113630 (program): 1 + 2n + 3n^2 + 4n^3 + 5n^4 + 6n^5 + 7n^6 + 8n^7 + 9n^8.
  • A113632 (program): 1 + 2n + 3n^2 + 4n^3 + 5n^4 + 6n^5 + 7n^6 + 8n^7 + 9n^8 + 10*n^9.
  • A113636 (program): In the sequence of positive integers add 1 to each nonprime number.
  • A113637 (program): In the sequence of positive integers subtract 1 from each nonprime number.
  • A113638 (program): In the sequence of nonnegative integers subtract 1 from each prime number.
  • A113646 (program): a(n) is the smallest composite integer which is >= n.
  • A113655 (program): Invert blocks of three in the sequence of natural numbers.
  • A113657 (program): Decimal expansion of 1/1089.
  • A113679 (program): Expansion of (1-x-2x^2)/(1-x).
  • A113680 (program): Riordan array ((1-x-2x^2)/(1-x),x).
  • A113684 (program): Expansion of x(1-x^2-x^3)/((1-x)(1-x-x^2))^2.
  • A113704 (program): Triangular indicator function for divisibility, read by rows.
  • A113724 (program): A variant of Golomb’s sequence using even numbers: a(n) is the number of times 2*n+2 occurs, starting with a(1) = 2.
  • A113742 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 5 multiples of n-1, n-2, …, 1, for n>=1.
  • A113743 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 6 multiples of n-1, n-2, …, 1.
  • A113744 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 7 multiples of n-1, n-2, …, 1, for n>=1.
  • A113745 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 8 multiples of n-1, n-2, …, 1, for n>=1.
  • A113746 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 9 multiples of n-1, n-2, …, 1, for n>=1.
  • A113747 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 10 multiples of n-1, n-2, …, 1, for n>=1.
  • A113748 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 11 multiples of n-1, n-2, …, 1, for n>=1.
  • A113753 (program): a(n) = Fibonacci(n-1) + prime(n).
  • A113754 (program): Number of possible squares on an n^2 X n^2 grid.
  • A113763 (program): Non-multiples of 13, or numbers not divisible by 13.
  • A113768 (program): a(1) = 1, a(n+1) = a(n) + floor(a(n)^(1/3)).
  • A113770 (program): Partial sums of A113311(n)^2.
  • A113778 (program): Invert blocks of four in the sequence of natural numbers.
  • A113779 (program): Each term is the sum of the next two digits.
  • A113790 (program): In each block of 5 consecutive natural numbers, swap first and 2nd and swap 4th and 5th.
  • A113801 (program): Numbers that are congruent to 1, 13 mod 14.
  • A113802 (program): Numbers that are congruent to 2, 12 mod 14.
  • A113803 (program): Numbers that are congruent to 3, 11 mod 14.
  • A113804 (program): Numbers that are congruent to 4 or 10 mod 14.
  • A113805 (program): Numbers that are congruent to 5, 9 mod 14.
  • A113806 (program): Numbers that are congruent to 6, 8 mod 14.
  • A113828 (program): a(n) = Sum[2^(A047260(i)-1), i,1,n ].
  • A113835 (program): a(n) = a(n-1) + 2^(A007494(n-1)).
  • A113836 (program): a(n) = Sum[2^(A001651(i-1)-1), i,1,n ].
  • A113841 (program): a(n) = a(n-1) + 2^A047240(n) for n>1, a(1)=1.
  • A113854 (program): a(n) = sum(2^(A047240(i)-1), i=1..n).
  • A113859 (program): Expansion of (7-14x+6x^2)/((1-x)(2x^2-4*x+1)); related to the binomial transform of Pell numbers A000129 (see formula and comment for A007070).
  • A113861 (program): a(n) = (1/9)((6n - 7)*2^(n-1) - (-1)^n).
  • A113867 (program): a(n) = a(n-1) + 2^(A047258(n)) for n>1, a(1)=1.
  • A113870 (program): a(n) = a(n-1) + 2^(k(n)), where k(n) is the n-th term of the sequence formed by k(1)=0 together with the numbers A042963.
  • A113876 (program): a(n) = a(n-1) + 2^(k(n)), where k(n) is the n-th term of the sequence formed by k(1)=0 together with the numbers A042964.
  • A113894 (program): a(n) = binomial(2n, n) * binomial(5+2n, n).
  • A113901 (program): Product of omega(n) and bigomega(n) = A001221(n)*A001222(n), where omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.
  • A113909 (program): Square table of odd numbers which are neither squares nor one less than squares, read by antidiagonals.
  • A113923 (program): A Farey like level n=2 rational function as a coefficient expansion.
  • A113935 (program): a(n) = prime(n) + 3.
  • A113954 (program): Expansion of (1-2x^2)/((1-2x)(1+x)^2).
  • A113957 (program): Sum of the divisors of n which are not divisible by 7.
  • A113968 (program): Series expansion of Farey rational polynomial based on A112627.
  • A113975 (program): Devil’s Farey: coefficient expansion of a quadratic over quadratic that has 123 roots and a Farey p[1/2]=1 ( correction).
  • A113978 (program): a(n)=Sum(d n)(10^(n-d)).
  • A113979 (program): Number of compositions of n with an even number of 1’s.
  • A113980 (program): Number of compositions of n with an odd number of 1’s.
  • A113998 (program): Reverse of triangle A051731.
  • A113999 (program): a(n) = Sum_ k, k n 10^(k-1).
  • A114003 (program): Rows sums of triangle A114002.
  • A114040 (program): a(0) = 1, a(1) = 9, a(n) = 6*a(n-1) - a(n-2) - 4.
  • A114047 (program): x such that x^2 - 13*y^2 = 1.
  • A114049 (program): x such that x^2 - 21*y^2 = 1.
  • A114052 (program): x such that x^2 - 27*y^2 = 1.
  • A114054 (program): Decimal expansion of 998998998998998998998998998/9.
  • A114104 (program): a(n) = A114103(n)/n.
  • A114112 (program): a(1)=1, a(2)=2; thereafter a(n) = n+1 if n odd, n-1 if n even.
  • A114113 (program): a(n) = sum k=1 to n (A114112(k)). (For n>=2, a(n) = sum k=1 to n (A014681(k)) =sum k=1 to n (A103889(k)).).
  • A114114 (program): An invertible partition matrix.
  • A114119 (program): Row sums of triangle A114118.
  • A114121 (program): Expansion of (sqrt(1 - 4x) + (1 - 2x))/(2(1 - 4x)).
  • A114143 (program): The possible sums of the final scores of completed American football games where both teams score.
  • A114182 (program): F(4n) - 2n - 1 where F(n) = Fibonacci numbers. Also, the floor of the log base phi of sequence A090162 (phi = (1+Sqrt(5))/2).
  • A114185 (program): a(n) = Fibonacci(2*n) - n - 1.
  • A114186 (program): Running sums of consecutive integers with all primes set to 2.
  • A114209 (program): Number of permutations of [n] having exactly two fixed points and avoiding the patterns 123 and 231.
  • A114211 (program): a(n) = (5n^3+12n^2+n+6)/6.
  • A114219 (program): Number triangle (k-(k-1)0^(n-k))[k<=n].
  • A114220 (program): a(n) = Sum_ k=0..floor(n/2) k-(k-1)*0^(n-2k).
  • A114239 (program): a(n) = (n+1)(n+2)^3*(n+3)(n^2 + 4n + 5)/120.
  • A114242 (program): a(n) = (n+1)(n+2)^2(n+3)^2(n+4)(2n+5)/720.
  • A114243 (program): a(n) = (n+1)(n+2)^2*(n+3)(n+4)(3n+5)/240.
  • A114244 (program): a(n) = (n+1)(n+2)^2*(n+3)(7n^2 + 28n + 30)/360.
  • A114253 (program): a(n) = C(5+2n,5+n)C(10+2*n,0+n).
  • A114254 (program): Sum of all terms on the two principal diagonals of a 2n+1 X 2n+1 square spiral.
  • A114283 (program): Sequence array for binomial transform of Jacobsthal numbers A001045(n+1).
  • A114284 (program): Riordan array ((1-3*x)/(1-x), x).
  • A114285 (program): Expansion of (1-3x)/((1-x)(1-x^2)).
  • A114307 (program): Length of the cycle for Lucas numbers mod 10^n.
  • A114311 (program): a(n) = n! - n(n-1)/2.
  • A114327 (program): Table T(n,m) = n - m read by upwards antidiagonals.
  • A114347 (program): Cumulative sum of triple factorial numbers a(n) = n!!! (A007661).
  • A114364 (program): a(n) = n*(n+1)^2.
  • A114389 (program): Bisection of A065621.
  • A114390 (program): A065621(n^2).
  • A114434 (program): To obtain a(n), write the n-th composite number as a product of primes, add 1 to each prime and multiply.
  • A114444 (program): a(n) = 16n(n+2).
  • A114458 (program): Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2).
  • A114459 (program): Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2)+sqrt(n+3).
  • A114479 (program): Kekulé numbers for certain benzenoids.
  • A114480 (program): Kekulé numbers for certain benzenoids.
  • A114514 (program): The digits on a numerical pad from upper left to lower right.
  • A114562 (program): The first occurrence of n in A111701.
  • A114569 (program): a(n) = 9*4^n - 1.
  • A114570 (program): Let the decimal expansion of n be d_1 d_2 … d_k; then a(n) = Sum_ i=1..k d_i^(k+1-i).
  • A114574 (program): a(n) = p*p! where p = prime(n).
  • A114607 (program): Start with 1 0 1 0 then add a one every time (e.g. 1 1 0 1 1 1 0 1 1 1 1 0 …).
  • A114619 (program): 2*A079291 (twice squares of Pell numbers).
  • A114620 (program): 2*A084158 (twice Pell triangles).
  • A114633 (program): a(n) = (n+1)(n+2)/2 * Sum_ k=0..floor(n/2) n!/(n-2k)!.
  • A114637 (program): Nonnegative numbers excluding 1 and 2.
  • A114646 (program): Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-4).
  • A114647 (program): Expansion of (3 -4x -3x^2)/((1-x^2)(1-2x-x^2)); a Pellian-related sequence.
  • A114696 (program): Expansion of (1+4x+x^2)/((1-x^2)(1-2*x-x^2)); a Pellian-related sequence.
  • A114697 (program): Expansion of (1+x+x^2)/((1-x^2)(1-2x-x^2)); a Pellian-related sequence.
  • A114698 (program): Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-3).
  • A114743 (program): a(1) =4, a(2) = 6, a(n+1) = least composite number of the form k*(a(n-1)) - a(n), not included earlier.
  • A114752 (program): a(2n)=2n, a(2n+1)=4n+1.
  • A114753 (program): First column of A114751.
  • A114761 (program): a(n) = (floor(sqrt(2)*10^n))^2.
  • A114766 (program): a(n) = floor(sqrt(8)*10^n)^2.
  • A114778 (program): Cumulative product of triple factorial A007661.
  • A114779 (program): Cumulative product of quadruple factorial A007662.
  • A114790 (program): Cumulative product of quintuple factorial A085157.
  • A114796 (program): Cumulative product of sextuple factorial A085158.
  • A114799 (program): Septuple factorial, 7-factorial, n!7, n!!!!!!!, a(n) = n*a(n-7) if n > 1, else 1.
  • A114800 (program): Octuple factorial, 8-factorial, n!8, n!!!!!!!!.
  • A114805 (program): Cumulative sum of quintuple factorial numbers n!!!!! (A085157).
  • A114806 (program): Nonuple factorial, 9-factorial, n!9, n!!!!!!!!!.
  • A114853 (program): a(n) = floor(n^n/n!!).
  • A114870 (program): a(n) = A002627(n+1) - A002627(n) - n!.
  • A114889 (program): a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n)+a(i) is not a power of 3, for i=1,…, n-1.
  • A114890 (program): First differences of A114889.
  • A114891 (program): Numbers that are the smallest element of a k-cycle (k > 1) of permutation A114861.
  • A114948 (program): a(n) = n^2 + 10.
  • A114949 (program): a(n) = n^2 + 6.
  • A114955 (program): A 2/3-power Fibonacci sequence.
  • A114958 (program): a(n) = 62^(n+1) - 5(n+1) - 4.
  • A114960 (program): Expansion of (-1+3x-5x^2+4x^3) / ((1-2x)(2x^2-1)*(x-1)^2).
  • A114962 (program): a(n) = n^2 + 14.
  • A114963 (program): a(n) = n^2 + 22.
  • A114964 (program): a(n) = n^2 + 30.
  • A114965 (program): n^2 + 34.
  • A114982 (program): Expansion of x(3-x^2)/(1-3x).
  • A114984 (program): Coefficients of cubic equations in the form w^2=4x^3-g2x-g3 Weierstrass elliptic form whose solutions approximate zeta zeros.
  • A114986 (program): Characteristic function of (A000201 prefixed with 0).
  • A115006 (program): Row 2 of array in A114999.
  • A115007 (program): Row 3 of array in A114999.
  • A115012 (program): Sum_ i=1..n, gcd(5,i)=1 i.
  • A115014 (program): Sum_ i=1..n, gcd(6,i)=1 i.
  • A115015 (program): Sum_ i=1..n (gcd(7,i)=1) i.
  • A115020 (program): Count backwards from 100 in steps of 7.
  • A115025 (program): a(n) = n-th element of n-th row of triangle shown below.
  • A115030 (program): Number of distinct sums of subsets of the first n prime numbers.
  • A115032 (program): Expansion of (5-14x+x^2)/((1-x)(x^2-18*x+1)).
  • A115036 (program): Even terms of A116883.
  • A115056 (program): a(n) = n(n^2-1)(3*n+2).
  • A115061 (program): a(n) is the number of occurrences of the n-th prime number in A051697.
  • A115065 (program): Number of points with integer coordinates inside the equilateral triangle with base [0,n].
  • A115067 (program): a(n) = (3*n^2 - n - 2)/2.
  • A115098 (program): a(0)=2, a(n)=3*a(n-1)-3.
  • A115099 (program): a(0)=4, a(n) = 3*a(n-1) - 4.
  • A115102 (program): a(0)=2, a(1)=8, a(n)=a(n-1)+2*a(n-2).
  • A115112 (program): Number of different ways to select n elements from two sets of n elements under the precondition of choosing at least one element from each set.
  • A115113 (program): a(n) = 3a(n-1) + 4a(n-2), with a(0) = 2, a(1) = 6.
  • A115125 (program): A sequence related to Catalan numbers A000108.
  • A115129 (program): Partial sums of A005587. Fourth column of triangle A115127.
  • A115130 (program): Partial sums of A005557.
  • A115132 (program): Partial sums of A064059.
  • A115133 (program): Partial sums of A064061.
  • A115140 (program): O.g.f. inverse of Catalan A000108 o.g.f.
  • A115141 (program): Convolution of A115140 with itself.
  • A115180 (program): Beatty sequence for (Champernowne constant)*10 = 1.234567891011121314….
  • A115181 (program): Beatty sequence for (Cc/(Cc-1)) with Cc = 1.234567891011121314… = 10*(Champernowne constant).
  • A115205 (program): a(n) = binomial(n, 9) + 1.
  • A115217 (program): Diagonal sums of “correlation triangle” for 2^n.
  • A115218 (program): Triangle read by rows: zeroth row is 0; to get row n >= 1, append next 2^n numbers to end of previous row.
  • A115243 (program): G.f.: (4x^2 + 2x)/(4x^3 - x^2 - 4x + 1).
  • A115257 (program): Partial sums of binomial(2n,n)^2.
  • A115264 (program): Diagonal sums of correlation triangle for floor((n+2)/2).
  • A115266 (program): Row sums of correlation triangle for floor((n+3)/3).
  • A115269 (program): Row sums of correlation triangle for floor((n+4)/4).
  • A115271 (program): Partial sums of floor((n+4)/4)^2.
  • A115273 (program): Floor(n/3)*(n mod 3).
  • A115274 (program): a(n) = n + A115273(n), where A115273(n) = 0 for n = 1..3.
  • A115283 (program): Diagonal sums of correlation triangle for 3-2*0^n.
  • A115285 (program): Diagonal sums of correlation triangle for 1,3,4,4,4,…(A113311).
  • A115286 (program): a(n) = (1/6)(n^6+3n^4+12n^3+8n^2).
  • A115291 (program): Expansion of (1+x)^3/(1-x).
  • A115293 (program): Row sums of correlation triangle for (1+x)^3/(1-x).
  • A115295 (program): Partial sums of squares of A115291(n).
  • A115299 (program): Greatest digit of n + least digit of n. Different from A088133.
  • A115302 (program): Permutation of natural numbers generated by 3-rowed array shown below.
  • A115326 (program): E.g.f.: exp(x/(1-2x))/sqrt(1-4x^2).
  • A115327 (program): E.g.f.: exp(x + 3/2*x^2).
  • A115328 (program): E.g.f: exp(x/(1-3x))/sqrt(1-9x^2).
  • A115329 (program): E.g.f.: exp(x + 2*x^2).
  • A115330 (program): E.g.f: exp(x/(1-4x))/sqrt(1-16x^2).
  • A115331 (program): E.g.f.: exp(x+5/2*x^2).
  • A115332 (program): E.g.f: exp(x/(1-5x))/sqrt(1-25x^2).
  • A115335 (program): a(0) = 3, a(1) = 5, a(2) = 1, and a(n) = (2^(1 + n) - 11*(-1)^n)/3 for n > 2.
  • A115338 (program): a(n)=F([sqrt(n)]), where [k]=integer part of k and F(n) is the Fibonacci sequence.
  • A115339 (program): a(2n-1)=F(n+1), a(2n)=L(n), where F(n) and L(n) are the Fibonacci and the Lucas sequences.
  • A115341 (program): a(n) = abs(A154879(n+1)).
  • A115342 (program): 1 + (n-6)*2^(n-1).
  • A115346 (program): Triangle read by rows: T(n,k) = Fibonacci(k+2) - 1.
  • A115356 (program): Matrix (1,x)+(x,x^2) in Riordan array notation.
  • A115357 (program): Period 6: repeat [1,1,1,0,2,0].
  • A115360 (program): Period 6: repeat [1,-1,1,0,0,0].
  • A115362 (program): Row sums of ((1,x) + (x,x^2))^(-1)*((1,x)-(x,x^2))^(-1) (using Riordan array notation).
  • A115364 (program): a(n) = A000217(A001511(n)), where A001511 is one more than the 2-adic valuation of n, and A000217(n) is the n-th triangular number, binomial(n+1, 2).
  • A115378 (program): a(n) = number of positive integers k < n such that n XOR k = (n+k).
  • A115384 (program): Partial sums of Thue-Morse numbers A010060.
  • A115390 (program): Binomial transform of tribonacci sequence A000073.
  • A115419 (program): Numbers having a 1 in position 3 of their binary expansion.
  • A115420 (program): Numbers having a 1 in position 4 of their binary expansion.
  • A115451 (program): Expansion of 1/((1+x)(1-2x)*(1+x^2)).
  • A115454 (program): Composite positive integers written in base 2.
  • A115489 (program): Number of monic irreducible polynomials of degree 3 in GF(2^n)[x].
  • A115490 (program): Number of monic irreducible polynomials of degree 4 in GF(2^n)[x].
  • A115500 (program): Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4].
  • A115504 (program): Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4,x5].
  • A115512 (program): Number triangle (1,x)+(x,x^3) expressed in terms of Riordan arrays.
  • A115514 (program): Triangle read by rows: row n >= 1 lists first n positive members of A004526 (integers repeated) in decreasing order.
  • A115516 (program): The mode of the bits of n (using 0 if bimodal).
  • A115517 (program): The mode of the bits of n (using 1 if bimodal).
  • A115519 (program): n(1+3n+6*n^2)/2.
  • A115535 (program): Numbers k such that the concatenation of k with 4*k gives a square.
  • A115536 (program): Numbers k such that the square of k is the concatenation of two numbers m and 4*m.
  • A115561 (program): a(n) = lpf((n/lpf(n))/lpf(n/lpf(n))), where lpf=A020639, least prime factor.
  • A115562 (program): a(n) = number of distinct squarefree ternary (cyclic) sequences uniquely containing every possible length-n substring.
  • A115565 (program): a(n) = 5n^4 - 10n^3 + 20n^2 - 15n + 11.
  • A115567 (program): a(n) = C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
  • A115598 (program): Consider all Pythagorean triples (X,X+1,Z) ordered by increasing Z; sequence gives Z-(X+1) values.
  • A115599 (program): Consider all Pythagorean triples (X,X+1,Z) ordered by increasing Z; sequence gives Z-X values.
  • A115605 (program): Expansion of -x^2(2 + x - 2x^2 - x^3 + 2x^4) / ( (x-1)(1+x)(1 + x + x^2)(x^2 - x + 1)(x^2 + 4x - 1)*(x^2 - x - 1) ).
  • A115618 (program): 1 + (n+6)*2^(n-1).
  • A115634 (program): Expansion of (1-4x^2)/(1-x^2).
  • A115639 (program): First column of divide-and-conquer triangle A115636.
  • A115659 (program): Permutation of natural numbers generated by 2-rowed array shown below.
  • A115716 (program): A divide-and-conquer sequence.
  • A115730 (program): a(n) = a(n-3)+A001654(n-1) with a(0)=0, a(1)=0 and a(2)=1.
  • A115754 (program): Decimal expansion of sqrt(3/2).
  • A115789 (program): a(n) = (floor((n+1)Pi) - floor(nPi)) mod 2.
  • A115790 (program): 1 - (Floor((n+1)Pi)-Floor(nPi)) mod 2.
  • A115792 (program): A dihedial D1 elliptical transform on A000073.
  • A115836 (program): Self-describing sequence. The n-th integer of the sequence indicates how many integers of the sequence are strictly < 2n.
  • A115851 (program): G.f. x^2(-1+x+x^2)/((1-x)(2x-1)(x+1)*(x^2+1)).
  • A115852 (program): Dihedral D3 elliptical invariant transform on A000045: a[n+1]/a[n]= Phi^4=((1+Sqrt[5])/2)^4.
  • A115878 (program): a(n) is the number of positive solutions of the Diophantine equation x^2 = y(y+n).
  • A115880 (program): Largest positive x satisfying the Diophantine equation x^2 = y*(y+n), a(n)=0 if there are no solutions.
  • A115881 (program): a(n) is the largest positive y satisfying the Diophantine equation x^2=y(y+n). a(n)=0 if there are no solutions.
  • A115902 (program): Expansion of (1-8*x)^(-3/2).
  • A115903 (program): Expansion of (1-12*x)^(-3/2).
  • A115953 (program): Periodic 1,-1,0,0,1,-2,1,0,0,-1,1,-1 .
  • A115955 (program): Product of A115952 and summing matrix (1/(1-x),x).
  • A115960 (program): Numbers n having exactly 6 distinct prime factors, the largest of which is greater than or equal to sqrt(n) (i.e., sqrt(n)-rough numbers with exactly 6 distinct prime factors).
  • A115964 (program): Denominator of sum_ i=1..n 1/prime(i)^3.
  • A115971 (program): a(0) = 0. If a(n) = 0, then a(2^n) through a(2^(n+1)-1) are each equal to 1. If a(n) = 1, then a(m + 2^n) = a(m) for each m, 0 <= m <= 2^n -1.
  • A116073 (program): Sum of the divisors of n that are not divisible by 5.
  • A116081 (program): Final nonzero digit of n^n.
  • A116082 (program): a(n) = C(n,7) + C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
  • A116127 (program): Number of numbers that are congruent to 2, 4 mod 6 between prime(n) and prime(n+1) inclusive.
  • A116138 (program): a(n) = 3^n * n*(n + 1).
  • A116144 (program): a(n) = 4^n * n*(n+1).
  • A116149 (program): a(n) = sum of n consecutive cubes after n^3.
  • A116150 (program): a(n) = Sum_ j=1..n (3^j + (-2)^j).
  • A116156 (program): a(n) = 5^n * n*(n + 1).
  • A116164 (program): a(n) = 6^n * n*(n+1).
  • A116165 (program): a(n) = 7^n * n*(n+1).
  • A116166 (program): a(n) = 8^n * n*(n+1).
  • A116176 (program): a(n) = 9^n * n*(n+1).
  • A116178 (program): Stewart’s choral sequence: a(3n) = 0, a(3n-1) = 1, a(3n+1) = a(n).
  • A116367 (program): Sums of rows of the triangle in A116366.
  • A116386 (program): Number of calendar weeks in the year n (starting at n=0 for the year 2000).
  • A116400 (program): E.g.f. Bessel_I(2,2x)+Bessel_I(3,2x)+Bessel_I(4,2x).
  • A116404 (program): Expansion of (1-x)/((1-x)^2 - x^2(1+x)^2).
  • A116415 (program): a(n) = 5a(n-1) - 3a(n-2).
  • A116453 (program): Third smallest number with exactly n prime factors.
  • A116454 (program): Smallest m such that A116452(m) = n.
  • A116468 (program): Permutation of natural numbers generated by 2-rowed array shown below.
  • A116470 (program): All distinct Fibonacci and Lucas numbers.
  • A116471 (program): Values 2*(n -+ 1)^2 sorted.
  • A116483 (program): Expansion of (1 + x) / (5x^2 - 2x + 1).
  • A116508 (program): a(n) = C( C(n,2), n) for n >= 1.
  • A116520 (program): a(0) = 0, a(1) = 1; a(n) = max 4*a(k) + a(n-k) 1 <= k <= n/2 , for n > 1.
  • A116522 (program): a(0)=1, a(1)=1, a(n)=7a(n/2) for n=2,4,6,…, a(n)=6a((n-1)/2)+a((n+1)/2) for n=3,5,7,….
  • A116523 (program): a(0)=1, a(1)=1, a(n) = 17a(n/2) for n=2,4,6,…, a(n) = 16a((n-1)/2) + a((n+1)/2) for n=3,5,7,….
  • A116524 (program): a(0)=1, a(1)=1, a(n) = 13a(n/2) for n=2,4,6,…, a(n) = 12a((n-1)/2) + a((n+1)/2) for n=3,5,7,….
  • A116525 (program): a(0)=1, a(1)=1, a(n) = 11a(n/2) for even n, and a(n) = 10a((n-1)/2) + a((n+1)/2) for odd n >= 3.
  • A116526 (program): a(0)=1, a(1)=1, a(n) = 9a(n/2) for even n >= 2, and a(n) = 8a((n-1)/2) + a((n+1)/2) for odd n >= 3.
  • A116530 (program): a(n) = 3*a(n-1), with a(1) = 20.
  • A116551 (program): Permutation of natural numbers generated by 3-rowed array shown below.
  • A116556 (program): a(n) = 2a(n-1) + 2a(n-2), a(0)=0, a(1)=4.
  • A116568 (program): Difference between n and the absolute value of the difference between number of nonprimes not exceeding n and number of primes not exceeding n.
  • A116572 (program): a(n) = floor(prime(n)/5) for n > 2, a(1) = a(2) = 1.
  • A116579 (program): a(1) = a(2) = 1; a(n) = floor(prime(n)/6) for n > 2.
  • A116588 (program): Array read by antidiagonals: T(n,k) = max(2^(n - k), 2^(k - n)).
  • A116609 (program): a(n) = 13^n modulo n.
  • A116668 (program): a(n) = (5*n^2 + n + 2)/2.
  • A116689 (program): Partial sums of dodecahedral numbers (A006566).
  • A116699 (program): Number of permutations of length n which avoid the patterns 123 and 4312.
  • A116701 (program): Number of permutations of length n that avoid the patterns 132, 4321.
  • A116702 (program): Number of permutations of length n which avoid the patterns 123, 3241.
  • A116711 (program): Number of permutations of length n which avoid the patterns 123, 3214, 4312.
  • A116713 (program): Number of permutations of length n which avoid the patterns 123, 2431, 4132.
  • A116717 (program): Number of permutations of length n which avoid the patterns 231, 1423, 3214.
  • A116720 (program): Number of permutations of length n which avoid the patterns 213, 1234, 4312.
  • A116721 (program): Number of permutations of length n which avoid the patterns 123, 3142, 4312; or avoid the patterns 123, 3421, 4231.
  • A116722 (program): Number of permutations of length n which avoid the patterns 312, 1324, 3421; or avoid the patterns 312, 1324, 2341, etc.
  • A116723 (program): We have one bead labeled i for every i=1, 2, …; a(n) = number of necklaces that can be made using any subset of the first n beads.
  • A116725 (program): Number of permutations of length n which avoid the patterns 132, 3421, 4231.
  • A116727 (program): Number of permutations of length n which avoid the patterns 321, 2134, 3412.
  • A116728 (program): Number of permutations of length n which avoid the patterns 321, 1243, 2134.
  • A116730 (program): Number of permutations of length n which avoid the patterns 321, 1342, 1423.
  • A116731 (program): Number of permutations of length n which avoid the patterns 321, 2143, 3124; or avoid the patterns 132, 2314, 4312, etc.
  • A116733 (program): Number of permutations of length n which avoid the patterns 321, 1324, 2341.
  • A116734 (program): Number of permutations of length n which avoid the patterns 231, 1432, 4123.
  • A116735 (program): Number of permutations of length n which avoid the patterns 231, 1234, 4312; or avoid the patterns 312, 1234, 1432, etc.
  • A116738 (program): Number of permutations of length n which avoid the patterns 3214, 4123, 4132.
  • A116757 (program): Number of permutations of length n which avoid the patterns 1324, 2314, 4312.
  • A116774 (program): Number of permutations of length n which avoid the patterns 2143, 2341, 4312; or avoid the patterns 1234, 1432, 3412.
  • A116796 (program): Number of permutations of length n which avoid the patterns 2314, 3241, 4132.
  • A116845 (program): Number of permutations of length n which avoid the patterns 231, 12534.
  • A116882 (program): A number n is included if (highest odd divisor of n)^2 <= n.
  • A116913 (program): Inverse Moebius transform of pentagonal numbers.
  • A116921 (program): a(n) = largest integer <= n/2 which is coprime to n.
  • A116922 (program): a(n) = smallest integer >= n/2 which is coprime to n.
  • A116939 (program): Lexicographically earliest sequence such that each i occurs exactly i+1 times and succeeding terms differ exactly by -1 or +1.
  • A116940 (program): Greatest m such that A116939(m) = n.
  • A116941 (program): Permutation of the natural numbers in conjunction with A116939 and A003056.
  • A116948 (program): Riordan array ((1+2x^2)/(1-x^3),x).
  • A116952 (program): a(n) = 3*a(n-1) + 5 with a(0) = 1.
  • A116955 (program): a(n+1) = a(n) + (if a(n) is odd then (next odd square) else (next even square)), a(0) = 1.
  • A116966 (program): a(n) = n + 1,2,0,1 according as n == 0,1,2,3 mod 4.
  • A116969 (program): If n mod 2 = 0 then 32^(n-1)+n-1 else 32^(n-1)+n.
  • A116970 (program): a(n) = (3^n - 7)/2.
  • A116971 (program): a(n) = (352^((2(3n+2) + 2)/3) - 2(3*n+2) - 46)/9.
  • A116972 (program): a(n) = 113^n - 2n - 10.
  • A116973 (program): If n mod 2 = 0 then (3^(n+3)-19)/8 else (3^(n+3)-1)/8.
  • A116974 (program): Numbers n for which the sum of the proper divisors equals the product of the proper divisors.
  • A116995 (program): Pentagonal numbers with prime indices.
  • A116996 (program): Partial sums of A116966.
  • A117004 (program): a(n) = sigma(n) - A079667(n).
  • A117054 (program): Number of ordered ways of writing n = i + j, where i is a prime and j is of the form k*(k+1), k > 0.
  • A117066 (program): Partial sums of cupolar numbers (1/3)(n+1)(5n^2+7n+3) (A096000).
  • A117080 (program): a(n) = 2a(n-1)+a(n-3)+1 with a(1)=1, a(2)=3, a(3)=8.
  • A117081 (program): a(n) = 36n^2 - 810n + 2753, producing the conjectured record number of 45 primes in a contiguous range of n for quadratic polynomials, i.e., abs(a(n)) is prime for 0 <= n < 44.
  • A117088 (program): a(n) = (11*5^n - 7)/4.
  • A117110 (program): The (1,1)-entry of the vector v[n]=Mv[n-1], where M is the 3 x 3 matrix [[0,-1/r,r],[ -1/r,-2/r,1],[r,1,2+2/r]], r being the golden ratio and v[0] is the column matrix [0,1,1].
  • A117123 (program): n minus the number of 0’s in binary expansion of n.
  • A117142 (program): Number of partitions of n in which any two parts differ by at most 2.
  • A117143 (program): Number of partitions of n in which any two parts differ by at most 3.
  • A117152 (program): Sum of product of Fibonacci and triangular numbers.
  • A117187 (program): Expansion of (1+x)c(x^2)/((1-x^2*c(x^2))sqrt(1-4x^2)), c(x) the g.f. of A000108.
  • A117188 (program): Expansion of (1-x^2)/(1+x^2+x^4).
  • A117189 (program): Binomial transform of the tribonacci sequence A000073 (shifted left twice).
  • A117197 (program): a(n) = (n^3 - 1)^3.
  • A117199 (program): Expansion of 1/(1-x^2) + x/(1-x^3) + x^2/(1-x^4).
  • A117202 (program): Binomial transform of n*F(n).
  • A117216 (program): Number of points in the standard root system version of the D_4 lattice having L_infinity norm n.
  • A117230 (program): Start with 1 and repeatedly reverse the digits and add 1 to get the next term.
  • A117248 (program): Number of down steps at start of segment n of A079051.
  • A117261 (program): Row sums of triangle A117260.
  • A117263 (program): Row sums of triangle A117262; also, self-convolution of A117264.
  • A117292 (program): a(n) = (n-phi(n))^phi(n).
  • A117295 (program): a(n) = phi(n)*(n-phi(n))
  • A117302 (program): Number of cases in which the first player gets killed in a Russian roulette game when 7 players use a gun with n chambers and the number of the bullets can be from 1 to n. In the game they do not rotate the cylinder after the game starts.
  • A117304 (program): Numbers with an even number of digits such that the second half is twice the first half.
  • A117364 (program): a(n) = largest prime less than the largest prime dividing n (or 1 if there is no such prime).
  • A117365 (program): a(n) = largest prime less than the smallest prime dividing n (or 1 if there is no such prime).
  • A117366 (program): a(n) = smallest prime greater than the largest prime dividing n.
  • A117367 (program): a(n) = smallest prime greater than the smallest prime dividing n.
  • A117368 (program): a(n) = largest prime less than the smallest prime dividing (2n-1).
  • A117373 (program): Expansion of (1 - 3x)/(1 - x + x^2).
  • A117378 (program): Expansion of (1-4*x)/(1-x+x^2).
  • A117397 (program): Column 3 of triangle A117396.
  • A117399 (program): Column 1 (divided by 2) of triangle A117398, which is the matrix log of A117396.
  • A117401 (program): Triangle T(n,k) = 2^(k*(n-k)), read by rows.
  • A117403 (program): a(n) = Sum_ k=0..floor(n/2) 2^((n-2k)k) for n>=0.
  • A117412 (program): Sum of the interior angles of an n-sided polygon, in gradians.
  • A117441 (program): Periodic with repeating part 1,1,0,1,-1,0,-1,-1,0,-1,1,0 .
  • A117444 (program): Period 5: Repeat [0, 1, 2, -2, -1].
  • A117447 (program): Expansion of (1 + 2x + 3x^2 + x^3)/(1 + x - x^3 - x^4).
  • A117450 (program): Expansion of (1-x+x^2+x^5)/((1-x)^2*(1-x^5)).
  • A117451 (program): Expansion of (1-x+x^2+x^5)/((1-x)*(1-x^5)).
  • A117452 (program): Periodic 2, -1, 1, 0, 0 - 0^n.
  • A117485 (program): Expansion of x^9/((1-x)(1-x^2)(1-x^3))^2.
  • A117495 (program): Product of a prime number p and the number of primes smaller than p.
  • A117502 (program): Triangle, row sums = A001595.
  • A117520 (program): Triangular numbers for which the digital root is also a triangular number.
  • A117521 (program): Start with 1 and repeatedly reverse the digits and add 2 to get the next term.
  • A117560 (program): a(n) = n*(n^2 - 1)/2 - 1.
  • A117561 (program): Floor(n(n^3-n-3)/(2(n-1))).
  • A117567 (program): Riordan array ((1+x^2)/(1-x^3),x).
  • A117569 (program): Expansion of (1+x+x^2)/(1+x^2).
  • A117571 (program): Expansion of (1+2x^2)/((1-x)(1-x^3)).
  • A117572 (program): Expansion of (1+2x^2)/((1-x^2)(1-x^3)).
  • A117573 (program): Expansion of (1+2x^2)/((1-x)(1-x^2)(1-x^3)).
  • A117575 (program): Expansion of (1-x^3)/((1-x)(1+2x^2)).
  • A117585 (program): a(n) = 2*a(n-1) + a(n-2) + n.
  • A117589 (program): See Comments line.
  • A117590 (program): a(n) = ceiling(x(n)), where x(n) = 3*x(n-1)/2 and x(1) = 1.
  • A117591 (program): a(n) = 2^n + Fibonacci(n).
  • A117592 (program): a(n) = a(3n) = a(3n+1) = a(3n+2)/2 with a(0)=1.
  • A117614 (program): a(0)=1, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.
  • A117615 (program): a(0)=0, a(1)=1, a(n)=4a(n-1)+2 for n =3,5,7,…, a(n)=4a(n-1) for n =2,4,6,….
  • A117616 (program): a(0)=0, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.
  • A117617 (program): a(n) = 5*a(n-1) + 3 with a(0) = 1.
  • A117619 (program): a(n) = n^2 + 7.
  • A117625 (program): Maximum number of regions defined by n zigzag-lines in the plane when a zigzag-line is defined as consisting of two parallel infinite half-lines joined by a straight line segment.
  • A117642 (program): a(n) = 3*n^3.
  • A117643 (program): a(n) = n*(a(n-1)-1) starting with a(0)=3.
  • A117644 (program): Number of distinct pairs a < b with nonzero decimal digits such that a + b = 10^n.
  • A117647 (program): a(2n) = A014445(n), a(2n+1) = A015448(n+1).
  • A117662 (program): n(n-1)(n-2)*(n+3)/12.
  • A117665 (program): n times the n-th n-gonal number.
  • A117667 (program): a(n) = n^n-n^(n-1)-n^(n-2)-n^(n-3)-…-n^3-n^2-n.
  • A117671 (program): a(n) = binomial(3*n+1, n+1).
  • A117673 (program): a(n) is the least k such that k2prime(n) + 1 is prime.
  • A117676 (program): Squares for which the digital root is also a square.
  • A117677 (program): a(n) = number of divisors of n^2 (excluding 1 and n^2).
  • A117691 (program): Expansion of -(x^7+x^6+x^5-2x^3-3x^2-3x-4) / ((x-1)^2(x+1)^2*(x^2+1)^2).
  • A117694 (program): (n^n + n)/2.
  • A117717 (program): Maximal number of regions obtained by a straight line drawing of the complete bipartite graph K_ n,n .
  • A117722 (program): A000045(A003622(n)).
  • A117727 (program): Partial sums of A051109.
  • A117748 (program): Triangular numbers divisible by 3.
  • A117762 (program): a(1)=6; for n>1, a(n) = prime(n)*(prime(n)^2-1)/2.
  • A117767 (program): a(n) is the differences between the smallest square greater than prime(n) and the largest square less than prime(n), where prime(n) = A000040(n) is the n-th prime number.
  • A117793 (program): Pentagonal numbers divisible by 5.
  • A117794 (program): Hexagonal numbers divisible by 6.
  • A117797 (program): Decagonal numbers divisible by 10.
  • A117800 (program): Start with 1 and repeatedly reverse the digits and add 5 to get the next term.
  • A117802 (program): Numbers with an “a” in Dutch.
  • A117804 (program): Natural position of n in the string 12345678910111213….
  • A117812 (program): a(n) = n^(2*n) - 1.
  • A117818 (program): a(n) = n if n is 1 or a prime, otherwise a(n) = n divided by the least prime factor of n (A032742(n)).
  • A117828 (program): Start with 1 and repeatedly reverse the decimal digits and add 4 to get the next term.
  • A117829 (program): Start with 3 and repeatedly reverse the digits and add 4 to get the next term.
  • A117830 (program): Let S_m be the infinite sequence formed by starting with m and repeatedly reversing the digits and adding 4 to get the next term. For all m < 1015, S_m enters the cycle of length 54 whose terms are shown here.
  • A117841 (program): Start with 1 and repeatedly reverse the digits and add 10 to get the next term.
  • A117842 (program): Partial sum of smallest prime >= n (A007918).
  • A117855 (program): Number of nonzero palindromes of length n (in base 3).
  • A117856 (program): Number of palindromes of length n (in base 4).
  • A117857 (program): Number of palindromes of length n (in base 5).
  • A117858 (program): Number of palindromes of length n (in base 6).
  • A117859 (program): Number of palindromes of length n (in base 7).
  • A117860 (program): Number of palindromes of length n (in base 8).
  • A117861 (program): Number of palindromes of length n (in base 9).
  • A117862 (program): Number of palindromes (in base 3) below 3^n.
  • A117863 (program): Number of palindromes (in base 4) below 4^n.
  • A117864 (program): Number of palindromes (in base 5) below 5^n.
  • A117865 (program): Number of palindromes (in base 6) below 6^n.
  • A117866 (program): Number of palindromes (in base 7) below 7^n.
  • A117867 (program): Number of palindromes (in base 8) below 8^n.
  • A117868 (program): Number of palindromes (in base 9) below 9^n.
  • A117869 (program): Partial sums of floor(e^n).
  • A117887 (program): Number of labeled trees on <= n nodes.
  • A117898 (program): Number triangle 2^abs(L(C(n,2)/3) - L(C(k,2)/3))*[k<=n] where L(j/p) is the Legendre symbol of j and p.
  • A117899 (program): Expansion of (1 + 2x + 5x^2 + 3x^3 + 2x^4)/(1-x^3)^2.
  • A117904 (program): Number triangle [k<=n]*0^abs(L(C(n,2)/3)-L(C(k,2)/3)) where L(j/p) is the Legendre symbol of j and p.
  • A117905 (program): Expansion of (1+2x+2x^2)/((1-x^3)(1+x-x^3-x^4)).
  • A117908 (program): Chequered (or checkered) triangle for odd prime p=3.
  • A117909 (program): Count, inserting 0 after every even number.
  • A117910 (program): Expansion of (1+x+x^2+x^4)/((1-x^3)(1-x^6)).
  • A117926 (program): a(n) = n^floor(sqrt(n)).
  • A117943 (program): a(1) = 0, a(2) = 1; a(3n) = a(n); if every third term (a(3), a(6), a(9), …) is deleted, this gives back the original sequence.
  • A117947 (program): T(n,k)=L(C(n,k)/3) where L(j/p) is the Legendre symbol of j and p.
  • A117948 (program): Sum of the divisors of pentagonal numbers.
  • A117950 (program): a(n) = n^2 + 3.
  • A117951 (program): a(n) = n^2 + 5.
  • A117961 (program): Hexagonal numbers with prime indices.
  • A117962 (program): Partial sums of hexagonal numbers with prime indices.
  • A117964 (program): A117963 mod 2.
  • A117966 (program): Balanced ternary enumeration (based on balanced ternary representation) of integers; write n in ternary and then replace 2’s with (-1)’s.
  • A117973 (program): a(n) = 2^(wt(n)+1), where wt() = A000120().
  • A117998 (program): Decimal number generated by the binary bits of the n-th generation of the Rule 102 elementary cellular automaton.
  • A118002 (program): a(0) = 0. a(n) = a(n-1) + (largest integer <= n which is coprime to a(n-1)).
  • A118003 (program): a(n) = largest integer <= n which is coprime to A118002(n-1). a(n) = A118002(n) - A118002(n-1).
  • A118004 (program): a(n) = 9^n - 4^n.
  • A118005 (program): a(n) = ((-1)^n*5^(n+1) + 9^(n+1))/14.
  • A118006 (program): Define a sequence of binary words by w(1) = 01 and w(n+1) = w(n)w(n)Reverse[w(n)]. Sequence gives the limiting word w(infinity).
  • A118011 (program): Complement of the Connell sequence (A001614); a(n) = 4*n - A001614(n).
  • A118013 (program): Triangle read by rows: T(n,k) = floor(n^2/k), 1<=k<=n.
  • A118014 (program): Sum_ k=1..n floor(n^2/k).
  • A118015 (program): a(n) = floor(n^2/5).
  • A118057 (program): a(n) = 8n^2 - 4n - 3.
  • A118058 (program): a(n) = 49n^2 - 28n - 20.
  • A118059 (program): 288n^2 - 168n - 119.
  • A118060 (program): a(n) = 1681n^2 - 984n - 696.
  • A118061 (program): 9800n^2-5740n-4059
  • A118070 (program): Numbers with exactly one even decimal digit.
  • A118074 (program): Start with 1 and repeatedly reverse the digits and add 41 to get the next term.
  • A118075 (program): Start with 1 and repeatedly reverse the digits and add 42 to get the next term.
  • A118087 (program): Start with 1 and repeatedly reverse the digits and add 43 to get the next term.
  • A118090 (program): Start with 1 and repeatedly reverse the digits and add 44 to get the next term.
  • A118091 (program): Start with 1 and repeatedly reverse the digits and add 46 to get the next term.
  • A118102 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 94” initiated with a single ON (black) cell.
  • A118111 (program): Binary representation of n-th iteration of the Rule 190 elementary cellular automaton starting with a single black cell.
  • A118112 (program): a(n) = binomial(3n,n) mod (n+1).
  • A118124 (program): Triangle T(n,m) = (n+m)^2+n+m+41, read by rows.
  • A118136 (program): 2 + (2*n! mod n+1).
  • A118137 (program): Sum of decimal digits of two successive natural numbers.
  • A118145 (program): Start with 1 and repeatedly reverse the digits and add 47 to get the next term.
  • A118146 (program): Start with 1 and repeatedly reverse the digits and add 49 to get the next term.
  • A118147 (program): Start with 1 and repeatedly reverse the digits and add 50 to get the next term.
  • A118148 (program): Start with 1 and repeatedly reverse the digits and add 51 to get the next term.
  • A118149 (program): Start with 1 and repeatedly reverse the digits and add 52 to get the next term.
  • A118150 (program): Start with 1 and repeatedly reverse the digits and add 53 to get the next term.
  • A118151 (program): Start with 1 and repeatedly reverse the digits and add 54 to get the next term.
  • A118152 (program): Start with 1 and repeatedly reverse the digits and add 56 to get the next term.
  • A118153 (program): Start with 1 and repeatedly reverse the digits and add 57 to get the next term.
  • A118154 (program): Start with 1 and repeatedly reverse the digits and add 58 to get the next term.
  • A118155 (program): Start with 1 and repeatedly reverse the digits and add 59 to get the next term.
  • A118156 (program): Start with 1 and repeatedly reverse the digits and add 61 to get the next term.
  • A118157 (program): Start with 1 and repeatedly reverse the digits and add 62 to get the next term.
  • A118158 (program): Start with 1 and repeatedly reverse the digits and add 63 to get the next term.
  • A118159 (program): Start with 1 and repeatedly reverse the digits and add 64 to get the next term.
  • A118160 (program): Start with 1 and repeatedly reverse the digits and add 48 to get the next term.
  • A118161 (program): Start with 1 and repeatedly reverse the digits and add 55 to get the next term.
  • A118162 (program): Start with 1 and repeatedly reverse the digits and add 60 to get the next term.
  • A118163 (program): Start with 1 and repeatedly reverse the digits and add 65 to get the next term.
  • A118170 (program): x for which abs(n^n-x!) is minimal for given n.
  • A118175 (program): Binary representation of n-th iteration of the Rule 220 elementary cellular automaton starting with a single black cell.
  • A118180 (program): Triangle T(n, k) = 3^(k*(n-k)), read by rows.
  • A118185 (program): Triangle T(n,k) = 4^(k*(n-k)) for n>=k>=0, read by rows.
  • A118186 (program): Row sums of triangle A118185: a(n) = Sum_ k=0..n 4^(k*(n-k)) for n>=0.
  • A118190 (program): Triangle T(n,k) = 5^(k*(n-k)) for n >= k >= 0, read by rows.
  • A118200 (program): Start with 1 and repeatedly reverse the digits and add 66 to get the next term.
  • A118214 (program): Start with 1 and repeatedly reverse the digits and add 67 to get the next term.
  • A118215 (program): Start with 1 and repeatedly reverse the digits and add 68 to get the next term.
  • A118216 (program): Start with 1 and repeatedly reverse the digits and add 69 to get the next term.
  • A118217 (program): Start with 1 and repeatedly reverse the digits and add 70 to get the next term.
  • A118218 (program): Start with 1 and repeatedly reverse the digits and add 71 to get the next term.
  • A118220 (program): Start with 1 and repeatedly reverse the digits and add 72 to get the next term.
  • A118221 (program): Start with 1 and repeatedly reverse the digits and add 73 to get the next term.
  • A118225 (program): Start with 1 and repeatedly reverse the digits and add 74 to get the next term.
  • A118226 (program): Start with 1 and repeatedly reverse the digits and add 76 to get the next term.
  • A118237 (program): Start with 14 and repeatedly reverse the digits and add 1 to get the next term.
  • A118238 (program): Start with 15 and repeatedly reverse the digits and add 1 to get the next term.
  • A118239 (program): Engel expansion of cosh(1).
  • A118254 (program): Start with 16 and repeatedly reverse the digits and add 1 to get the next term.
  • A118263 (program): a(3n) = 2^n, a(3n+1) = 3^n, a(3n+2) = 4^n.
  • A118264 (program): Coefficient of q^n in (1-q)^3/(1-3q); dimensions of the enveloping algebra of the derived free Lie algebra on 3 letters.
  • A118265 (program): Coefficient of q^n in (1-q)^4/(1-4q); dimensions of the enveloping algebra of the derived free Lie algebra on 4 letters.
  • A118266 (program): Coefficient of q^n in (1-q)^5/(1-5q); dimensions of the enveloping algebra of the derived free Lie algebra on 5 letters.
  • A118277 (program): Generalized 9-gonal (or enneagonal) numbers: m(7m - 5)/2 with m = 0, 1, -1, 2, -2, 3, -3, …
  • A118286 (program): Numbers n such that n == 0 (mod 4) or n == 2 (mod 12).
  • A118293 (program): Start with 18 and repeatedly reverse the digits and add 1 to get the next term.
  • A118294 (program): Start with 19 and repeatedly reverse the digits and add 1 to get the next term.
  • A118295 (program): Start with 20 and repeatedly reverse the digits and add 1 to get the next term.
  • A118296 (program): Start with 21 and repeatedly reverse the digits and add 1 to get the next term.
  • A118297 (program): Start with 22 and repeatedly reverse the digits and add 1 to get the next term.
  • A118298 (program): Start with 23 and repeatedly reverse the digits and add 1 to get the next term.
  • A118299 (program): Start with 24 and repeatedly reverse the digits and add 1 to get the next term.
  • A118304 (program): Start with 25 and repeatedly reverse the digits and add 1 to get the next term.
  • A118310 (program): a(n) = gcd(n,m(n)), where m(n) is the n-th nonprime positive integer (1 or composite).
  • A118312 (program): Number of squares on infinite chessboard that a knight can reach in n moves from a fixed square.
  • A118321 (program): Decimal expansion of 8/105.
  • A118358 (program): Records in A086793.
  • A118360 (program): Start with 1; repeatedly reverse the digits when the number is written in binary and add 2 to get the next term.
  • A118375 (program): Minimum over all permutations b of 1..n of sum b(i)*b^ -1 (i).
  • A118402 (program): Row sums of triangle A118401.
  • A118403 (program): Unsigned row sums of triangle A118401; a(n) = A118402(n^2-n+2), where A118402 is the row sums of triangle A118400.
  • A118406 (program): Unsigned row sums of triangle A118404.
  • A118414 (program): a(n) = (2*n - 1) * (2^n - 1).
  • A118415 (program): (4*n - 3) * 2^(n - 1).
  • A118417 (program): a(n) = (2*n + 1) * 2^(n + 1).
  • A118425 (program): Number of binary sequences of length n containing exactly one subsequence 001.
  • A118442 (program): Column 0 of triangle A118441, which is the matrix log of triangle A118435.
  • A118465 (program): a(n) = 8*n^3 + n.
  • A118498 (program): a(n) = 11n^20 + 11n^2 + 152821.
  • A118512 (program): Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_11. This reaches a cycle of length 9 in 18 steps.
  • A118513 (program): Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_13. This reaches a cycle of length 9 in 15 steps.
  • A118517 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_1. This reaches a cycle of length 3 in 1 step.
  • A118518 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_2. This reaches a cycle of length 6 in 3 steps.
  • A118519 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_3. This reaches a cycle of length 6 in 3 steps.
  • A118520 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_5. This reaches a cycle of length 6 in 2 steps.
  • A118521 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_6. This reaches a cycle of length 6 in 2 steps.
  • A118525 (program): Start with 1 and repeatedly reverse the digits and add 6 to get the next term.
  • A118526 (program): Start with 1 and repeatedly reverse the digits and add 7 to get the next term.
  • A118527 (program): Start with 1 and repeatedly reverse the digits and add 8 to get the next term.
  • A118528 (program): Start with 1 and repeatedly reverse the digits and add 11 to get the next term.
  • A118529 (program): Start with 1 and repeatedly reverse the digits and add 12 to get the next term.
  • A118530 (program): Start with 1 and repeatedly reverse the digits and add 13 to get the next term.
  • A118531 (program): Start with 1 and repeatedly reverse the digits and add 14 to get the next term.
  • A118532 (program): Start with 1 and repeatedly reverse the digits and add 15 to get the next term.
  • A118533 (program): Start with 1 and repeatedly reverse the digits and add 16 to get the next term.
  • A118534 (program): a(n) is the largest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists.
  • A118535 (program): Start with 1 and repeatedly reverse the digits and add 20 to get the next term.
  • A118536 (program): Start with 1 and repeatedly reverse the digits and add 36 to get the next term.
  • A118538 (program): a(n) = A000040(n+1) - 6.
  • A118543 (program): Start with 1 and repeatedly reverse the digits and add 25 to get the next term.
  • A118558 (program): a(n) = (2^n-1)^4 - 2.
  • A118586 (program): Numbers whose binary expansion contains group of at least two 1’s followed by a nonempty group of 0’s.
  • A118602 (program): Start with 1 and repeatedly reverse the digits and add 21 to get the next term.
  • A118603 (program): Start with 1 and repeatedly reverse the digits and add 22 to get the next term.
  • A118606 (program): Start with 1 and repeatedly reverse the digits and add 17 to get the next term.
  • A118607 (program): Start with 1 and repeatedly reverse the digits and add 18 to get the next term.
  • A118608 (program): Start with 1 and repeatedly reverse the digits and add 19 to get the next term.
  • A118609 (program): Start with 1 and repeatedly reverse the digits and add 23 to get the next term.
  • A118610 (program): Start with 1 and repeatedly reverse the digits and add 24 to get the next term.
  • A118613 (program): Start with 1 and repeatedly reverse the digits and add 27 to get the next term.
  • A118614 (program): Start with 1 and repeatedly reverse the digits and add 28 to get the next term.
  • A118615 (program): Start with 1 and repeatedly reverse the digits and add 26 to get the next term.
  • A118616 (program): Start with 1 and repeatedly reverse the digits and add 29 to get the next term.
  • A118617 (program): Start with 1 and repeatedly reverse the digits and add 31 to get the next term.
  • A118618 (program): Start with 1 and repeatedly reverse the digits and add 32 to get the next term.
  • A118619 (program): Start with 1 and repeatedly reverse the digits and add 33 to get the next term.
  • A118620 (program): Start with 1 and repeatedly reverse the digits and add 45 to get the next term.
  • A118631 (program): Start with 1 and repeatedly reverse the digits and add 34 to get the next term.
  • A118632 (program): Start with 1 and repeatedly reverse the digits and add 35 to get the next term.
  • A118633 (program): Start with 1 and repeatedly reverse the digits and add 37 to get the next term.
  • A118634 (program): Start with 1 and repeatedly reverse the digits and add 38 to get the next term.
  • A118635 (program): Start with 1 and repeatedly reverse the digits and add 39 to get the next term.
  • A118636 (program): Start with 1 and repeatedly reverse the digits and add 40 to get the next term.
  • A118637 (program): Start with 1 and repeatedly reverse the digits and add 30 to get the next term.
  • A118640 (program): Result of left concatenation of the next Roman-numeral symbol.
  • A118649 (program): Row sums for A106597.
  • A118658 (program): a(n) = 2*F(n-1) = L(n) - F(n), where F(n) and L(n) are Fibonacci and Lucas numbers respectively.
  • A118663 (program): Index of the least prime dividing the n-th composite number: A000720(A020639(A002808(n))).
  • A118667 (program): a(n) = a(n-1)+ ((abs(2^a(n-1)*a(n-1)) mod 10).
  • A118719 (program): Cubes for which the digital root is also a cube.
  • A118729 (program): Infinite square array which contains the 8 numbers 4r^2 - 3r, 4r^2 - 2r, …, 4r^2 + 4r in row r.
  • A118738 (program): Number of ones in binary expansion of 5^n.
  • A118742 (program): Numbers n for which the expression n!/(n+1) is an integer.
  • A118749 (program): Largest prime <= 3*n.
  • A118751 (program): Smallest prime >= 3*n.
  • A118753 (program): First prime after 4n. Smallest prime >= 4*n. Bisection of A060264.
  • A118754 (program): Smallest prime >= 5*n.
  • A118755 (program): Smallest prime >= 6*n.
  • A118760 (program): A118758(A118758(n)).
  • A118777 (program): a(0) = 1; n > 0: a(n) = a(n-1) + d, d = -/+1 if n is prime/nonprime.
  • A118821 (program): 2-adic continued fraction of zero, where a(n) = 2 if n is odd, -A006519(n/2) otherwise.
  • A118822 (program): Numerators of the convergents of the 2-adic continued fraction of zero given by A118821.
  • A118824 (program): 2-adic continued fraction of zero, where a(n) = -2 if n is odd, A006519(n/2) otherwise.
  • A118825 (program): Numerators of the convergents of the 2-adic continued fraction of zero given by A118824.
  • A118827 (program): 2-adic continued fraction of zero, where a(n) = 1 if n is odd, otherwise -2*A006519(n/2).
  • A118828 (program): Numerators of the convergents of the 2-adic continued fraction of zero given by A118827.
  • A118830 (program): 2-adic continued fraction of zero, where a(n) = -1 if n is odd, 2*A006519(n/2) otherwise.
  • A118831 (program): Numerators of the convergents of the 2-adic continued fraction of zero given by A118830.
  • A118880 (program): Cube numbers equal to sum of decimal digits of n.
  • A118881 (program): Square of sum of decimal digits of n.
  • A118952 (program): Characteristic function of numbers that can be written as p+2^k, where p is prime and p less than 2^k (A118957).
  • A118953 (program): Number of ways to write the n-th prime as 2^k + p, where p is prime and p < 2^k.
  • A118966 (program): a(n) = (n+1)/2 if n occurs among the first n-1 terms of the sequence, otherwise a(n) = 2*n - 1.
  • A118971 (program): a(n) = 4binomial(5n+3,n)/(4*n+4).
  • A118979 (program): O.g.f: -12x^3/(-1+x)/(-1+2x)/(-1+3x) = -2-2/(-1+3x)-6/(-1+x)+6/(-1+2*x) .
  • A119031 (program): Add and Reverse: a(n) = the reversal of (a(n-1)+d), case a(1)=1 and d=4.
  • A119032 (program): a(n+2)=18a(n+1)-a(n)+8.
  • A119281 (program): Number of counting rods to represent n in the ancient Chinese rod numeral system.
  • A119282 (program): Alternating sum of the first n Fibonacci numbers.
  • A119327 (program): Expansion of (1-4x+12x^2-16x^3+8x^4)/(1-x)^5.
  • A119332 (program): Expansion of (1+x)/(1-2x^4).
  • A119336 (program): Expansion of (1-x)^4/((1-x)^6 - x^6).
  • A119346 (program): Sequence of nim-values for the game in which two players alternately cut off one inch or root two inches from a piece of string of length n. Player who runs out of string loses.
  • A119360 (program): a(n) = Sum_ i=1..n, j=1..n i! mod j.
  • A119387 (program): a(n) is the number of binary digits (1’s and nonleading 0’s) which remain unchanged in their positions when n and (n+1) are written in binary.
  • A119408 (program): Decimal equivalent of the binary string generated by the n X n identity matrix.
  • A119412 (program): a(n) = n*(n+11).
  • A119413 (program): 16*n-12.
  • A119416 (program): n * (smallest prime greater than largest prime factor of n).
  • A119476 (program): a(1)=1, a(n)=a((n+1)/2)+1 if n is odd, a(n)=a(n/2)+2 if n is even.
  • A119477 (program): a(1)=1, a(n) = a((n+1)/2) + 2 if n is odd, a(n) = a(n/2) + 1 if n is even.
  • A119479 (program): Length of longest run of consecutive integers having exactly n divisors.
  • A119502 (program): Triangle read by rows, T(n,k) = (n-k)!, for n>=0 and 0<=k<=n.
  • A119505 (program): The Pi-th digit of Pi where the digit value of 0 is interpreted as decimal 10.
  • A119522 (program): Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers.
  • A119536 (program): 3n^3 + 3n.
  • A119549 (program): Binomial( Catalan(n), 4).
  • A119578 (program): a(n) = (n + n^2)binomial(2n,n)/2.
  • A119579 (program): a(n) = (n + n^2)(binomial(2n, n)).
  • A119580 (program): (n^2+n^3)(binomial(2n,n)).
  • A119581 (program): (2n+n^2)(binomial(2*n,n))/2.
  • A119582 (program): (n^2+n^3)(binomial(2n,n))/2.
  • A119587 (program): 2^n + 1 - 2*Fibonacci(n+1).
  • A119610 (program): Number of cases in which the first player is killed in a Russian roulette game where 5 players use a gun with n chambers and the number of bullets can be from 1 to n. Players do not rotate the cylinder after the game starts.
  • A119616 (program): Second elementary symmetric function of divisors of n.
  • A119617 (program): Integers of the form c(n)/b(n) where c(n+1)=c(n)+(n+1)^4 with c(0)=1 and b(n+1)=b(n)+(n+1)^2 with b(0)=1.
  • A119622 (program): Numbers n such that no group of order n is a Con-Cos group.
  • A119625 (program): Start with 17 and repeatedly reverse the digits and add 1 to get the next term.
  • A119633 (program): a(n) = (A046717(n))^3.
  • A119635 (program): a(n) = n(1 + n^2)2^n.
  • A119651 (program): Number of different values of exactly n standard American coins (pennies, nickels, dimes and quarters).
  • A119652 (program): Number of different values of <= n standard American coins (pennies, nickels, dimes and quarters).
  • A119653 (program): Denominator of BernoulliB[2p] divided by 6, where p=Prime[n].
  • A119674 (program): Number of states of the minimal deterministic finite automaton that accepts binary strings that represent numbers that are divisible by n.
  • A119681 (program): Odd numbers n such that 2n-1 is prime.
  • A119688 (program): a(n) = n!! mod (n+1).
  • A119690 (program): n! mod n*(n+1)/2.
  • A119692 (program): Binomial(2n,n)fib(n).
  • A119693 (program): Binomial(2n,n)fib(n)/2.
  • A119701 (program): nbinomial(2n, n)*Fibonacci(n).
  • A119702 (program): n^2binomial(2n, n)*Fibonacci(n).
  • A119703 (program): n^3binomial(2n, n)*Fibonacci(n).
  • A119713 (program): First differences are 2, 5, 5, 9, 9, 9, 14, 14, 14, 14, …, that is, A000096 with m-th term repeated m times (m>=1).
  • A119771 (program): Product of n^2 and n-th tetrahedral number: n^3(n+1)(n+2)/6.
  • A119789 (program): Fibonacci Logarithms used to get a triangular array.
  • A119837 (program): a(n)=(2n)!/n!-(2n)!/(n-1)!.
  • A119900 (program): Triangle read by rows: T(n,k) is the number of binary words of length n with k strictly increasing runs, for 0<=k<=n.
  • A119910 (program): Period 6: repeat [1, 3, 2, -1, -3, -2].
  • A119913 (program): Number of directed simple cycles in the complete graph K_n.
  • A119915 (program): Number of ternary words of length n and having exactly one run of 0’s of odd length.
  • A119916 (program): Number of runs of 0’s of odd length in all ternary words of length n.
  • A119930 (program): Sum of the numbers of the matrix A111490 along a boustrophedon path: a11, a11+a12, a11+a12+a21, etc.
  • A119959 (program): p^2-p+1 central polygonal numbers with prime indices A002061(prime(n)).
  • A119969 (program): Sum k>=0, C(2^k-1,n-2*(2^k-1)) .
  • A119972 (program): Flag n when the first difference of the decimal encoding of the Gray code is negative.
  • A119992 (program): a(n) = n-th positive integer which is coprime to n!.
  • A119996 (program): Numerator of Sum_ k=1..n 1/(Fibonacci(k)*Fibonacci(k+2)).
  • A120007 (program): Mobius transform of sum of prime factors of n with multiplicity (A001414).
  • A120054 (program): Binomial(n+3,4)*4^4.
  • A120069 (program): Denominators of partial sums of a convergent series involving scaled Catalan numbers A000108.
  • A120071 (program): a(n) = n*(n+20).
  • A120096 (program): a(n) = (A046717(n))^2 (starting with n=1).
  • A120112 (program): Row sums of number triangle A120111.
  • A120134 (program): a(1)=4; a(n) = floor((8 + Sum_ k=1..n-1 a(k))/2).
  • A120135 (program): a(1)=5; a(n)=floor((11+sum(a(1) to a(n-1)))/2).
  • A120136 (program): a(1)=7; a(n)=floor((14+sum(a(1) to a(n-1)))/2).
  • A120137 (program): a(1)=8; a(n)=floor((17+sum(a(1) to a(n-1)))/2).
  • A120138 (program): a(1)=10; a(n)=floor((20+sum(a(1) to a(n-1)))/2).
  • A120139 (program): a(1)=11; a(n)=floor((23+sum(a(1) to a(n-1)))/2).
  • A120140 (program): a(1)=13; a(n)=floor((26+sum(a(1) to a(n-1)))/2).
  • A120141 (program): a(1)=14; a(n)=floor((29+sum(a(1) to a(n-1)))/2).
  • A120142 (program): a(1)=16; a(n)=floor((32+sum(a(1) to a(n-1)))/2).
  • A120143 (program): a(1)=17; a(n)=floor((35+sum(a(1) to a(n-1)))/2).
  • A120144 (program): a(1)=19; a(n)=floor((38+sum(a(1) to a(n-1)))/2).
  • A120145 (program): a(1)=20; a(n)=floor((41+sum(a(1) to a(n-1)))/2).
  • A120146 (program): a(1)=22; a(n)=floor((44+sum(a(1) to a(n-1)))/2).
  • A120147 (program): a(1)=23; a(n)=floor((47+sum(a(1) to a(n-1)))/2).
  • A120148 (program): a(1)=25; a(n)=floor((50+sum(a(1) to a(n-1)))/2).
  • A120149 (program): a(1)=2; a(n)=floor((7+sum(a(1) to a(n-1)))/3).
  • A120150 (program): a(1)=3; a(n)=floor((11+sum(a(1) to a(n-1)))/3).
  • A120151 (program): a(1)=5; a(n)=floor((15+sum(a(1) to a(n-1)))/3).
  • A120152 (program): a(1)=6; a(n)=floor((19+sum(a(1) to a(n-1)))/3).
  • A120153 (program): a(1)=7; a(n)=floor((23+sum(a(1) to a(n-1)))/3).
  • A120154 (program): a(1)=9; a(n)=floor((27+sum(a(1) to a(n-1)))/3).
  • A120155 (program): a(1)=10; a(n)=floor((31+sum(a(1) to a(n-1)))/3).
  • A120156 (program): a(1)=11; a(n)=floor((35+sum(a(1) to a(n-1)))/3).
  • A120157 (program): a(1)=13; a(n)=floor((39+sum(a(1) to a(n-1)))/3).
  • A120158 (program): a(1)=14; a(n)=floor((43+sum(a(1) to a(n-1)))/3).
  • A120159 (program): a(1)=15; a(n)=floor((47+sum(a(1) to a(n-1)))/3).
  • A120160 (program): a(n) = ceiling(Sum_ i=1..n-1 a(i)/4) for n >= 2 starting with a(1) = 1.
  • A120161 (program): a(1)=2; a(n)=floor((9+sum(a(1) to a(n-1)))/4).
  • A120162 (program): a(1)=3; a(n)=floor((14+sum(a(1) to a(n-1)))/4).
  • A120163 (program): a(1)=4; a(n)=floor((19+sum(a(1) to a(n-1)))/4).
  • A120164 (program): a(1)=6; a(n)=floor((24+sum(a(1) to a(n-1)))/4).
  • A120165 (program): a(1)=7; a(n)=floor((29+sum(a(1) to a(n-1)))/4).
  • A120166 (program): a(1)=8; a(n)=floor((34+sum(a(1) to a(n-1)))/4).
  • A120167 (program): a(1)=9; a(n)=floor((39+sum(a(1) to a(n-1)))/4).
  • A120168 (program): a(1)=11; a(n)=floor((44+sum(a(1) to a(n-1)))/4).
  • A120169 (program): a(1)=12; a(n)=floor((49+sum(a(1) to a(n-1)))/4).
  • A120170 (program): a(n) = ceiling( Sum_ i=1..n-1 a(i)/5 ), a(1)=1.
  • A120171 (program): a(1)=2; a(n)=floor((11+sum(a(1) to a(n-1)))/5).
  • A120172 (program): a(1)=3; a(n)=floor((17+sum(a(1) to a(n-1)))/5).
  • A120173 (program): a(1)=4; a(n)=floor((23+sum(a(1) to a(n-1)))/5).
  • A120174 (program): a(1)=5; a(n)=floor((29+sum(a(1) to a(n-1)))/5).
  • A120175 (program): a(1)=7; a(n)=floor((35+sum(a(1) to a(n-1)))/5).
  • A120176 (program): a(1)=8; a(n)=floor((41+sum(a(1) to a(n-1)))/5).
  • A120177 (program): a(1)=9; a(n)=floor((47+sum(a(1) to a(n-1)))/5).
  • A120178 (program): a(n)=ceiling( sum_ i=1..n-1 a(i)/6), a(1)=1.
  • A120179 (program): a(1)=2; a(n)=floor((13+sum(a(1) to a(n-1)))/6).
  • A120180 (program): a(1)=3; a(n)=floor((20+sum(a(1) to a(n-1)))/6).
  • A120181 (program): a(1)=4; a(n)=floor((27+sum(a(1) to a(n-1)))/6).
  • A120182 (program): a(1)=5; a(n)=floor((34+sum(a(1) to a(n-1)))/6).
  • A120183 (program): a(1)=6; a(n)=floor((41+sum(a(1) to a(n-1)))/6).
  • A120184 (program): a(1)=8; a(n)=floor((48+sum(a(1) to a(n-1)))/6).
  • A120185 (program): a(1)=9; a(n)=floor((55+sum(a(1) to a(n-1)))/6).
  • A120186 (program): a(n) = ceiling( Sum_ i=1..n-1 a(i)/7 ), a(1) = 1.
  • A120187 (program): a(1)=2; a(n)=floor((15+sum(a(1) to a(n-1)))/7).
  • A120189 (program): a(1)=4; a(n)=floor((31+sum(a(1) to a(n-1)))/7).
  • A120190 (program): a(1)=5; a(n)=floor((39+sum(a(1) to a(n-1)))/7).
  • A120191 (program): a(1)=6; a(n)=floor((47+sum(a(1) to a(n-1)))/7).
  • A120192 (program): a(1)=7; a(n)=floor((55+sum(a(1) to a(n-1)))/7).
  • A120193 (program): a(1)=9; a(n)=floor((63+sum(a(1) to a(n-1)))/7).
  • A120194 (program): a(n) = ceiling( Sum_ i=1..n-1 a(i)/8 ), a(1)=1.
  • A120195 (program): a(1)=2; a(n)=floor((17+sum(a(1) to a(n-1)))/8).
  • A120197 (program): a(1)=4; a(n)=floor((35+sum(a(1) to a(n-1)))/8).
  • A120198 (program): a(1)=5; a(n)=floor((44+sum(a(1) to a(n-1)))/8).
  • A120199 (program): a(1)=6; a(n)=floor((53+sum(a(1) to a(n-1)))/8).
  • A120200 (program): a(1)=7; a(n)=floor((62+sum(a(1) to a(n-1)))/8).
  • A120201 (program): a(1)=8; a(n)=floor((71+sum(a(1) to a(n-1)))/8).
  • A120202 (program): a(n) = ceiling( sum_ i=1..n-1 a(i)/9), a(1)=1.
  • A120203 (program): a(1) = 2; a(n) = floor( (19 + Sum_ i=1..n-1 a(i)) /9).
  • A120205 (program): a(1)=4; a(n)=floor((39+sum(a(1) to a(n-1)))/9).
  • A120206 (program): a(1)=5; a(n)=floor((49+sum(a(1) to a(n-1)))/9).
  • A120207 (program): a(1)=6; a(n)=floor((59+sum(a(1) to a(n-1)))/9).
  • A120208 (program): a(1)=7; a(n)=floor((69+sum(a(1) to a(n-1)))/9).
  • A120209 (program): a(1)=8; a(n)=floor((79+sum(a(1) to a(n-1)))/9).
  • A120212 (program): “a” values providing solution x = b in A120211 (i.e., y^2 = b^2(a^2 - b)(b + 1) with a, b legs in primitive Pythagorean triangles).
  • A120246 (program): a(1) = 1. a((m(m+1)/2 +k) = m + a(k), 1 <= k <= m+1, m >= 1.
  • A120275 (program): Smallest prime factor of the odd Catalan number A038003(n).
  • A120278 (program): Sum[Sum[C(2k,k), k,1,m ], m,1,n ], where C(2k,k)=(2k)!/(k!)^2=A000984[k].
  • A120279 (program): a(n) = Sum[Sum[(i+j)!/i!/j!, i,1,j ], j,1,n ].
  • A120303 (program): Largest prime factor of Catalan number A000108(n).
  • A120304 (program): Catalan number minus 2, or ((2n)!/(n!*(n+1)!) - 2).
  • A120305 (program): a(n) = Sum_ i=0..n Sum_ j=0..n (-1)^(i+j) * (i+j)!/(i!j!).
  • A120321 (program): RF(7): refactorable numbers with 7 as smallest prime factor.
  • A120323 (program): Periodic sequence 0, 3, 1, 0, 1, 3.
  • A120324 (program): Periodic sequence 0, 1, 0, 4, 0, 1.
  • A120325 (program): Period 6: repeat [0, 0, 1, 0, 1, 0].
  • A120326 (program): Cumulative sum of the remainders when dividing primes by 3.
  • A120328 (program): Sum of three consecutive squares: a(n) = n^2 + (n + 1)^2 + (n + 2)^2.
  • A120353 (program): Sum of 5 consecutive powers of 3, starting with a power of 9.
  • A120354 (program): a(n) = 11*3^n.
  • A120370 (program): a(1) = 2. a(n) = a(n-1) + (maximum number of distinct primes dividing any earlier terms).
  • A120413 (program): Largest even number strictly less than n^2.
  • A120437 (program): Differences of A037314 (sum of base-3 digits of n = sum of base-9 digits of n).
  • A120444 (program): First differences of A004125.
  • A120454 (program): a(n) = ceiling(GPF(n)/LPF(n)) where GPF is greatest prime factor, LPF is least prime factor.
  • A120462 (program): Expansion of -2x(-3-2x+4x^2) / ((x-1)(2x+1)(2x-1)*(1+x)).
  • A120470 (program): 24^n +(-1)^n2^(n-1).
  • A120471 (program): 6 *A015518(n).
  • A120478 (program): Binomial(n+6,5)-binomial(n,5).
  • A120486 (program): Partial sums of A000188.
  • A120490 (program): 1 + Sum[ k^(n-1), k,1,n ].
  • A120501 (program): Meta-Fibonacci sequence a(n) with parameters s=2.
  • A120503 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=3.
  • A120507 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=4.
  • A120511 (program): a(n) = min j>0 : A006949(j) = n .
  • A120512 (program): a(n) = min j : A120501(j) = n .
  • A120513 (program): a(n) = min j : A120502(j) = n .
  • A120514 (program): a(n) = min j : A120503(j) = n .
  • A120515 (program): a(n) = min j : A120504(j) = n .
  • A120516 (program): a(n) = min j : A120505(j) = n .
  • A120517 (program): a(n) = min j : A120506(j) = n .
  • A120518 (program): a(n) = min j : A120507(j) = n .
  • A120519 (program): a(n) = min j : A120508(j) = n .
  • A120520 (program): a(n) = min j : A120509(j) = n .
  • A120521 (program): a(n) = min j : A120510(j) = n .
  • A120523 (program): First differences of successive meta-Fibonacci numbers A120501.
  • A120525 (program): First differences of successive generalized meta-Fibonacci numbers A120503.
  • A120533 (program): Primes having a prime number of digits.
  • A120571 (program): 2n^4+6n^2+4 = 2(n^2+1)(n^2+2).
  • A120573 (program): a(n) = n^5 + 3n^3 + 2n = n(n^2+1)(n^2+2).
  • A120580 (program): Hankel transform of sum k=0..n, C(2k,k) .
  • A120588 (program): G.f. is 1 + x*c(x), where c(x) is the g.f. of the Catalan numbers (A000108).
  • A120612 (program): For n>1, a(n) = 2a(n-1) + 15a(n-2); a(0)=1, a(1)=1.
  • A120613 (program): a(n) = floor(phi*floor(n/phi)) where phi=(1+sqrt(5))/2.
  • A120614 (program): a(n) = g(n+1) - g(n) where g(k) = floor(phi*floor(k/phi)) and phi = (1+sqrt(5))/2.
  • A120615 (program): a(n) = Sum_ k=0..n floor(phi*floor(n/phi)) where phi = (1+sqrt(5))/2.
  • A120617 (program): Hankel transform of g.f. 1/sqrt(1+4x^2).
  • A120632 (program): Number of numbers >1 up to 2*p(n) which are divisible by primes up to p(n).
  • A120634 (program): Decimal equivalent of A066335.
  • A120664 (program): Expansion of 2x(1-6x+12x^2)/(1-8x+19x^2-12*x^3).
  • A120689 (program): a(n) = 10a(n-1) - 16a(n-2), n>0.
  • A120694 (program): Sequence demonstrating the Pythagorean theorem.
  • A120699 (program): Lengths of set partitions.
  • A120701 (program): Number of unit circles which fit touching a circle of radius n-1, i.e., with their centers on a circle of radius n.
  • A120718 (program): Expansion of 3x/(1 - 2x^2 - 2*x + x^3).
  • A120728 (program): Floor of e^n, reduced modulo 3.
  • A120731 (program): Decimal expansion of 3 + sqrt(2)/10.
  • A120738 (program): a(n) = 4*n - A000120(n).
  • A120739 (program): a(n) = Sum k=0..n floor(C(n,k)/2).
  • A120740 (program): Numbers n such that n = Sum_digits[k*abs(n-k)] for some k>=0.
  • A120741 (program): a(n) = (7^n - 1)/2.
  • A120743 (program): a(n) = (1/2)(1 + 3i)^n + (1/2)(1 - 3i)^n where i = sqrt(-1).
  • A120775 (program): The (3,1)-entry of the matrix M^n, where M is the 3 X 3 matrix [0,1,1; 2,1,2; 1,2,2] (n>=1).
  • A120777 (program): One half of denominators of partial sums of a series for sqrt(2).
  • A120778 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/4.
  • A120781 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/8.
  • A120785 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/16.
  • A120845 (program): 2^n+3^n+5*n.
  • A120846 (program): a(n) = 3^n + 2^n + n.
  • A120848 (program): 2^n+3^n-n.
  • A120849 (program): 5n+3^n-2^n.
  • A120855 (program): Row sums of triangle A120854, which is the matrix log of triangle A117939.
  • A120864 (program): a(n) is the number j for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4k = 12n^2.
  • A120865 (program): a(n) is the number k for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4k = 12n^2.
  • A120866 (program): a(n) is the number j for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4k = 20n^2.
  • A120867 (program): a(n) is the number k for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4k = 20n^2.
  • A120868 (program): a(n) is the number k for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4k = 5n^2.
  • A120880 (program): G.f. satisfies: A(x) = A(x^3)(1 + 2x + x^2); thus a(n) = 2^A062756(n), where A062756(n) is the number of 1’s in the ternary expansion of n.
  • A120885 (program): Triangle read by rows where t(n,m) = ceiling(n/m).
  • A120891 (program): Number of primitive Pythagorean triangles with odd leg 2n-1.
  • A120892 (program): a(n)=3a(n-1)+3a(n-2)-a(n-3);a(0)=1,a(1)=0,a(2)=3. a(n)=4* a(n-1)+(-1)^n -a(n-2);a(0)=1,a(1)=0.
  • A120893 (program): a(n) = 3a(n-1) + 3a(n-2) - a(n-3); a(0)=1, a(1)=1, a(2)=5.
  • A120908 (program): Sum of the lengths of the drops in all ternary words of length n on 0,1,2 . The drops of a ternary word on 0,1,2 are the subwords 10,20 and 21, their lengths being the differences 1, 2 and 1, respectively.
  • A120926 (program): Number of isolated 0’s in all ternary words of length n on 0,1,2 .
  • A120940 (program): Alternating sum of the Fibonacci numbers multiplied by their (combinatorial) indices.
  • A120948 (program): 8n+3^n+5^n.
  • A120949 (program): 2n+3^n+5^n.
  • A120950 (program): 3^n+5^n-2n.
  • A120962 (program): Final digit (in decimal system) of n^(n^n), i.e., n^(n^n) mod 10.
  • A120969 (program): 8n+5^n-3^n.
  • A120978 (program): 2n+5^n-3^n.
  • A120990 (program): 5^n-3^n-2n.
  • A121048 (program): n + phi(n), for Euler totient function phi(n).
  • A121069 (program): Conjectured sequence for jumping champions greater than 1 (most common prime gaps up to x, for some x).
  • A121149 (program): Minimal number of vertices in a planar connected n-polyhex.
  • A121150 (program): Minimal number of vertices in an n-polyomino.
  • A121151 (program): Minimal number of vertices in an n-polytrimino (or n-polyiamond).
  • A121173 (program): Sequence S with property that for n in S, a(n) = a(1) + a(2) +…+ a(n-1) and for n not in S, a(n) = n+1.
  • A121177 (program): Catapolyoctagons (see Cyvin et al. for precise definition).
  • A121199 (program): 12n+7^n+5^n.
  • A121200 (program): 2n+7^n+5^n.
  • A121201 (program): 7^n+5^n-2n.
  • A121203 (program): 2n+7^n-5^n.
  • A121204 (program): -2n+7^n-5^n.
  • A121205 (program): “666” in bases 7 and higher rewritten in base 10.
  • A121206 (program): a(n) = (2n)! mod n(2n+1).
  • A121213 (program): 7^n-5^n.
  • A121238 (program): a(n) = (-1)^(1+n+A088585(n)).
  • A121239 (program): Decimal expansion of 10-e.
  • A121241 (program): Change 0 to -1 in A090678.
  • A121254 (program): Number of conjugated cycles composed of six carbons in (n,n)-nanotubes in terms of the number of naphthalene units.
  • A121255 (program): Number of conjugated cycles composed of ten carbons in (n,n)-nanotubes in terms of the number of naphthalene units.
  • A121257 (program): Number of conjugated cycles composed of six carbons in (1,1)-nanotubes in terms of the number of naphthalene units.
  • A121259 (program): Numbers n such that (3n^2+1)/4 is prime.
  • A121262 (program): The characteristic function of the multiples of four.
  • A121273 (program): Number of different n-dimensional convex regular polytopes that can tile n-dimensional space.
  • A121289 (program): a(n) = n/(largest triangular number dividing n).
  • A121290 (program): a(n) = (2^prime(n) - 8)/24 for n>=2.
  • A121318 (program): Molecular topological indices of the path graphs P_n
  • A121324 (program): Number of digits in quotient R_(nR_n) /(R_n)^2, where R_n=A002275(n),nR_n=A053422(n).
  • A121340 (program): List of triples 1^(2^k), 2^(2^k), 3^(2^k) for k>0.
  • A121358 (program): Least prime factor of pyramidal number A000292(n), a(1) = 1.
  • A121361 (program): Expansion of f(x^1, x^5) * psi(x^2) in powers of x where psi(), f() are Ramanujan theta functions.
  • A121365 (program): a(n) = 6a(n-1) - 9a(n-2) + n + 1.
  • A121377 (program): ASCII codes for decimal digits.
  • A121378 (program): EBCDIC codes for decimal digits.
  • A121389 (program): a(n) = 10^Fibonacci(n) - 1.
  • A121401 (program): a(n)=((sqrt(3)+1)^n+(sqrt(3)-1)^n)^2/2^(n+1).
  • A121444 (program): Expansion of f(x^3, x^9) * f(x, x^2) in powers of x where f(, ) is Ramanujan’s general theta functions.
  • A121451 (program): Maximum product over partitions into parts of the form 3k+2.
  • A121453 (program): Numbers m such that (m mod k) > (m+2 mod k) with least value of k = 5.
  • A121461 (program): Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having last ascent of length k (1<=k<=n).
  • A121470 (program): Expansion of x(1+5x+2x^2+x^3)/((1+x)(1-x)^3).
  • A121471 (program): a(n) = 9n^2/4 -4n +19/8 -3*(-1)^n/8.
  • A121488 (program): a(n) = 8n^2 - floor(nsqrt(8))^2.
  • A121489 (program): Diagonal of array A121490.
  • A121496 (program): Run lengths of successive numbers in A068225.
  • A121499 (program): Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(29^2) = 1/841.
  • A121505 (program): Hit triangle for unit circle area (Pi) approximation problem described in A121500.
  • A121509 (program): a(n) = 5n^2/2 - 5n + 13/4 - (-1)^n/4.
  • A121511 (program): a(n) = a(n-1) + a(n-4) - a(n-5).
  • A121512 (program): a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=1, a(2)=4, a(3)=10, a(4)=4.
  • A121517 (program): a(n) = 4a(n-1) + 4a(n-2) - a(n-3); a(0)=1, a(1)=1, a(2)=7.
  • A121536 (program): Smallest m such that m^3>=n^2.
  • A121544 (program): Sum of all proper base 4 numbers with n digits (those not beginning with 0).
  • A121559 (program): Final result (0 or 1) under iterations of r mod (max prime p <= r) starting at r = n.
  • A121561 (program): The number of iterations of “subtract the largest prime less than or equal to the current value” to go from n to the limiting value 0 or 1.
  • A121567 (program): Fibonacci[ (p - 1) ], where p = Prime[n].
  • A121568 (program): Fibonacci[ (p - 1)/2 ], where p = Prime[n].
  • A121569 (program): a(n) = Fibonacci((prime(n)+3)/2) - 1.
  • A121578 (program): Values m of number pairs (m,n) which yield associated matching times on the clock with interchanged hour and minute hands for corresponding n in A121577.
  • A121580 (program): Number of cells in column 1 of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121582 (program): Number of cells in column 2 of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121586 (program): Number of columns in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121607 (program): (n^3+n)*3^n.
  • A121628 (program): Nonnegative k such that 3*k + 1 is a perfect cube.
  • A121646 (program): a(n) = Fibonacci(n-1)^2 - Fibonacci(n)^2.
  • A121663 (program): a(0) = 1; if n = 2^k, a(n) = k+2, otherwise a(n)=(A000523(n)+2)*a(A053645(n)).
  • A121670 (program): a(n) = n^3 - 3*n.
  • A121671 (program): Real part of (1 + n*i)^5.
  • A121688 (program): G.f.: Sum_ n>=0 x^n * (1+x)^(2^n).
  • A121706 (program): a(n) = Sum_ k=1..n-1 k^n.
  • A121718 (program): Write 0, 1, …, n in base 3 and add as if they were decimal numbers.
  • A121722 (program): Triangle T(n,k) = 1 + kn(n+1)/2, read by rows.
  • A121726 (program): Sum sequence A000522 then subtract 0,1,2,3,4,5,…
  • A121782 (program): Series expansion for mean-squared radius of gyration of rectangles on square lattice.
  • A121801 (program): Expansion of 2x^2(3-x)/((1+x)(1-3x+x^2)).
  • A121807 (program): Partial sums of A004676.
  • A121816 (program): Conjectured chromatic number of the square of an outerplanar graph G^2 as a function of the maximum degree of a vertex of G.
  • A121823 (program): (3^p+p)/(p+1) with (p + 1) odd prime > 3.
  • A121839 (program): Decimal expansion of Sum_ k>=1 1/C(k), where C(k) is a Catalan Number (A000108).
  • A121844 (program): Excess of n^3 over previous prime.
  • A121858 (program): Smallest odd number having p(n) divisors, where p(n) is the n-th prime=A000040(n).
  • A121892 (program): Row sums of triangle in A066094.
  • A121896 (program): Let M be the matrix defined in A111490. Sequence gives M(1,1), M(1,2)+M(1,2)+M(2,2), M(1,3)+M(2,3)+M(3,1)+M(3,2)+M(3,3), etc.
  • A121907 (program): Expansion of g.f.: (1 + x + x^2)/(1 - 2x - 2x^2).
  • A121924 (program): Number of splitting steps that one can take with a sequence of n 2’s.
  • A121925 (program): a(n) = floor(n*(Pi^e + e^Pi)).
  • A121929 (program): a(n) = ceiling(n*(e^Pi + Pi^e)).
  • A121937 (program): a(n) = least m >= 2 such that (n mod m) > (n+2 mod m).
  • A121948 (program): Floor of n-th 3-almost prime / n.
  • A121968 (program): a(n) = 2*a(n-1) - a(n-2) + n + 1.
  • A121990 (program): Expansion of x(1+9x+2x^2)/((1-x)(1-3*x+x^2)).
  • A121991 (program): a(n) = 3*a(n-1) - a(n-2) - a(n-3) + 12.
  • A121997 (program): Count up to n, n times.
  • A122002 (program): a(0)=5; otherwise a(n) = (n mod 4) if n is odd, a(n) = h + 4, where h = (highest odd divisor of n) mod 4 if n is even.
  • A122006 (program): Expansion of x^2(1-x)/((1-3x)(1-3x^2)).
  • A122007 (program): Expansion of 2x^2(1-2x) / ((3x-1)(3x^2-1)).
  • A122008 (program): Expansion of (2x-1)(x-1)x / ((3x-1)(3x^2-1)).
  • A122027 (program): Largest integer m such that every n-tournament contains a transitive (i.e., acyclic) sub-tournament with at least m vertices.
  • A122033 (program): a(n) = 2a(n-1) - 2(n-2)*a(n-2), with a(0)=1, a(1)=2.
  • A122041 (program): a(n) = 2*a(n-1) - 1 for n>1, a(1)=23.
  • A122046 (program): Partial sums of floor(n^2/8).
  • A122047 (program): Degree of the polynomial P(n,x), defined by a Somos-6 type sequence: P(n,x)=(x^(n-1)P(n-1,x)P(n-5,x) + P(n-2,x)*P(n-4,x))/P(n-6,x), initialized with P(n,x)=1 at n<0.
  • A122056 (program): A Somos 9-Hone exponent type recursion: a(n) = (x^(n-1)a(n - 1)a(n - 8) - a(n - 4)a(n - 5))/a(n - 9).
  • A122061 (program): First pentagonal number, 2nd hexagonal number, 3rd heptagonal number, 4th octagonal number and then repeat the same pattern: 5th pentagonal, 6th hexagonal, 7th heptagonal, 8th octagonal, etc.
  • A122069 (program): a(n) = 3a(n-1) + 9a(n-2) for n > 1, with a(0)=1, a(1)=3.
  • A122072 (program): Greatest prime less than 10n.
  • A122074 (program): a(0)=1, a(1)=6, a(n) = 7a(n-1) - 2a(n-2).
  • A122088 (program): Add 10, subtract 5, add 10, subtract 5, ad infinitum.
  • A122092 (program): a(n) = (n-2)a(n-1) - (n-1)a(n-2), with a(0)=1, a(1)=1.
  • A122102 (program): a(n) = Sum_ k=1..n prime(k)^4.
  • A122103 (program): Sum of the fifth powers of the first n primes.
  • A122117 (program): a(n) = 3a(n-1) + 4a(n-2), with a(0)=1, a(1)=2.
  • A122124 (program): Numbers n such that 25 divides Sum[ Prime[k]^n, k,1,n ].
  • A122186 (program): First row sum of the 4 X 4 matrix M^n, where M= 10, 9, 7, 4 , 9, 8, 6, 3 , 7, 6, 4, 2 , 4, 3, 2, 1 .
  • A122187 (program): First row sum of the matrix M^n, where M is the 3 X 3 matrix [[6, 5, 3], [5, 4, 2], [3, 2, 1]] (n>=0).
  • A122188 (program): Triangle read by rows, formed from the coefficients of characteristic polynomials of the following sequence of matrices: 2 X 2 0, 1 , 1, 1 , 3 X 3 0, 1, 0 , 0, 0, 1 , 1, 1, 1 , 4 X 4 0, 1,0, 0 , 0, 0, 1, 0 , 0, 0, 0, 1 , 1, 1, 1, 1 , 5 X 5 0, 1, 0, 0, 0 , 0, 0, 1, 0, 0 , 0, 0, 0, 1, 0 , 0, 0, 0, 0, 1 , 1, 1, 1, 1, 1 , …
  • A122196 (program): Fractal sequence: count down by 2’s from successive integers.
  • A122197 (program): Fractal sequence: count up to successive integers twice.
  • A122199 (program): Permutation of natural numbers: a recursed variant of A122155.
  • A122219 (program): Period 9: repeat 5, 4, 5, 4, 3, 4, 5, 4, 5.
  • A122220 (program): a(n) = (prime(n)^6-prime(n)^2))/20.
  • A122229 (program): a(n) = A014486(A122228(n)).
  • A122247 (program): Partial sums of A005187.
  • A122248 (program): a(n) - a(n-1) = A113474(n).
  • A122250 (program): Partial sums of A004128.
  • A122263 (program): a(n) = 2a(n-1)-a(n-2)+2(Prime[n+1]-Prime[n]).
  • A122264 (program): 2 X 2 vector matrix Markov of a Prime gap affine type.
  • A122366 (program): Triangle read by rows: T(n,k) = binomial(2*n+1,k), 0 <= k <= n.
  • A122367 (program): Dimension of 3-variable non-commutative harmonics (twisted derivative). The dimension of the space of non-commutative polynomials in 3 variables which are killed by all symmetric differential operators (where for a monomial w, d_ xi ( xi w ) = w and d_ xi ( xj w ) = 0 for i != j).
  • A122391 (program): Dimension of 2-variable non-commutative harmonics (Hausdorff derivative). The dimension of the space of non-commutative polynomials in 2 variables which are killed by all symmetric differential operators (where for a monomial w, d_ xi ( w ) = sum over all subwords of w deleting xi once).
  • A122414 (program): Triangle T(n,k) for 1 <= k <= n read by rows, where T(n,k) = 1 if gcd(n,k) is prime, 0 otherwise.
  • A122431 (program): Riordan array ((1+x)^3,x).
  • A122432 (program): Riordan array (1/(1+x)^3,x).
  • A122434 (program): Expansion of (1+x)^3/(1+x+x^2).
  • A122437 (program): Allowable values of the “dropping time” of the Collatz (3x+1) iteration.
  • A122461 (program): Repetitions of even numbers four times.
  • A122471 (program): a(n)=7*a(n-1)-n for n> 0, a(0)=1.
  • A122485 (program): Values of A083097(k) such that A083097(k) = A083097(k+1) - 1.
  • A122491 (program): a(n) = n * Fibonacci(n) - Sum_ i=0..n Fibonacci(i).
  • A122497 (program): Let f(S) denote the interchange of 1’s and 2’s in S. Let S_0 = 1, S_ N+1 = f(S_N).S_N, where the dot indicates concatenation. Sequence gives S_0.S_1.S_2.S_3….
  • A122507 (program): Triangular in which row n contains first n terms of A018805.
  • A122515 (program): a(n) = A007504(n)-A046992(n).
  • A122522 (program): a(n) = a(n - 2) + a(n - 8).
  • A122551 (program): Denominators of the coefficients of the series for InverseErf(x).
  • A122552 (program): a(0)=a(1)=a(2)=1, a(n) = a(n-1) + a(n-2) + 2*a(n-3) for n > 2.
  • A122553 (program): a(0)=1, a(n)=3 for n > 0.
  • A122554 (program): Let S(1)= 1 and, for n>1 let S(n) be the smallest set containing x, 2x and x+2 for each element x in S(n-1). a(n) is the number of elements in S(n).
  • A122558 (program): a(0)=1, a(1)=3, a(n)=4a(n-1)+3a(n-2) for n>1.
  • A122562 (program): a(n) = n^3 + 114 * n.
  • A122571 (program): a(1)=a(2)=1, a(n) = 14*a(n-1) - a(n-2).
  • A122573 (program): Expansion of x(1 + x)(1 - 3x^2)/(1 - 4x^2 + x^4).
  • A122576 (program): G.f.: (1-2x+6x^2-2x^3+x^4)/((x-1)^3(x+1)^4).
  • A122586 (program): Leading digit of n expressed in base 3.
  • A122587 (program): Leading digit of n in base 4.
  • A122601 (program): a(n)=(n-th prime +1) modulo 7.
  • A122606 (program): n^(n+1) mod 7.
  • A122619 (program): n_ 2n .
  • A122620 (program): n_ n+1 .
  • A122638 (program): n+1 _n.
  • A122639 (program): n_ 2n+1 .
  • A122649 (program): Difference between the double factorial of the n-th nonnegative odd number and the double factorial of the n-th nonnegative even number.
  • A122650 (program): Fibonacci numbers starting at F(23).
  • A122652 (program): a(0) = 0, a(1) = 4; for n > 1, a(n) = 10*a(n-1) - a(n-2).
  • A122653 (program): a(n) = 10*a(n-1) - a(n-2) with a(0)=0, a(1)=6.
  • A122656 (program): n*floor(n/2)^2.
  • A122657 (program): a(n) = if n mod 2 = 1 then (n^2-1)*n^3/4 else n^5/4.
  • A122658 (program): a(n) = if n mod 2 = 1 then n^3*(n-1)^2/2 else n^5/2.
  • A122670 (program): If n mod 4 = 2 or n mod 4 = 3 then a(n) = 0 else let m=floor(n/4), then a(n) = (2*m)!/m!.
  • A122678 (program): Related to number of n-circum-C_5 H_5 systems.
  • A122679 (program): Related to number of n-circum-C_5 H_5 systems.
  • A122701 (program): a(0)=0, a(n) = 2*a(floor(n/2)) + n - 1 for n > 0.
  • A122709 (program): a(0)=1; thereafter a(n) = 9*n-3.
  • A122743 (program): Number of normalized polynomials of degree n in GF(2)[x,y].
  • A122746 (program): G.f.: 1/((1-2x)(1-2*x^2)).
  • A122747 (program): Bishops on an n X n board (see Robinson paper for details).
  • A122754 (program): 10*n-A101306(n).
  • A122756 (program): Odd-indexed terms, a(n) = 2^n. Even-indexed terms, a(n) = floor(2^n+2^(n-1)).
  • A122769 (program): Numbers k such that k^2 is of the form 3m^2 + 2m + 1 (A056109).
  • A122770 (program): Numbers k such that A056109(k) is a square.
  • A122788 (program): (1,3)-entry of the 3 X 3 matrix M^n, where M = 0, -1, 1 , 1, 1, 0 , 0, 1, 1 .
  • A122793 (program): Connell sum sequence (partial sums of the Connell sequence).
  • A122794 (program): Connell (3,2)-sum sequence (partial sums of the (3,2)-Connell sequence).
  • A122795 (program): Connell (5,3)-sum sequence (partial sums of the (5,3)-Connell sequence)
  • A122796 (program): Connell (3,5)-sum sequence (partial sums of the (3,5)-Connell sequence)
  • A122797 (program): A P_3-stuttered arithmetic progression with a(n+1)=a(n) if n is a triangular number, a(n+1)=a(n)+1 otherwise.
  • A122798 (program): A P_5-stuttered arithmetic progression with a(n+1) = a(n) if n is a pentagonal number, a(n+1) = a(n)+4 otherwise.
  • A122799 (program): A P_7-stuttered arithmetic progression with a(n+1)=a(n) if n is not a heptagonal number, a(n+1)=a(n)+2 otherwise.
  • A122800 (program): A P_4-stuttered arithmetic progression with a(n+1)=a(n) if n is square, a(n+1)=a(n)+2 otherwise.
  • A122803 (program): Powers of -2.
  • A122825 (program): a(n) = n + number of previous prime terms, a(1) = 1.
  • A122840 (program): a(n) is the number of 0’s at the end of n when n is written in base 10.
  • A122841 (program): Greatest k such that 6^k divides n.
  • A122874 (program): List of pairs n+7, 13-n, n >= 0.
  • A122876 (program): a(0)=1, a(1)=1, a(2)=2, a(n) = a(n-1) - a(n-2) for n>2.
  • A122878 (program): Periodic sequence of period 21 related to a simple scheduling problem.
  • A122879 (program): Periodic sequence of period 21.
  • A122895 (program): Characteristic function of natural numbers with number of divisors equal to a Fibonacci number.
  • A122918 (program): Expansion of (1+x)^2/(1+x+x^2)^2.
  • A122931 (program): Row sums of triangular array A122930.
  • A122952 (program): Decimal expansion of 3*Pi.
  • A122958 (program): a(0)=1, a(n) = 2 - 2^(n-1) for n>0.
  • A122968 (program): 27th powers: a(n) = n^27.
  • A122969 (program): 28th powers: a(n) = n^28.
  • A122970 (program): 29th powers: a(n) = n^29.
  • A122973 (program): Number of vertices on the surface of an icosahedron.
  • A122983 (program): a(n) = (2 + (-1)^n + 3^n)/4.
  • A122999 (program): G.f.: 1/(1 - x - 25*x^2).
  • A123001 (program): Binary numbers that start 10…
  • A123010 (program): a(n) = 5a(n-1) + a(n-2) - 5a(n-3), for n>4, with a(1)=1, a(2)=0, a(3)=4, a(4)=16.
  • A123022 (program): a(n) = n!b(n) where b(n) = (n-4)b(n-2)/(n*(n-1)) and b(0) = b(1) = 1.
  • A123023 (program): a(n) = (n-1)*a(n-2), a(0)=1, a(1)=0.
  • A123066 (program): (Number of numbers <= n with an odd number of distinct prime factors) - (number of numbers <= n with an even number of distinct prime factors).
  • A123068 (program): Numbers represented by the “Little Methuselah” quadratic form x^2 + 2y^2 + yz + 4*z^2.
  • A123072 (program): Bishops on an 8n+1 X 8n+1 board (see Robinson paper for details).
  • A123087 (program): Sequence of numbers such that a(2*n) + a(n) = n and a(n) is the smallest number such that a(n) >= a(n-1).
  • A123094 (program): Sum of first n 12th powers.
  • A123095 (program): Sum of first n 11th powers.
  • A123108 (program): a(n) = a(n-1) + a(n-2) - a(n-3), for n > 3, with a(0)=1, a(1)=0, a(2)=1, a(3)=1.
  • A123109 (program): a(0) = 1, a(1) = 3, a(n) = 3*a(n-1) + 3 for n > 1.
  • A123110 (program): Triangle T(n,k), 0 <= k <= n, read by rows given by [0,1,0,0,0,0,0,0,0,0,…] DELTA [1,0,-1,1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A123121 (program): Length of the n-th Zimin word (A082215(n)).
  • A123123 (program): Numbers n such that, modulo k with 2<=k<=n, only one of the residues is equal to 2.
  • A123128 (program): Add n to the n-th difference between consecutive primes.
  • A123135 (program): a(n) = n^3 plus sum of digits of n^3.
  • A123138 (program): The n-th digit of a(n-1) gives the position of digit n in a(n), a(1)=263514.
  • A123152 (program): a(n) = (n-th decimal digit of Pi) + 1.
  • A123157 (program): Sum of digits of the squares of prime numbers.
  • A123166 (program): Row sums of A123162.
  • A123167 (program): Continued fraction for c=sqrt(2)(exp(sqrt(2))+1)/(exp(sqrt(2))-1). a(2n-1) = 8n-6, a(2n) = 4*n-1.
  • A123168 (program): Continued fraction for c = sqrt(2)*(exp(sqrt(2))-1)/(exp(sqrt(2))+1).
  • A123169 (program): Continued fraction for sqrt(1/2)*(exp(sqrt(1/2))-1)/(exp(sqrt(1/2))+1).
  • A123183 (program): a(1)=-1; a(2)=-1; a(3)=-2; a(n) = 4a(n-1) - 3a(n-2) for n >= 4.
  • A123194 (program): a(n) = (n+1)*Fibonacci(n+2) + 3.
  • A123197 (program): (2n+1)(n+1)(2n^2+3*n-1).
  • A123198 (program): a(n)=[(n+1)(2n-1)]^2.
  • A123203 (program): A007318 * [1, 1, 4, 4, 4,…].
  • A123208 (program): Start with 1, then alternately add 2 or double.
  • A123219 (program): Expansion of -x(x^4 + 52x^3 - 122x^2 - 28x + 1) / ((x-1)(x^2 - 34x + 1)(x^2 + 6x + 1)).
  • A123231 (program): Row sums of A123230.
  • A123251 (program): Continued fraction for sqrt(2)*tan(1/sqrt(2)).
  • A123253 (program): Sum of 7th powers of digits of n.
  • A123270 (program): a(0)=1, a(1)=1, a(n) = 5a(n-1) + 4a(n-2).
  • A123273 (program): a(0) = 1; a(n) = the number of earlier terms, a(k), where gcd(a(k), a(floor(k/2))) = 1.
  • A123290 (program): Number of distinct binomial(n,2)-tuples of zeros and ones that are obtained as the collection of all 2 X 2 minor determinants of a 2 X n matrix over GF(2).
  • A123293 (program): Number of permutations of n distinct letters (ABCD…) each of which appears 4 times and having n-3 fixed points.
  • A123296 (program): Number of permutations of n distinct letters (ABCD…) each of which appears 5 times and having n-2 fixed points.
  • A123316 (program): Triangle read by rows: T(n,k)=(k+1)*n!/2 (1<=k<=n).
  • A123326 (program): Let M be the matrix defined in A111490. Sequence gives the sum of the elements of the submatrices (from the upper left element): M(1,1); M(1,1)+M(1,2)+M(1,2)+M(2,2); M(1,1)+M(1,2)+M(1,3)+M(2,1)+M(2,2)+M(2,3)+M(3,1)+M(3,2)+M(3,3), etc.
  • A123327 (program): a(n) = A000203(n) + A004125(n).
  • A123329 (program): Let M be the matrix defined in A111490. Sequence gives M(2,1)-M(1,2), M(2,1)+M(3,1)+M(3,2)-M(1,2)-M(1,3)-M(2,3), etc.
  • A123331 (program): Expansion of (c(q)^2/(3c(q^2))-1)/2 in powers of q where c(q) is a cubic AGM function.
  • A123335 (program): a(n) = -2*a(n-1) + a(n-2) for n>1, a(0)=1, a(1)=-1.
  • A123344 (program): Expansion of (1+3x)/(1+2x).
  • A123347 (program): Number of words of length n over the alphabet 1,2,3,4,5 such that 1 is not followed by an odd letter.
  • A123348 (program): Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
  • A123350 (program): a(n) = (n^4 + 2n^3 + 5n^2 + 4)/4.
  • A123357 (program): Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
  • A123358 (program): Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
  • A123363 (program): a(n) = n^3 + (-1)^(n+1).
  • A123365 (program): Values of k such that A046530(k) = (k+2)/3, where A046530(k) is the number of distinct residues of cubes mod k.
  • A123367 (program): a(n) = (n! - 2^n)/8, n >= 4.
  • A123384 (program): Number of bits in binary expansion of 10^n.
  • A123385 (program): a(n) = (n!)^2/2.
  • A123387 (program): Number of triangular numbers <= n-th prime.
  • A123390 (program): Triangle read by rows: n-th row starts with n and continues with half the previous value as long as that is even.
  • A123478 (program): Coefficients of series giving the best rational approximations to sqrt(7).
  • A123479 (program): Coefficients of series giving the best rational approximations to sqrt(6).
  • A123480 (program): Coefficients of the series giving the best rational approximations to sqrt(3).
  • A123482 (program): Coefficients of the series giving the best rational approximations to sqrt(11).
  • A123509 (program): Rohrbach’s problem: a(n) is the largest integer such that there exists a set of n integers that is a basis of order 2 for (0, 1, …, a(n)-1).
  • A123520 (program): Number of vertical dominoes in all possible tilings of a 2n X 3 grid by dominoes.
  • A123522 (program): Not of the form n + [log_10 n].
  • A123554 (program): Triangle read by rows: T(n,k) = number of labeled loopless digraphs with n nodes and k arcs (n >= 1, 0 <= k <= n*(n-1)).
  • A123564 (program): The infinite Fibonacci word reencoded by writing successive non-overlapping pairs of bits as decimal numbers.
  • A123567 (program): Recursive sum of 2*Omega(n), where Omega(n) is the sequence A001222.
  • A123575 (program): The Kruskal-Macaulay function L_3(n).
  • A123578 (program): The Kruskal-Macaulay function M_2(n).
  • A123582 (program): Values of k associated with A123728.
  • A123596 (program): Squares alternating with triangular numbers.
  • A123620 (program): Expansion of (1 + x + x^2) / (1 - 3x - 3x^2).
  • A123635 (program): Residue mod 3 of average of n-th and (n+1)st odd primes.
  • A123640 (program): Consider the 2^n compositions of n per row and mark only those ending in an odd part.
  • A123642 (program): a(n) = n! - 2^n.
  • A123650 (program): a(n) = 1 + n^2 + n^3 + n^5.
  • A123656 (program): a(n) = 1 + n^4 + n^6.
  • A123663 (program): Number of shared edges in a spiral of n unit squares.
  • A123667 (program): a(n) = n * 2^bigomega(n).
  • A123680 (program): a(n) = Sum_ k=0..n C(n+k-1,k)*k!.
  • A123681 (program): a(n) = (1/(n+1)) * Sum_ k=0..n C(n+k-1,k)*k! = A123680(n)/(n+1).
  • A123684 (program): Alternate A016777(n) with A000027(n).
  • A123720 (program): a(n) = 2^n + 2^(n-1) - n.
  • A123726 (program): Denominators of fractional partial quotients appearing in a continued fraction for the power series Sum_ n>=0 x^(2^n - 1)/(n+1)^s.
  • A123737 (program): Partial sums of (-1)^floor(n*sqrt(2)).
  • A123740 (program): Characteristic sequence for Wythoff AB-numbers A003623.
  • A123752 (program): a(n) = 7*a(n-2), a(0) = 1, a(1) = 2.
  • A123753 (program): Partial sums of A070941.
  • A123854 (program): Denominators in an asymptotic expansion for the cubic recurrence sequence A123851.
  • A123860 (program): a(n) = ceiling( (7 + sqrt(49+24*n))/2 ).
  • A123865 (program): a(n) = n^4 - 1.
  • A123866 (program): a(n) = n^6 - 1.
  • A123867 (program): a(n) = n^10 - 1.
  • A123868 (program): a(n) = n^12 - 1.
  • A123871 (program): Expansion of g.f.: (1+x+x^2)/(1-4x-4x^2).
  • A123884 (program): Expansion of phi(x) * phi(-x^6) / chi(-x^2) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A123903 (program): Total number of “Emperors” in all tournaments on n labeled nodes.
  • A123919 (program): Number of numbers congruent to 2 or 4 mod 6 and <= n.
  • A123920 (program): Number of numbers congruent to 2 or 4 mod 6 between n and 2n inclusive.
  • A123932 (program): a(0) = 1, a(n) = 4 for n > 0.
  • A123941 (program): The (1,2)-entry in the 3 X 3 matrix M^n, where M = 2, 1, 1 , 1, 1, 0 , 1, 0, 0 .
  • A123968 (program): a(n) = n^2 - 3.
  • A123972 (program): a(n) = n^3 - n^2 - 2n + 1.
  • A124007 (program): Number of permutations of n distinct letters (ABCD…) each of which appears thrice with n-3 fixed points.
  • A124011 (program): Add three, add six, add nine, ….
  • A124072 (program): First differences of A129819.
  • A124080 (program): 10 times triangular numbers: a(n) = 5n(n + 1).
  • A124087 (program): 9th column of Catalan triangle A009766.
  • A124088 (program): 10th column of Catalan triangle A009766.
  • A124089 (program): Binomial(n,6)-1.
  • A124090 (program): C(n,7)-1.
  • A124093 (program): Triangular numbers alternating with squares.
  • A124107 (program): Numbers n such that n is the sum of the augmenting factorials of the digits of n, e.g. 733 = 7 + 3! + (3!)!.
  • A124115 (program): a(n) = 2*prime(n) - prime(n+1) + 2.
  • A124133 (program): a(n) = (-1/2)Sum_ i1 + i2 + i3 = 2n ((2n)!/(i1! i2! i3!))B(i1), where B are the Bernoulli numbers (with i1, i2, i3 >= 1).
  • A124148 (program): Fibonacci triangle read by rows; the triangles below read by rows. Analog of A124171.
  • A124152 (program): a(n) = Fibonacci(6, n).
  • A124156 (program): Thickness of complete graph K_n.
  • A124158 (program): Maximal number of edges in a rectangle visibility graph with n nodes.
  • A124166 (program): 100*(10^n-1)/9.
  • A124167 (program): a(n) = 10*(10^n-1).
  • A124171 (program): Sequence obtained by reading the triangles shown below by rows.
  • A124174 (program): Sophie Germain triangular numbers tr: 2*tr+1 is also a triangular number.
  • A124179 (program): Prime(R(p)) where Prime(i) is the i-th prime and R(p) is the value of the reverse of the digits of prime p.
  • A124180 (program): Prime(R(n)) where Prime(i) is the i-th prime and R(n) is the value of the reverse of the digits of n.
  • A124195 (program): a(1)=1. a(n) = n - GCD(a(n-1),n).
  • A124197 (program): Number of subsets S of 1,2,3,…,n , including the empty subset, such that if x and y are in S with x<y and x+y even, then (x+y)/2 is also in S.
  • A124203 (program): a(n) = 2n + “reverse of n-written-in-binary” + 2.
  • A124204 (program): Numbers k such that 20*k + 1 is prime.
  • A124229 (program): Numerator of g(n) defined by g(1)=1, g(2n)=1/g(n)+1, g(2n+1)=g(2n).
  • A124230 (program): Denominator of g(n) defined by g(1)=1, g(2n)=1/g(n)+1, g(2n+1)=g(2n).
  • A124258 (program): Triangle whose rows are sequences of increasing and decreasing squares: 1; 1,4,1; 1,4,9,4,1; …
  • A124296 (program): a(n) = 5F(n)^2 - 5F(n) + 1, where F(n) = Fibonacci(n).
  • A124297 (program): a(n) = 5F(n)^2 + 5F(n) + 1, where F(n) = Fibonacci(n).
  • A124302 (program): Number of set partitions with at most 3 blocks; number of Dyck paths of height at most 4; dimension of space of symmetric polynomials in 3 noncommuting variables.
  • A124303 (program): Number of set partitions of length <= 4; sum of first 4 columns of triangle of Stirling numbers of 2nd kind; dimension of space of symmetric polynomials in 4 noncommuting variables.
  • A124349 (program): Numbers of directed Hamiltonian cycles on the n-prism graph.
  • A124350 (program): a(n) = 4n(floor(n^2/2)+1). For n>=3, this is the number of directed Hamiltonian paths on the n-prism graph.
  • A124351 (program): Order of the automorphism group of the n-prism graph.
  • A124353 (program): Number of (directed) Hamiltonian circuits on the n-antiprism graph.
  • A124354 (program): Orders of the automorphisms groups of the n-antiprism graph.
  • A124355 (program): Number of (directed) Hamiltonian cycles on the complete graph K_n.
  • A124356 (program): Number of (directed) Hamiltonian cycles on the Moebius ladder graph M_n (for n>=4).
  • A124363 (program): a(n) = n^3 + 71*n + 1
  • A124388 (program): 27*n+18.
  • A124399 (program): a(n) = 4^(n - bitcount(n)) where bitcount(n) = A000120(n).
  • A124400 (program): a(n) = a(n-1) + 3*a(n-2) - a(n-4), with a(0)=1, a(1)=1, a(2)=4, a(3)=7.
  • A124434 (program): LCM (least common multiple) of A001043 (sum of consecutive primes) and A001223 (difference of consecutive primes).
  • A124437 (program): Experience Points thresholds for levels in the P&P-RPG “Das Schwarze Auge” (DSA, aka “The Dark Eye”).
  • A124479 (program): From the game of Quod: number of “squares” on an n X n array of points with the four corner points deleted.
  • A124502 (program): a(1)=a(2)=1; thereafter, a(n+1) = a(n) + a(n-1) + 1 if n is a multiple of 5, otherwise a(n+1) = a(n) + a(n-1).
  • A124610 (program): a(n) = 5a(n-1) + 2a(n-2), n > 1; a(0) = a(1) = 1.
  • A124625 (program): Even numbers sandwiched between 1’s.
  • A124642 (program): Antidiagonal sums of A096465.
  • A124647 (program): a(n) = (2n + 1)*3^n.
  • A124657 (program): Factorials that are abundant numbers.
  • A124669 (program): Product of successive primes minus 2.
  • A124671 (program): Row sums of A126277 = binomial transform of (1, 2, 2, 3, 4, 4, 4,…)
  • A124678 (program): Number of conjugacy classes in PSL_2(p), p = prime(n).
  • A124696 (program): Number of base-3 circular n-digit numbers with adjacent digits differing by 1 or less.
  • A124698 (program): Number of base 5 circular n-digit numbers with adjacent digits differing by 1 or less.
  • A124741 (program): a(n) = largest of those positive integers which are coprime to both n and n+1 and which are <= n.
  • A124754 (program): Alternating sum of compositions in standard order.
  • A124757 (program): Zero-based weighted sum of compositions in standard order.
  • A124759 (program): Sum of products of consecutive terms for compositions in standard order.
  • A124778 (program): Number of unlabeled unordered rooted forests associated with compositions in standard order.
  • A124797 (program): Sum of cyclic permutations of 123…n seen as number written in base n+1: ((n+1)^n-1)*(n+1)/2.
  • A124805 (program): Number of base 4 circular n-digit numbers with adjacent digits differing by 2 or less.
  • A124808 (program): Number of numbers k <= n such that k^2 + 1 is squarefree.
  • A124820 (program): Expansion of (1-x)/(1-4x+3x^2-x^3).
  • A124861 (program): Expansion of 1/(1-x-3x^2-4x^3-2x^4).
  • A124867 (program): Numbers that are the sum of 3 distinct primes.
  • A124868 (program): Natural numbers that are not the sum of 3 distinct primes.
  • A124897 (program): mu(n^2 + 1), mu = A008683.
  • A124899 (program): Sierpinski quotient ((2n-1)^(2n-1) + 1)/(2n) = A014566(2n-1)/(2n).
  • A124923 (program): a(n) = n^(n-1) + 1.
  • A124925 (program): Interlaced triples: a(3n+1)=1, a(3n+2) = 2n+3, a(3n+3)= A028387(n).
  • A124927 (program): Triangle read by rows: T(n,0)=1, T(n,k)=2*binomial(n,k) if k>0 (0<=k<=n).
  • A124928 (program): Triangle read by rows: T(n,0) = 1, T(n,k) = 3*binomial(n,k) if k>=0 (0<=k<=n).
  • A125082 (program): a(n) = n^4 - n^3 - n^2 - n - 1.
  • A125083 (program): a(n) = n^5-n^4-n^3-n^2-n-1.
  • A125089 (program): First nonzero digit of solution to log_n(z) = -z, where log_n stands for the base-n logarithm.
  • A125117 (program): First differences of A034887.
  • A125128 (program): a(n) = 2^(n+1) - n - 2, or partial sums of main diagonal of array A125127 of k-step Lucas numbers.
  • A125130 (program): Successive sums of consecutive primes that form a triangular grid.
  • A125145 (program): a(n) = 3a(n-1) + 3a(n-2). a(0) = 1, a(1) = 4.
  • A125168 (program): a(n) = gcd(n, A032741(n)) where A032741(n) is the number of proper divisors of n.
  • A125169 (program): a(n) = 16*n + 15.
  • A125176 (program): Row sums of A125175.
  • A125180 (program): a(n) = 2*a(n-1) + prime(n) - prime(n-1), a(1)=2, where prime(n) denotes the n-th prime.
  • A125200 (program): n(4n^2 + n -1)/2.
  • A125201 (program): a(n) = 8n^2 - 7n + 1.
  • A125202 (program): a(n) = 4n^2 - 6n + 1.
  • A125254 (program): Smallest prime divisor of 4n-1 that is of the form 4k-1.
  • A125255 (program): Smallest prime divisor of 4n-1.
  • A125256 (program): Smallest odd prime divisor of n^2 + 1.
  • A125266 (program): Number of repetitions in A007918.
  • A125287 (program): a(n) = mu(n) * A000217(n).
  • A125299 (program): Numbers starting with a consonant.
  • A125518 (program): a(n) = tau(n) * prime(n).
  • A125521 (program): a(n) is the minimal difference between two distinct n-digit numbers with property that when one of them is typed into a calculator and rotated 180 degrees, the other one is seen.
  • A125558 (program): Central column of triangle A090181.
  • A125575 (program): Initial digit of squares of primes.
  • A125577 (program): a(0) = 1; for n >= 1, a(n) = n^2 - a(n-1).
  • A125592 (program): Evil numbers (A001969) multiplied by 2.
  • A125598 (program): a(n) = ((n+1)^(n-1)-1)/n.
  • A125602 (program): Centered triangular numbers that are prime.
  • A125603 (program): Numbers n such that 3n(n-1)/2 + 1 is prime.
  • A125641 (program): Square of the (3,1)-entry of the 3 X 3 matrix M^n, where M = [1,0,0; 1,1,0, 1,i,1].
  • A125650 (program): Numerator of n(n+3)/(4(n+1)(n+2)) = sum(k=1..n, 1/(k(k+1)(k+2)) ).
  • A125651 (program): Numbers k such that A125650(k) is a perfect square.
  • A125652 (program): Numbers m such that m^2=A125650(k) for some k (belonging A125651).
  • A125678 (program): a(0) = 1; for n>0, a(n) = (a(n-1)^2 reduced mod n) + 1.
  • A125682 (program): a(n) = (6^n-1)*3/5.
  • A125687 (program): The base 6 numbers 4 44 444 4444 44444 … converted to base 10.
  • A125725 (program): Numbers whose base-7 representation is 222….2.
  • A125729 (program): Numbers whose base 7 representation is 555….5.
  • A125758 (program): Numbers congruent to 4 or 7 mod 9.
  • A125791 (program): a(n) = 2^(n(n-1)(n-2)/6) for n>=1.
  • A125811 (program): Number of coefficients in the n-th q-Bell number as a polynomial in q.
  • A125816 (program): a(n) = ((1+sqrt(13))^n + (1-sqrt(13))^n)/2.
  • A125817 (program): a(n) = ((1 + 3sqrt(2))^n - (1 - 3sqrt(2))^n)/(2*sqrt(2)).
  • A125818 (program): a(n) = ((1 + 3sqrt(2))^n + (1 - 3sqrt(2))^n)/2.
  • A125823 (program): Numbers whose base 7 representation is 4444….4.
  • A125824 (program): Denominator of n!/3^n.
  • A125831 (program): a(n) = (5^n - 1)/2.
  • A125833 (program): Numbers whose base 5 representation is 333333…….3.
  • A125835 (program): Numbers whose base 8 or octal representation is 22222222…….2.
  • A125836 (program): Numbers whose base 8 or octal representation is 555555555……5.
  • A125837 (program): Numbers whose base 8 or octal representation is 6666666……6.
  • A125857 (program): Numbers whose base-9 representation is 22222222…….2.
  • A125911 (program): Product of the even divisors of n.
  • A125913 (program): Sprague-Grundy values for octal game .144.
  • A125916 (program): Sprague-Grundy values for octal game .15 (Guiles).
  • A125925 (program): Sprague-Grundy values for octal game .351.
  • A125962 (program): Numbers whose base-9 representation is 555555555……5.
  • A125993 (program): A106486-encodings of combinatorial games with value -1.
  • A126001 (program): A106486-encodings of nonnegative combinatorial games, i.e., games whose value is >= 0.
  • A126019 (program): a(0)=1, a(1)=2; for n>1, a(n)=3a(n-1)+4a(n-2)+5.
  • A126023 (program): a(0)=0, a(1)=1; for n>1, a(n) = a(n-1)*(a(n-1)+a(n-2)).
  • A126026 (program): Conjectured upper bound on area of the convex hull of any edge-to-edge connected system of regular unit hexagons (n-polyhexes).
  • A126073 (program): Sum of numbers <= n which are multiples of 3 or 5 but not 15.
  • A126109 (program): a(n) = (5*10^n + 1)/3.
  • A126114 (program): Ultimate fixed-point under the mapping n->f(n), where f(n)=n if n is square else f(n)=n-Floor(Sqrt(n)).
  • A126116 (program): a(n) = a(n-1) + a(n-3) + a(n-4), with a(0)=a(1)=a(2)=a(3)=1.
  • A126119 (program): Numerators of sequence of fractions with e.g.f. (1+x)/(1-x)^(3/2).
  • A126120 (program): Catalan numbers (A000108) interpolated with 0’s.
  • A126167 (program): Number of primitive exponential amicable pairs (i,j) with i<j and i<=10^n.
  • A126184 (program): Number of hex trees with n edges and having no nonroot nodes of outdegree 2.
  • A126192 (program): Product of the even divisors of 2n.
  • A126199 (program): a(n) = prime(n)*prime(n+1) + prime(n) + prime(n+1).
  • A126235 (program): Minimum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k.
  • A126236 (program): Maximum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k.
  • A126237 (program): Length of row n in table A126014.
  • A126264 (program): a(n) = 5n^2 + 3n.
  • A126269 (program): Numbers n such that hcl(n,n) < hcl(n,n-1) where hcl(n,i) is the Huffman code length; see comments.
  • A126271 (program): a(n) = order of Galois group of the polynomial P(x) + n if P(x) + n (after dividing by the gcd of its coefficients) is irreducible, otherwise a(n) = 0, where P(x) = 128x^8 - 256x^6 + 160x^4 - 32x^2 + 1.
  • A126274 (program): Partial sum of A005915.
  • A126275 (program): Moment of inertia of all magic squares of order n.
  • A126281 (program): a(n) is the least m to satisfy the requirements of A052130.
  • A126284 (program): a(n) = 52^n - 4n - 5.
  • A126325 (program): Triangle read by rows: T(n,k) = binomial(2*n+1, n-k) (1 <= k <= n).
  • A126328 (program): Rounded value of n!/(n(n+1)/2); A000142(n)/A000217(n).
  • A126332 (program): Numbers n such that 10n + 13 is prime.
  • A126335 (program): a(n) = n(4n^2+5*n-3)/2.
  • A126358 (program): Number of base 4 n-digit numbers with adjacent digits differing by one or less.
  • A126387 (program): Read binary expansion of n from the left; keep track of the excess of 1’s over 0’s that have been seen so far; sequence gives maximum(excess of 1’s over 0’s).
  • A126391 (program): a(1)=1; for n>1: a(n) = sum of all subsets of (a(1),..,a(n-1)).
  • A126420 (program): a(n) = n^3 - n - 1.
  • A126423 (program): a(n) = n^4 - n - 1.
  • A126426 (program): a(n) = n^5 - n - 1.
  • A126431 (program): a(n) = n * 10^n.
  • A126446 (program): Column 0 of triangle A126445; a(n) = binomial( binomial(n+2,3), n).
  • A126447 (program): Column 1 of triangle A126445; a(n) = C( C(n+3,3) - 1, n).
  • A126451 (program): Column 0 of triangle A126450; a(n) = C( C(n+2,3) + 1, n).
  • A126452 (program): Column 1 of triangle A126450; a(n) = C( C(n+3,3), n).
  • A126455 (program): Column 0 of triangle A126454; a(n) = C( C(n+2,3) + 2, n).
  • A126456 (program): Column 1 of triangle A126454; a(n) = C( C(n+3,3) + 1, n).
  • A126458 (program): Column 0 of triangle A126457; a(n) = C( C(n+2,3) + 3, n).
  • A126459 (program): Column 1 of triangle A126457; a(n) = C( C(n+3,3) + 2, n).
  • A126473 (program): Number of strings over a 5 symbol alphabet with adjacent symbols differing by three or less.
  • A126560 (program): a(n) = gcd(4(n+1)(n+2), n(n+3)), periodic with 8-cycle 4,2,2,4,8,2,2,8.
  • A126562 (program): Number of intersections of at least four edges in a cube of n X n X n smaller cubes.
  • A126587 (program): a(n) is the number of integer lattice points inside the right triangle with legs 3n and 4n (and hypotenuse 5n).
  • A126592 (program): Sum of numbers less than or equal to n which are multiples of 3 or 5.
  • A126605 (program): Final three digits of 2^n.
  • A126606 (program): Fixed point of transformation of the seed sequence 0,2 .
  • A126614 (program): a(n) = (2^prime(n) + 1)/3.
  • A126644 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4,5,6 and at least one of digits 7,8,9.
  • A126645 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4 and 5, at least one of digits 6,7 and at least one of digits 8,9.
  • A126646 (program): a(n) = 2^(n+1) - 1.
  • A126664 (program): Continued fraction expansion of sqrt(3)/2.
  • A126665 (program): a(n) = -n^2 + 9n + 53.
  • A126696 (program): Tenth-squares: floor(n/10)*ceiling(n/10).
  • A126719 (program): a(n) = -n^2 + 9n + 23.
  • A126759 (program): a(0) = 1; a(2n) = a(n); a(3n) = a(n); otherwise write n = 6i+j, where j = 1 or 5 and set a(n) = 2i+2 if j = 1, otherwise a(n) = 2i+3.
  • A126760 (program): a(0) = 0, a(2n) = a(n), a(3n) = a(n), a(6n+1) = 2n + 1, a(6n+5) = 2n + 2.
  • A126773 (program): a(n) = largest divisor of n which is coprime to the largest proper divisor of n. (a(1)=1.).
  • A126785 (program): Numbers k such that 10*k + 11 is prime.
  • A126792 (program): Removing the first, fourth, seventh, tenth … term of the sequence yields the original sequence, augmented by 1.
  • A126804 (program): a(n) = (2n)! / (n-1)!.
  • A126812 (program): Ramanujan numbers (A000594) read mod 4.
  • A126813 (program): Ramanujan numbers (A000594) read mod 8.
  • A126825 (program): Ramanujan numbers (A000594) read mod 3.
  • A126826 (program): Ramanujan numbers (A000594) read mod 9.
  • A126832 (program): Ramanujan numbers (A000594) read mod 5.
  • A126862 (program): Numbers n that have a component C(1,1) when expanded in the binomial basis of order t=3.
  • A126867 (program): Largest even semiprime <= n^2.
  • A126868 (program): a(n) = (n+1)!! mod n.
  • A126869 (program): a(n) = Sum_ k = 0..n binomial(n,floor(k/2))*(-1)^(n-k).
  • A126883 (program): a(n) = (2^0)(2^1)(2^2)*(2^3)…(2^n)-1 = 2^T(n) - 1 where T(n) = A000217(n) is the n-th triangular number.
  • A126884 (program): a(n) = (2^0)(2^1)(2^2)*(2^3)…(2^n)+1 = 2^T_n+1 (cf. A000217).
  • A126890 (program): Triangle read by rows: T(n,k) = n(n+2k+1)/2, 0 <= k <= n.
  • A126900 (program): Coordination sequence for 6-dimensional cyclotomic lattice Z[zeta_18].
  • A126930 (program): Inverse binomial transform of A005043.
  • A126935 (program): Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(n,3).
  • A126950 (program): a(1) = 1; for n>1, a(n) = the smallest number p > a(n-1) such that (a(n-1)+p)/2 is a cube.
  • A126951 (program): List of pairs: k followed by k^3.
  • A126964 (program): a(n) = 2n(6*n-1).
  • A126965 (program): a(n) = (2n)!(2n-1)/(2^nn!).
  • A126972 (program): Number of distinct values taken by the entropy for permutations of [1..n], where the entropy of a permutation pi is Sum_ k=1..n (pi(k)-k)^2.
  • A126978 (program): a(n) = 104*n + 9977.
  • A126979 (program): a(n) = 24*n + 233.
  • A126980 (program): a(n) = 14*n + 47.
  • A126995 (program): a(n) = binomial(prime(n+2), 3).
  • A126996 (program): a(n) = binomial(prime(3+n), prime(3)).
  • A126997 (program): a(n) = binomial(prime(4+n), prime(4)).
  • A126998 (program): a(n) = binomial(prime(n+5), prime(5)).
  • A127032 (program): Maximal value of m such that 5^m <= n! : a(n) = floor( log(n!) / log(5) ).
  • A127040 (program): a(n) = binomial(floor((3n+4)/2)),floor(n/2)).
  • A127064 (program): a(0)=1. a(n) = a(prime(n)(mod n)) + 1, where prime(n) is the n-th prime.
  • A127069 (program): Number of lines in a Pauli graph of order n.
  • A127109 (program): n! in base 5.
  • A127110 (program): n! in base 3.
  • A127112 (program): n! in base 4.
  • A127113 (program): n! in base 6.
  • A127114 (program): n! in base 7.
  • A127115 (program): n! in base 8.
  • A127116 (program): n! in base 9.
  • A127146 (program): Q(n,4), where Q(m,k) is defined in A127080 and A127137.
  • A127147 (program): Q(n,5), where Q(m,k) is defined in A127080 and A127137.
  • A127148 (program): Q(n,6), where Q(m,k) is defined in A127080 and A127137.
  • A127161 (program): Integers whose aliquot sequences terminate by encountering a prime number.
  • A127191 (program): Related to the function “shin” - see reference for precise definition.
  • A127197 (program): Numerator of n-th Van der Waerden-Ulam binary measure of the primes.
  • A127207 (program): Half-indexed Lucas numbers a(n)=round(sqrt((1+sqrt(5))/2)^n) a(2n)=L(n)=A000032, so a(n)=L(n/2).
  • A127210 (program): a(n) = 3^n*Lucas(n), where Lucas = A000204.
  • A127211 (program): a(n) = 4^n*Lucas(n), where Lucas = A000204.
  • A127226 (program): a(0)=2, a(1)=2, a(n) = 2a(n-1) + 6a(n-2).
  • A127227 (program): a(n)= numerator of ((n + 3)! - (n - 3)!)/(n!).
  • A127228 (program): a(n)= numerator of ((n + 4)! - (n - 4)!)/(n!).
  • A127229 (program): a(n)= numerator of ((n + 5)! - (n - 5)!)/(n!).
  • A127230 (program): a(n) = (2n)! - 1.
  • A127231 (program): a(n) = (2n)! + 1.
  • A127236 (program): A Thue-Morse binomial triangle.
  • A127239 (program): Central coefficients of Thue-Morse binomial triangle A127236.
  • A127240 (program): Partial sums of central coefficients of Thue-Morse binomial triangle A127236.
  • A127241 (program): A Thue-Morse triangle.
  • A127243 (program): Triangle whose k-th column is generated by (1+A010060(1+k)x)*x^k.
  • A127245 (program): Row sums of a signed Thue-Morse related triangle.
  • A127246 (program): Row sums of a Thue-Morse related triangle.
  • A127250 (program): Sequence consisting of 1,3 or 5 with 3’s occurring at the odious indices given by A091855 and 5’s occurring at twice these odious indices.
  • A127252 (program): Sequence composed of 1 and -1 with the -1’s occurring at odious indexed positions given by A091855.
  • A127254 (program): (0,1) sequence whose zero positions are indexed by twice the odious numbers given by A091855.
  • A127255 (program): Partial sums of A127252.
  • A127261 (program): a(0)=2, a(1)=2, a(n) = 2a(n-1) + 10a(n-2).
  • A127262 (program): a(0)=2, a(1)=2, a(n) = 2a(n-1) + 12a(n-2).
  • A127267 (program): a(n) = floor(n/pi(n)), where pi(n)=A000720(n) is the number of primes <=n.
  • A127276 (program): Hankel transform of A127275.
  • A127282 (program): Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A126315/A126316.
  • A127316 (program): a(n) = 2n^2 - 4n + 73.
  • A127321 (program): First 4-dimensional hyper-tetrahedral coordinate; repeat m C(m+3,4) times; 4-D analog of A056556.
  • A127329 (program): Semiprimes equal to the sum of three primes in arithmetic progression.
  • A127330 (program): Begin with the empty sequence and a starting number s = 0. At step k (k >= 1) append the k consecutive numbers s to s+k-1 and change the starting number (for the next step) to 2s+2.
  • A127365 (program): Signed repeated natural numbers.
  • A127369 (program): (n^3+n)*4^n.
  • A127407 (program): Negative value of coefficient of x^(n-2) in the characteristic polynomial of a certain n X n integer circulant matrix.
  • A127408 (program): Negative value of coefficient of x^(n-3) in the characteristic polynomial of a certain n X n integer circulant matrix.
  • A127419 (program): Recurrence: a(n) = a(n-1) + floor( (sqrt(8 * a(n-1) - 7) - 1)/2 ) for n>=2 with a(0)=1, a(1)=2.
  • A127421 (program): Numbers whose decimal expansion is a concatenation of 2 consecutive increasing nonnegative numbers.
  • A127423 (program): a(1) = 1; for n > 1, a(n) = n concatenated with n - 1.
  • A127427 (program): a(n) = v_3( (6n)! ) - v_3( (3n)! ), where v_3(N) is the 3-adic valuation A007949(N).
  • A127428 (program): v_5( (10n)! ) - v_5( (5n)! ), where v_p(N) is the p-adic valuation defined in A112765.
  • A127451 (program): Beatty sequence for 1/(1 - e^Pi + Pi^e), complement of A127450.
  • A127473 (program): a(n) = phi(n)^2.
  • A127507 (program): Triangle read by rows: T(n,k) = mu(n) where 1<=k<=n and mu=A008683.
  • A127509 (program): Number of n-tuples where each entry is chosen from the subsets of 1,2,3 such that the intersection of all n entries contains exactly one element.
  • A127511 (program): a(n) = mu(n) * 2^(n-1).
  • A127513 (program): Partial sums of A127511.
  • A127540 (program): Number of odd-length branches starting at the root in all ordered trees with n edges.
  • A127546 (program): a(n) = F(n)^2 + F(n+1)^2 + F(n+2)^2, where F(n) denotes the n-th Fibonacci number.
  • A127547 (program): a(n) = 13n + 4.
  • A127554 (program): Sum of the digits of left factorial !n.
  • A127575 (program): Numbers n such that 16n+15 is prime.
  • A127576 (program): Primes of the form 16n+15.
  • A127630 (program): Expansion of (1+x-x^2-x^3)/(1+x^2)^2.
  • A127647 (program): Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n).
  • A127648 (program): Triangle read by rows: row n consists of n zeros followed by n+1.
  • A127669 (program): Number of numbers mapped to A127668(n) with the map described there.
  • A127670 (program): Discriminants of Chebyshev S-polynomials A049310.
  • A127692 (program): Expansion of psi(x^4) + x * psi(x^12) in powers of x where psi() is a Ramanujan theta function.
  • A127693 (program): Expansion of psi(x^2) + x * psi(x^10) in powers of x where psi() is a Ramanujan theta function.
  • A127694 (program): Absolute value of coefficient of x^3 in polynomial whose zeros are 5 consecutive integers starting with the n-th integer.
  • A127698 (program): Sum of n-th triangular number and its reversal.
  • A127701 (program): Infinite lower triangular matrix with (1, 2, 3, …) in the main diagonal, (1, 1, 1, …) in the subdiagonal and the rest zeros.
  • A127705 (program): Row sums of A127704.
  • A127708 (program): Number of non-commutative rings with 1 containing n elements.
  • A127712 (program): Row sums of the inverse of the triangle A(n,k) = 1/F(n+1) if k <= n <= 2k, 0 otherwise.
  • A127713 (program): A bisection of the row sums of the inverse of the triangle A(n,k) = 1/F(n+1) if k <= n <= 2k, 0 otherwise.
  • A127721 (program): Floor of square root of sum of squares of n consecutive numbers.
  • A127722 (program): Floor of square root of sum of squares of n consecutive odd numbers.
  • A127723 (program): Floor of square root of sum of squares of the first n consecutive even numbers.
  • A127733 (program): Square of A127648 = Triangle read by rows, n^2 preceded by (n-1) zeros.
  • A127736 (program): a(n) = n(n^2+2n-1)/2.
  • A127739 (program): Triangle read by rows, in which row n contains the triangular number T(n) = A000217(n) repeated n times; smallest triangular number greater than or equal to n.
  • A127750 (program): Row sums of inverse of number triangle A(n,k) = 1/(2n+1) if k <= n <= 2k, 0 otherwise.
  • A127752 (program): Row sums of inverse of number triangle A(n,k) = 1/(3n+1) if k <= n <= 2k, 0 otherwise.
  • A127769 (program): a(n)=3C(4n-2,2n)/(2n+1)-20^n.
  • A127773 (program): Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
  • A127774 (program): Triangle read by rows: row n consists of n-1 zeros followed by A000292(n).
  • A127775 (program): Triangle read by rows: row n consists of n-1 zeros followed by 2n-1.
  • A127778 (program): Triangle T(n,k) = A002411(k) read by rows.
  • A127780 (program): A127775 * A002260 as infinite lower triangular matrices.
  • A127802 (program): a(0) = 1, a(n) = 3*A036987(n), n>1.
  • A127804 (program): a(2n)=4^n, a(4n+3)-(2^(4n+3)+2^(2*n+1))=a(n).
  • A127854 (program): Largest number k such that k^2 divides A007781(6n+1).
  • A127858 (program): Positive integers n such that r(n^2)=r(n)^2, where r is the cyclic replacement map of the digits d of n in base 12, that is, d->d+1 if d<11 and d->0 if d=11.
  • A127859 (program): a(n)=r(A127858(n)) where A127858 is the sequence of positive integers with the property that r(n^2)=r(n)^2 and where r if the cyclic replacement map of the digits d of n in base 12 defined by d->d+1 if d<11 and d->0 if d=11.
  • A127860 (program): a(n)=A127858(n)^2 where A127858 is the sequence of positive integers with the property that r(n^2)=r(n)^2 and where r if the cyclic replacement map of the digits d of n in base 12 defined by d->d+1 if d<11 and d->0 if d=11.
  • A127861 (program): a(n)=A127859(n)^2 where A127859(n)=r(A127858(n)) and A127858 is the sequence of positive integers with the property that r(n^2)=r(n)^2, where r if the cyclic replacement map of the digits d of n in base 12 defined by d->d+1 if d<11 and d->0 if d=11.
  • A127864 (program): Number of tilings of a 2xn board with 1x1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).
  • A127873 (program): a(n) = (n^3)/2 + (3n^2)/2 + 3n + 3.
  • A127876 (program): Integers of the form (x^3)/6 + (x^2)/2 + x + 1.
  • A127878 (program): a(n) = n^4 + 4n^3 + 12n^2 + 24*n + 24.
  • A127883 (program): a(n) = 60*(n^5/120 + n^4/24 + n^3/6 + n^2/2 + n + 1).
  • A127884 (program): a(n) = floor(Fibonacci(n)/n).
  • A127904 (program): Smallest m such that A008687(m) = n.
  • A127906 (program): a(n) = (n in base 10) * (n in base 2).
  • A127917 (program): Product of three numbers: n-th prime, previous number, and following number.
  • A127918 (program): Half of product of three numbers: n-th prime, previous and following number.
  • A127919 (program): 1/3 of product of three numbers: the n-th prime, the previous number and the following number.
  • A127920 (program): 1/6 of product of three numbers: n-th prime, previous and following number.
  • A127921 (program): 1/12 of product of three numbers: n-th prime, previous and following number.
  • A127922 (program): 1/24 of product of three numbers: n-th prime, previous and following number.
  • A127932 (program): a(4n) = 4n+1, a(4n+1) = a(4n+2) = a(4n+3) = 4n+4.
  • A127934 (program): a(8n)=8n+1, a(8n+1)=a(8n+2)=a(8n+3)=8n+5, a(8n+4)=8n+6, a(8n+5)=a(8n+6)=a(8n+7)=8n+8.
  • A127943 (program): a(n) = 2^binomial(n+1,2)/A046161(n).
  • A127944 (program): Partial sums of A093049.
  • A127945 (program): Hankel transform of central coefficients of (1+k*x-2x^2)^n, k arbitrary integer.
  • A127946 (program): Hankel transform of central coefficients of (1+k*x-3x^2)^n, k arbitrary integer.
  • A127947 (program): Hankel transform of central coefficients of (1+k*x+5x^2)^n, k arbitrary integer.
  • A127948 (program): Triangle, A004736 * A127899.
  • A127949 (program): A000012 as an infinite lower triangular matrix with all 1’s; A127899 = a simple transform; then A000012 * A127899. Given A051340, change all 1’s to -1. Triangle read by rows, (n-1) -1’s followed by “n”.
  • A127960 (program): a(n) = n^2*3^n.
  • A127961 (program): A007583(n) written in binary.
  • A127968 (program): a(n) = F(n+1) + (1-(-1)^n)/2, where F() = Fibonacci numbers A000045.
  • A127973 (program): a(2n)=A060632(n); a(2n+1)=A048896(n)/2.
  • A127975 (program): Repeat 3^n three times.
  • A127976 (program): a(n) = ((6n + 10)/27)2^(n-1) + ((-1)^(n-1))(6n + 5)/27.
  • A127980 (program): a(n) = (n + 2/3)2^(n-1) - 1/2 - (-1)^(n-1)(1/6).
  • A127981 (program): a(n) = (n + 1/3)2^(n-1) - 1/2 + (-1)^(n-1)(1/6).
  • A127982 (program): Numbers of the form (n - 1/3)2^(n) - n/2 + 1/4 + (-1)^n/12.
  • A127983 (program): Numbers of the form (n - 2/3)*2^(n) - n/2 + 3/4 - (-1)^n/12.
  • A127984 (program): a(n) = (n/3 + 7/9)*2^(n - 1) + (-1)^n/9.
  • A127985 (program): a(n) = floor(2^n*(n/3 + 4/9)).
  • A127986 (program): a(n) = n! + 2^n - 1.
  • A127988 (program): Sequence determining the parity of A025748.
  • A127989 (program): a(n) = 2n^3 - 2n + 9.
  • A127993 (program): Minimum bowling score for a game with n strikes.
  • A128012 (program): a(n) = 3*A001399(n).
  • A128013 (program): a(n) = (n^3 +n)*5^n.
  • A128014 (program): Central binomial coefficients C(2n,n) repeated.
  • A128015 (program): Binomial coefficients C(2n+1,n) repeated.
  • A128016 (program): Expansion of (1+x+x^2+x^3)/(1-x^2+x^4).
  • A128017 (program): Expansion of (1+2x+x^2-x^3)/(1-x^2+x^4).
  • A128018 (program): Expansion of (1-4x)/(1-2x+4*x^2).
  • A128019 (program): Expansion of (1-3x)/(1+3x^2).
  • A128043 (program): (n^3+n)*6^n.
  • A128048 (program): (n^3+n)*8^n.
  • A128051 (program): (n^3+n)*7^n.
  • A128054 (program): Count, omitting numbers of the form 6k+4 and doubling multiples of 6.
  • A128055 (program): a(n)=2^A128054(n).
  • A128057 (program): Expansion of (1+x)/sqrt(1+4x^2).
  • A128059 (program): a(n) = numerator((2n-1)^2/(2(2*n)!)).
  • A128060 (program): a(n) = 2n - numerator((2n-1)^2/(2(2n)!)).
  • A128076 (program): Triangle T(n,k)=2*n-k, read by rows.
  • A128091 (program): Row sums of unsigned A128090.
  • A128092 (program): a(n) = largest multiple of n which is <= 2^n.
  • A128093 (program): a(n) = smallest multiple of n which is >= 2^n.
  • A128104 (program): a(n) = largest multiple of n which is < exp(n).
  • A128105 (program): a(n) = smallest multiple of n which is > exp(n).
  • A128130 (program): Expansion of (1-x)/(1+x^4); period 8: repeat [1,-1,0,0,-1,1,0,0].
  • A128135 (program): Row sums of A128134.
  • A128138 (program): A000012 * A128132.
  • A128139 (program): Triangle read by rows: matrix product A004736 * A128132.
  • A128151 (program): A002260 * A097806.
  • A128153 (program): The number of regular pentagons found by constructing n equally-spaced points on each side of the pentagon and drawing lines parallel to the pentagon sides, as well as lines connecting vertices.
  • A128162 (program): a(n) = 3^n modulo Fibonacci(n).
  • A128174 (program): Transform, (1,0,1,…) in every column.
  • A128177 (program): A128174 * A004736 as infinite lower triangular matrices.
  • A128183 (program): Row sums of A128182.
  • A128188 (program): Row sums of A128187.
  • A128201 (program): Union of positive squares and the odd numbers.
  • A128203 (program): Sum of the digits of n*(n+1).
  • A128206 (program): Inverse of number triangle A128207.
  • A128209 (program): Jacobsthal numbers(A001045) + 1.
  • A128213 (program): Expansion of (1-x+2x^2-2x^3)/(1-x+x^2)^2.
  • A128214 (program): Expansion of (1+2x+3x^2)/(1+x+x^2)^2.
  • A128217 (program): Nonnegative integers n such that the square-root of n differs from its nearest integer by less than 1/4.
  • A128218 (program): First differences of A128217.
  • A128219 (program): A000012 * A127701. a(1) = 1, a(2) = 2, a(3) = 2; by rows, n-1 terms of 2, 3, 4…followed by “n”.
  • A128220 (program): Triangle, A127701 * A000012.
  • A128221 (program): A128174 * A127701.
  • A128222 (program): A127701 * A128174.
  • A128223 (program): a(n) = if n mod 2 = 0 then n*(n+1)/2 otherwise (n+1)^2/2-1.
  • A128227 (program): Right border (1,1,1,…) added to A002260.
  • A128229 (program): A natural number transform, inverse of signed A094587.
  • A128233 (program): Average of p(n) and p(p(n)), where p(k) is the k-th prime.
  • A128251 (program): n^4 - 1 divided by its largest fourth power divisor.
  • A128309 (program): 2*A000069(n).
  • A128311 (program): Remainder upon division of 2^(n-1)-1 by n.
  • A128406 (program): a(n) = (n+1)2^(n(n+1)).
  • A128415 (program): Expansion of (1-4x^2)/(1+3x+4x^2).
  • A128422 (program): Projective plane crossing number of K_ 4,n .
  • A128427 (program): Last point where sum of n consecutive n-th powers does not exceed the next n-th power.
  • A128428 (program): Number of distinct prime factors of n^2+1.
  • A128429 (program): A linear recurrence sequence: a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-6).
  • A128445 (program): Number of facets of the Alternating Sign Matrix polytope ASM(n).
  • A128464 (program): Numbers that are congruent to 11, 17, 29 mod 30.
  • A128467 (program): a(n) = 30*n + 11.
  • A128468 (program): a(n) = 30*n + 17.
  • A128469 (program): Numbers of the form 30k+29 or possible lower bounds of twin primes pairs ending in 9.
  • A128470 (program): a(n) = 30*n + 1.
  • A128471 (program): 30*n+7.
  • A128473 (program): Numbers of the form 30*k+23 or numbers that cannot be part of a twin prime pair.
  • A128474 (program): Largest x such that 2^x divides n(n-3)!.
  • A128496 (program): Row sums of unsigned triangle A128495 = S(2;n,m) (sums of squares of Chebyshev’s S-polynomials).
  • A128514 (program): Triangle, Pell sequence in every column.
  • A128529 (program): Survivor of the Josephus problem, counting direction reversed after each step.
  • A128533 (program): a(n) = F(n)*L(n+2) where F=Fibonacci and L=Lucas numbers.
  • A128534 (program): a(n) = Fibonacci(n)*Lucas(n-1).
  • A128542 (program): a(n) = ((2n)^(2n) - 1)/((2n+1)*(2n-1)).
  • A128543 (program): a(n) = floor(2^(n-2)3n).
  • A128549 (program): Difference between triangular number and next perfect square.
  • A128587 (program): Row sums of A128586.
  • A128588 (program): A007318 * A128587.
  • A128615 (program): Expansion of x/(1+x+x^2-x^3-x^4-x^5).
  • A128624 (program): Row sums of A128623.
  • A128625 (program): Expansion of (1+3x)/(1-5x).
  • A128634 (program): Number of parallel permutations of length n.
  • A128650 (program): Number of polygons on n vertices with exactly three faces.
  • A128697 (program): Sum of the eighth powers of the first n Fibonacci numbers.
  • A128766 (program): Number of inequivalent n-colorings of the vertices of the 3D cube under full orthogonal group of the cube (of order 48).
  • A128782 (program): n^2*4^n.
  • A128784 (program): n^2*5^n.
  • A128785 (program): a(n) = n^2*6^n.
  • A128786 (program): n^2*7^n.
  • A128787 (program): n^2*8^n.
  • A128788 (program): n^2*9^n.
  • A128789 (program): n^3*2^n.
  • A128790 (program): n^3*4^n.
  • A128791 (program): n^3*5^n.
  • A128792 (program): n^3*6^n.
  • A128793 (program): n^3*7^n.
  • A128794 (program): n^3*8^n.
  • A128795 (program): n^3*9^n.
  • A128796 (program): a(n) = n(n-1)2^n.
  • A128797 (program): (n^2-n)*3^n.
  • A128798 (program): n(n-1)4^n.
  • A128799 (program): a(n) = n(n-1)5^n.
  • A128800 (program): n(n-1)6^n.
  • A128801 (program): a(n) = n(n-1)7^n.
  • A128802 (program): a(n) = n(n-1)8^n.
  • A128803 (program): n(n-1)9^n.
  • A128806 (program): a(n) = A001316(n) + A046092(n).
  • A128814 (program): a(0)=1, a(n)= Product(k*(k+1)/2+1, k=1..n).
  • A128822 (program): Number of solutions to x/3 + y/4 + z/6 < n with x,y,z>=1 .
  • A128831 (program): Number of n-tuples where each entry is chosen from the subsets of 1,2,3 such that the intersection of all n entries is empty.
  • A128832 (program): Number of n-tuples where each entry is chosen from the subsets of 1,2,3,4 such that the intersection of all n entries is empty.
  • A128833 (program): Number of n-tuples where each entry is chosen from the subsets of 1,2,3,4,5 such that the intersection of all n entries is empty.
  • A128834 (program): Periodic sequence 0,1,1,0,-1,-1,…
  • A128862 (program): Numbers simultaneously triangular and centered triangular.
  • A128863 (program): a(0)=1. For n >= 1, a(n) = number of positive divisors of (n+a(n-1)).
  • A128865 (program): Number of n-tuples where each entry is chosen from the subsets of 1,2,3,4 such that the intersection of all n entries contains exactly one element.
  • A128866 (program): Number of n-tuples where each entry is chosen from the subsets of 1,2,3,4,5 such that the intersection of all n entries contains exactly one element.
  • A128880 (program): Triangular numbers congruent to 1 or 5 mod 6.
  • A128882 (program): a(n) = n!! - 1.
  • A128889 (program): a(n) = (2^(n^2) - 1)/(2^n - 1).
  • A128893 (program): (1/p)(binomial(2p,p)+2*(p-1)), where p = n-th prime.
  • A128897 (program): a(n) = ((2n)^(2n-1)+1)/(2n+1).
  • A128913 (program): a(n) = n*pi(n).
  • A128917 (program): Pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891).
  • A128918 (program): a(n) = n(n+1)/2 if n is odd, otherwise (n-1)n/2 + 1.
  • A128919 (program): Numbers simultaneously heptagonal and centered heptagonal.
  • A128922 (program): Numbers simultaneously 10-gonal and centered 10-gonal.
  • A128929 (program): Diameter of a special type of regular graph of degree 4 whose order maintain an increase in form of an arithmetic progression.
  • A128930 (program): Prime(n) * pi(n).
  • A128960 (program): a(n) = (n^3 - n)*2^n.
  • A128961 (program): a(n) = (n^3 - n)*3^n.
  • A128962 (program): a(n) = (n^3 - n)*4^n.
  • A128963 (program): a(n) = (n^3 - n)*5^n.
  • A128964 (program): a(n) = (n^3-n)*6^n.
  • A128965 (program): a(n) = (n^3 - n)*7^n.
  • A128967 (program): (n^3-n)*8^n.
  • A128969 (program): a(n) = (n^3 - n)*9^n.
  • A128975 (program): a(n) = the number of unordered triples of integers (a,b,c) with a+b+c=n, whose bitwise XOR is zero. Equivalently, the number of three-heap nim games with n stones which are in a losing position for the first player.
  • A128985 (program): a(n) = (n^3 - n^2)*2^n.
  • A128986 (program): a(n) = (n^3 - n^2)*3^n.
  • A128987 (program): a(n) = (n^3 - n^2)*4^n.
  • A128988 (program): a(n) = (n^3 - n^2)*5^n.
  • A128989 (program): a(n) = (n^3 - n^2)*6^n.
  • A128990 (program): a(n) = (n^3 - n^2)*7^n.
  • A128991 (program): a(n) = (n^3 - n^2)*8^n.
  • A128992 (program): a(n) = (n^3 - n^2)*9^n.
  • A128999 (program): Start with an integer (in this case 1). First, add 5 or 6 if the integer is odd or even, respectively. Then divide by 2. Notice any a(1)<=5 converges to 5 and any a(1)>=6 converges to 6.
  • A129000 (program): Start with an integer (in this case, 1). First, add 5 or 8 if the integer is odd or even, respectively. Then divide by 2.
  • A129002 (program): a(n) = (n^3 + n^2)*2^n.
  • A129003 (program): (n^3+n^2)*3^n.
  • A129004 (program): (n^3+n^2)*4^n.
  • A129005 (program): (n^3+n^2)*5^n.
  • A129006 (program): (n^3+n^2)*6^n.
  • A129007 (program): (n^3+n^2)*7^n.
  • A129008 (program): (n^3+n^2)*8^n.
  • A129009 (program): (n^3+n^2)*9^n.
  • A129011 (program): a(n) = floor(n^(4/3)).
  • A129026 (program): a(n) = (1/2)(n^4 + 11n^3 + 53n^2 + 97n + 54).
  • A129027 (program): Odd-indexed terms of A129026.
  • A129028 (program): A129027(n)/4.
  • A129029 (program): a(n) = 8n^4+44n^3+106n^2+100n+30.
  • A129069 (program): Numbers n such that (n-3)/2 is prime.
  • A129070 (program): Numbers n such that (n-5)/4 is prime.
  • A129071 (program): Numbers n such that (n-7)/6 is prime.
  • A129072 (program): Numbers n such that (n-13)/12 is prime.
  • A129073 (program): Numbers n such that (n-8)/7 is prime.
  • A129074 (program): Numbers n such that (n-9)/8 is prime.
  • A129075 (program): Numbers n such that (n-4)/3 is prime.
  • A129076 (program): a(n) = sigma(sigma(sigma(sigma(n)))), where sigma(n) = sum of divisors of n.
  • A129080 (program): Expansion of g.f. x(x^4 - 5x^3 + 10x^2 - 12x + 4)/((1-x)^2(1 - 3x + 2*x^2 - x^3)).
  • A129109 (program): Sums of three consecutive hexagonal numbers.
  • A129111 (program): Sums of three consecutive heptagonal numbers.
  • A129132 (program): Partial sums of A051903.
  • A129142 (program): Start with the empty sequence and append in step k the consecutive numbers 2^k-1 to 2^k+k-2.
  • A129143 (program): Start with the empty sequence and append in step k the consecutive numbers 2^(k-1) to 2^(k-1)+k-1.
  • A129184 (program): Shift operator, right.
  • A129185 (program): Shift operator, left.
  • A129186 (program): Right shift operator generating 1’s in shifted spaces.
  • A129194 (program): a(n) = n^2*(3/4 - (-1)^n/4).
  • A129195 (program): a(n)=denominator(n!/4^n).
  • A129196 (program): a(n) = denominator(3*(3+(-1)^n)/(n+1)^3).
  • A129197 (program): a(n) = numerator( 3*(3+(-1)^n)/(n+1)^3 ).
  • A129202 (program): Denominator of 3*(3+(-1)^n) / (n+1)^2.
  • A129203 (program): a(n) = numerator(3/(n+1)^3)*(3/2 + (-1)^n/2).
  • A129204 (program): The denominator of 2/n^3.
  • A129229 (program): a(n) = floor(n*r)-a(n-1), where r is the golden mean, (1+sqrt(5))/2.
  • A129230 (program): a(n)=Floor(nr)+Floor((n-2)r)+Floor((n-4)r)+…+Floor(kr), where r = golden mean = (1 + sqrt(5))/2 and k=0 if n is even, k=1 if n is odd.
  • A129232 (program): a(n)=Floor(nr)+Floor((n-2)r)+Floor((n-4)r)+…+Floor(kr), where r = 2^(1/2) and k=0 if n is even, k=1 if n is odd.
  • A129235 (program): a(n) = 2*sigma(n) - tau(n), where tau(n) is the number of divisors of n (A000005) and sigma(n) is the sum of divisors of n (A000203).
  • A129252 (program): Smallest prime factor p of n such that p^p is a divisor of n, a(n)=1 if no such factor exists.
  • A129254 (program): Numbers n such that both n and n+1 have at least one divisor of the form p^e with p<=e, p prime.
  • A129283 (program): (Arithmetic derivative of n) + n.
  • A129296 (program): Number of divisors of n^2 - 1 that are not greater than n.
  • A129307 (program): Intersection of A000217 and A005098.
  • A129308 (program): a(n) is the number of positive integers k such that k*(k+1) divides n.
  • A129312 (program): A minimal 2 X 2 subdeterminant array.
  • A129326 (program): a(n) = (2n+1)(n-1)!.
  • A129337 (program): Maximal possible degree of a Chebyshev-type quadrature formula with n nodes, in the case of the constant weight function on [ -1,1].
  • A129342 (program): a(2n) = a(n) + 2^(2n), a(2n+1) = 2^(2n+1).
  • A129343 (program): a(2n) = a(n), a(2n+1) = 4n+1.
  • A129362 (program): a(n) = Sum_ k=floor((n+1)/2)..n J(k+1), J(k) = A001045(k).
  • A129370 (program): a(n)=n^2-(n-1)^2*(1-(-1)^n)/8.
  • A129371 (program): a(n)=sum k=0..floor(n/2), (n-k)^2 .
  • A129393 (program): Row sums of A129392.
  • A129401 (program): a(n) is the result of replacing with its successor prime each prime in the factorization of the n-th composite number.
  • A129403 (program): Minimal number of edges in e-free non-deterministic finite automata (NFA) for regular expression c_1?c_2?…c_n?.
  • A129428 (program): Centered 47-gonal numbers.
  • A129464 (program): Second column (m=1) of triangle A129462 (v=2 member of a certain family).
  • A129502 (program): For n=2^k, a(n) = binomial(k + 2, 2), else 0.
  • A129514 (program): a(n) = gcd(Sum_ k n k, Sum_ 1<k<n, k does not divide n k) = gcd(sigma(n), n(n+1)/2 - sigma(n)) = gcd(sigma(n), n(n+1)/2), where sigma(n) = A000203(n).
  • A129527 (program): a(2n) = a(n) + 2n, a(2n+1) = 2n + 1.
  • A129530 (program): a(n) = (1/2)n(n-1)*3^(n-1).
  • A129532 (program): 3n(n-1)4^(n-2).
  • A129538 (program): a(n) = smallest positive integer such that lcm(a(1), a(2), …, a(n)) is a multiple of the n-th triangular number n(n+1)/2.
  • A129543 (program): Gray code ordering of the prime numbers.
  • A129565 (program): A115359 * A000012 as infinite lower triangular matrices.
  • A129574 (program): Number of odd divisors of n plus the number of odd divisors of n - 1.
  • A129588 (program): Expansion of q^-1 * theta_2(q)^4 in powers of q^2.
  • A129589 (program): a(n) = 2*A000129(n) + A000129(n-1) - n.
  • A129597 (program): Central diagonal of array A129595.
  • A129598 (program): a(n) = n * A111089(n).
  • A129628 (program): Inverse Moebius transform of A001511.
  • A129654 (program): Number of different ways to represent n as general polygonal number P(m,r) = 1/2r((m-2)*r-(m-4)) = n>1, for m,r>1.
  • A129686 (program): Triangle read by rows: row n is 0^(n-3), 1, 0, 1.
  • A129688 (program): A129686 * A128174.
  • A129696 (program): Antidiagonal sums of triangular array T defined in A014430: T(j,k) = binomial(j+1, k)-1 for 1 <= k <= j.
  • A129726 (program): a(n) = a(n-1) + prime(n) - prime(n-1) + 2.
  • A129728 (program): a(n) = 2*(n-1) + Fibonacci(n).
  • A129743 (program): a(n) = -(u^n-1)*(v^n-1) with u = 2+sqrt(3), v = 2-sqrt(3).
  • A129744 (program): a(n) = -(u^n-1)*(v^n-1) with u = 1+sqrt(2), v = 1-sqrt(2).
  • A129753 (program): Floor(prime(n)/nonprime(n)).
  • A129756 (program): Repetitions of odd numbers four times.
  • A129760 (program): Bitwise AND of binary representation of n-1 and n.
  • A129765 (program): Triangle, (1, 1, 2, 2, 2,…) in every column.
  • A129768 (program): Number of odd nonprime numbers less than the n-th prime.
  • A129771 (program): Evil odd numbers.
  • A129787 (program): Ceiling(3^n/n).
  • A129788 (program): a(n) = ceiling(4^n/n).
  • A129789 (program): a(n) = ceiling(5^n/n).
  • A129790 (program): a(n) = ceiling(6^n/n).
  • A129791 (program): a(n) = ceiling(7^n/n).
  • A129792 (program): a(n) = ceiling(8^n/n).
  • A129793 (program): a(n) = ceiling(9^n/n).
  • A129794 (program): a(n) = floor(4^n/n).
  • A129795 (program): a(n) = floor(5^n/n).
  • A129796 (program): a(n) = floor(6^n/n).
  • A129797 (program): a(n) = floor(7^n/n).
  • A129798 (program): a(n) = floor(8^n/n).
  • A129799 (program): a(n) = floor(9^n/n).
  • A129801 (program): Triangle read by rows in which row m (m>=0) gives the numbers 2mn + 1 for n = 0, …, m.
  • A129803 (program): Triangular numbers that are the sum of three consecutive triangular numbers.
  • A129819 (program): Antidiagonal sums of triangular array T: T(j,k) = (k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j.
  • A129831 (program): Alternating sum of double factorials: n!! - (n-1)!! + (n-2)!! - … 1!!.
  • A129839 (program): a(n) = Stirling_2(n,3)^2.
  • A129863 (program): Sums of three consecutive pentagonal numbers.
  • A129867 (program): Row sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.
  • A129868 (program): Binary palindromic numbers with only one 0 bit.
  • A129889 (program): Write down n, then n*(n+1).
  • A129890 (program): a(n) = (2n+2)!! - (2n+1)!!.
  • A129895 (program): a(1)=1. a(n) = a(n-1) + number of triangular numbers among the first (n-1) terms of the sequence.
  • A129896 (program): a(1)=1. a(n) = a(n-1) + number of Fibonacci numbers among the first (n-1) terms of the sequence.
  • A129923 (program): (n+5)! / 5.
  • A129936 (program): (n-2)(n+3)(n+2)/6.
  • A129937 (program): The central binomial numbers Binomial[n,Floor[n/2] minus the SO(n) dimension as an algebraic projective variety dimension.
  • A129952 (program): Binomial transform of A124625.
  • A129953 (program): First differences of A129952.
  • A129954 (program): Second differences of A129952.
  • A129955 (program): Third differences of A129952.
  • A129957 (program): a(n) = n^3 if n is odd, n^3 + 1 otherwise.
  • A129958 (program): First differences of A129957.
  • A129959 (program): A129957(n) - n*(n-1)/2.
  • A129966 (program): Triangular numbers which are differences of squares.
  • A129972 (program): a(n) = 2*floor(log_2(n)) + 1.
  • A129979 (program): Left border of triangle A131088.
  • A129981 (program): Sum of n!!, with n>=0.
  • A130008 (program): Noncomposite numbers sandwiched between 1’s.
  • A130031 (program): Row sums of triangle A129467.
  • A130032 (program): Row sums of unsigned triangle A129467.
  • A130036 (program): Denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1 and sqrt(3)/2.
  • A130053 (program): G.f. A(x) = (1-x+x^2)/(1-x)^3 - x*[Sum_ n>=0 x^(n + 2^n)]/(1-x)^2 .
  • A130065 (program): a(n) = (n / GreatestPrimeFactor(n)) * SmallestPrimeFactor(n).
  • A130102 (program): E.g.f.: (e^x - x)^2.
  • A130103 (program): Expansion of e.g.f. e^(2x)-(1+x)*e^x+x.
  • A130104 (program): Expansion of x(1-3x+5x^2-2x^3)/((1-x)^3*(1-2x)).
  • A130119 (program): a(n) = gcd(n^2 - 19, 45).
  • A130123 (program): Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Triangle by columns, (2^k, 0, 0, 0, …).
  • A130124 (program): Triangle defined by A130123 * A002260, read by rows.
  • A130128 (program): Triangle read by rows: T(n,k) = (n - k + 1)*2^(k-1).
  • A130129 (program): (3n+1)2^n.
  • A130130 (program): a(0)=0, a(1)=1, a(n)=2 for n >= 2.
  • A130145 (program): Number of nonisomorphic orthogonal arrays OA(8*n+4,4,2,2).
  • A130151 (program): Period 6: repeat [1, 1, 1, -1, -1, -1].
  • A130154 (program): Triangle read by rows: T(n, k) = 1 + 2(n-k)(k-1) (1 <= k <= n).
  • A130165 (program): a(1)=1; a(n)=prime(mod(a(n-1),10)).
  • A130174 (program): a(n) = n-1 + (total number of digits in a(1), …, a(n-1)).
  • A130188 (program): Denominators of rationals r(n) related to the z-sequence of the Sheffer matrix A060821 for Hermite polynomials.
  • A130195 (program): Row sums of triangle A130194.
  • A130196 (program): Period 3: repeat [1, 2, 2].
  • A130198 (program): Single paradiddle. In percussion, the paradiddle is a four-note drum sticking pattern consisting of two alternating notes followed by two notes on the same hand.
  • A130205 (program): a(n) = n^2 - a(n-1) - a(n-2), with a(1) = 1 and a(2) = 2.
  • A130208 (program): Diagonalized matrix of A000203, Sigma(n).
  • A130213 (program): Order of modular group of degree 3^(n-1) + 1.
  • A130214 (program): Order of modular group of degree 5^(n-1)+1.
  • A130215 (program): Order of modular group of degree 7^(n-1)+1.
  • A130216 (program): a(0) = 3; a(n) = a(n-1) + (number of multiples of 3 so far in the sequence).
  • A130218 (program): Partial sums of A100119. Sum of first n of the n-th centered n-gonal numbers.
  • A130234 (program): Minimal index k of a Fibonacci number such that Fibonacci(k) >= n (the ‘upper’ Fibonacci Inverse).
  • A130235 (program): Partial sums of the ‘lower’ Fibonacci Inverse A130233.
  • A130236 (program): Partial sums of the ‘upper’ Fibonacci Inverse A130234.
  • A130237 (program): The ‘lower’ Fibonacci Inverse A130233(n) multiplied by n.
  • A130238 (program): Partial sums of A130237.
  • A130239 (program): Maximal index k of the square of a Fibonacci number such that Fib(k)^2 <= n (the ‘lower’ squared Fibonacci Inverse).
  • A130240 (program): Partial sums of A130239.
  • A130249 (program): Maximal index k of a Jacobsthal number such that A001045(k)<=n (the ‘lower’ Jacobsthal inverse).
  • A130250 (program): Minimal index k of a Jacobsthal number such that A001045(k) >= n (the ‘upper’ Jacobsthal inverse).
  • A130251 (program): Partial sums of A130249.
  • A130252 (program): Partial sums of A130250.
  • A130253 (program): Number of Jacobsthal numbers (A001045) <=n.
  • A130255 (program): Maximal index k of an odd Fibonacci number (A001519) such that A001519(k) = Fibonacci(2k-1) <= n (the ‘lower’ odd Fibonacci Inverse).
  • A130256 (program): Minimal index k of an odd Fibonacci number A001519 such that A001519(k) = Fibonacci(2*k-1) >= n (the ‘upper’ odd Fibonacci Inverse).
  • A130257 (program): Partial sums of the ‘lower’ odd Fibonacci Inverse A130255.
  • A130258 (program): Partial sums of the ‘upper’ odd Fibonacci Inverse A130256.
  • A130259 (program): Maximal index k of an even Fibonacci number (A001906) such that A001906(k) = Fib(2k) <= n (the ‘lower’ even Fibonacci Inverse).
  • A130260 (program): Minimal index k of an even Fibonacci number A001906 such that A001906(k) = Fib(2k) >= n (the ‘upper’ even Fibonacci Inverse).
  • A130261 (program): Partial sums of the ‘lower’ even Fibonacci Inverse A130259.
  • A130262 (program): Partial sums of the ‘upper’ even Fibonacci Inverse A130260.
  • A130269 (program): A002260 * A051340.
  • A130271 (program): Triangle read by rows: A051340^2.
  • A130290 (program): Number of nonzero quadratic residues modulo the n-th prime.
  • A130291 (program): Number of quadratic residues (including 0) modulo the n-th prime.
  • A130296 (program): Triangle read by rows: T[i,1]=i, T[i,j]=1 for 1 < j <= i = 1,2,3,…
  • A130299 (program): A130296 * A051340.
  • A130303 (program): A130296 * A000012.
  • A130312 (program): Each Fibonacci number F(n) appears F(n) times.
  • A130321 (program): Triangle, (2^0, 2^1, 2^2, …) in every column.
  • A130322 (program): A130321^2.
  • A130328 (program): Triangle of differences between powers of 2, read by rows.
  • A130330 (program): Triangle read by rows, the matrix product A130321 * A000012, both taken as infinite lower triangular matrices.
  • A130380 (program): Catalan numbers halved and rounded to the next integer.
  • A130404 (program): Partial sums of A093178.
  • A130423 (program): Main diagonal of array A[k,n] = n-th sum of 3 consecutive k-gonal numbers, k>2.
  • A130449 (program): a(0) = 1; a(n) = 4^(n+1)*a(n-1)+1.
  • A130453 (program): A097806 * A059268.
  • A130460 (program): Infinite lower triangular matrix,(1,0,0,0,…) in the main diagonal and (1,2,3,…) in the subdiagonal.
  • A130470 (program): Antidiagonal sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.
  • A130472 (program): A permutation of the integers: a(n) = (-1)^n * floor( (n+1)/2 ).
  • A130473 (program): Partial sums of A087172.
  • A130481 (program): a(n) = Sum_ k=0..n (k mod 3) (i.e., partial sums of A010872).
  • A130482 (program): a(n) = Sum_ k=0..n (k mod 4) (Partial sums of A010873).
  • A130483 (program): a(n) = Sum_ k=0..n (k mod 5) (Partial sums of A010874).
  • A130484 (program): a(n) = Sum_ k=0..n (k mod 6) (Partial sums of A010875).
  • A130485 (program): a(n) = Sum_ k=0..n (k mod 7) (Partial sums of A010876).
  • A130486 (program): a(n) = Sum_ k=0..n (k mod 8) (Partial sums of A010877).
  • A130487 (program): a(n) = Sum_ k=0..n (k mod 9) (Partial sums of A010878).
  • A130488 (program): a(n) = Sum_ k=0..n (k mod 10) (Partial sums of A010879).
  • A130489 (program): a(n) = Sum_ k=0..n (k mod 11) (Partial sums of A010880).
  • A130490 (program): a(n) = Sum_ k=0..n (k mod 12) (Partial sums of A010881).
  • A130493 (program): Triangle read by rows in which row n contains n! repeated n times.
  • A130494 (program): Row sums of triangle A130478.
  • A130496 (program): Repetition of even numbers, with initial zeros, five times.
  • A130497 (program): Repetition of odd numbers five times.
  • A130505 (program): a(n) = 3a(n-1) if n is odd, otherwise 6a(n-1).
  • A130507 (program): First differences of A130845.
  • A130508 (program): a(1)=2. a(2)=3. a(3)=1. a(n+3) = 3 + a(n), for all positive integers n.
  • A130509 (program): a(1)=3. a(2)=1. a(3)=2. a(n+3) = 3 + a(n), for all positive integers n.
  • A130517 (program): Triangle read by rows: row n counts down from n in steps of 2, then counts up the remaining elements in the set 1,2,…n , again in steps of 2.
  • A130518 (program): a(n) = Sum_ k=0..n floor(k/3). (Partial sums of A002264.)
  • A130519 (program): a(n) = Sum_ k=0..n floor(k/4). (Partial sums of A002265.)
  • A130520 (program): a(n) = Sum_ k=0..n floor(k/5). (Partial sums of A002266.)
  • A130526 (program): A permutation of the integers induced by the lower and upper Wythoff sequences.
  • A130543 (program): Multiplicative persistence of n!.
  • A130556 (program): A model of the atomic nucleus (Shell model of nucleus). A triangle.
  • A130566 (program): Pyramidal 47-gonal numbers.
  • A130567 (program): Expansion of x(2 - 7x + 2x^2)/((1-x)(1-4x)(1-2*x)).
  • A130568 (program): Generalized Beatty sequence 1+2floor(nphi), which contains infinitely many primes.
  • A130569 (program): Numbers of the form k*2^m + 1 for k odd, m >=1, that are not Proth numbers (A080075) (2^m <= k).
  • A130578 (program): Number of different possible rows (or columns) in an n X n crossword puzzle.
  • A130589 (program): a(n) = F(F(n)-1), where F(n) = A000045(n) (the Fibonacci numbers).
  • A130599 (program): Transformation of sequence 3^k by sandwiching it between 1’s.
  • A130602 (program): A shell geometric model of the atomic nucleus.
  • A130612 (program): Sum of the first 10^n squares.
  • A130624 (program): Binomial transform of A101000.
  • A130625 (program): First differences of A130624.
  • A130626 (program): Second differences of A130624.
  • A130630 (program): Periodic sequence with period 1 1 1 1 1 0 0 0 0.
  • A130632 (program): Number of natural numbers between d(n) and d(n+1), where d(n) denotes the number of divisors of n.
  • A130638 (program): a(n) = 1 iff d(n) = d(n+1), otherwise a(n)=0, where d(n) is the number of divisors of n, A000005.
  • A130652 (program): a(n) = 11^n - 2.
  • A130656 (program): Interlacing n^3/2 and n^2(n + 1)/2.
  • A130657 (program): Periodic (7 terms) 1 1 1 1 0 0 0.
  • A130658 (program): Period 4: repeat [1, 1, 2, 2].
  • A130659 (program): Period 4: repeat [0, 1, 2, 4].
  • A130664 (program): a(1)=1. a(n) = a(n-1) + (number of terms from among a(1) through a(n-1) which are factorials).
  • A130665 (program): a(n) = Sum_ k=0..n 3^wt(k), where wt() = A000120().
  • A130667 (program): a(1) = 1; a(n) = max 5*a(k) + a(n-k) 1 <= k <= n/2 for n > 1.
  • A130674 (program): a(n) = d(n)!, where d denotes the number of divisors of n.
  • A130675 (program): Factorial of bigomega(n).
  • A130692 (program): a(n) is the smallest number m such that the sum of the digits of n+m is n.
  • A130706 (program): a(0) = 1, a(1) = 2, a(n) = 0 for n > 1.
  • A130707 (program): a(n+3) = 3(a(n+2) - a(n+1)) + 2a(n).
  • A130713 (program): a(0)=a(2)=1, a(1)=2, a(n)=0 for n > 2.
  • A130716 (program): a(0)=a(1)=a(2)=1, a(n)=0 for n>2.
  • A130718 (program): 2*(prime(n)-2)!.
  • A130722 (program): The twice repeated nonnegative integers at even indices, the non-repeated nonnegative integers at odd indices.
  • A130723 (program): Least common multiple of 3 and n^2+n+1.
  • A130724 (program): a(n) = lcm(n,3) / gcd(n,3).
  • A130726 (program): Factorial of the largest prime less than or equal to n.
  • A130727 (program): List of triples 2n+1, 2n+3, 2n+2.
  • A130731 (program): Period 4: repeat [1, 2, 0, 0].
  • A130744 (program): a(n) = n(n+2)n!.
  • A130746 (program): Triangle red by rows: T(n,m) = binomial(n+m,1+n), 1<=m<=n.
  • A130748 (program): Place n points on each of the three sides of a triangle, 3n points in all; a(n) = number of nondegenerate triangles that can be constructed using these points (plus the 3 original vertices) as vertices.
  • A130750 (program): Binomial transform of A010882.
  • A130752 (program): Binomial transform of periodic sequence (2, 3, 1).
  • A130755 (program): Binomial transform of periodic sequence (3, 1, 2).
  • A130759 (program): Partial sums of A130707.
  • A130764 (program): ASCII codes for upper case letters.
  • A130765 (program): ASCII codes for lower case letters.
  • A130766 (program): 3n+2 sandwiched by tripled 3n+1 .
  • A130770 (program): One third of the least common multiple of 3 and n^2+n+1.
  • A130772 (program): Periodic sequence with period 2 2 0 -2 -2 0.
  • A130773 (program): a(0)=0, a(1)=2, a(n)=2n+1 for n >= 2.
  • A130775 (program): a(1) = 0; for n > 1: a(n) = 2*(prime(n)-1)!/(prime(n)+1).
  • A130778 (program): Period 6: repeat [1, -1, -3, -3, -1, 1].
  • A130779 (program): a(0)=a(1)=1, a(2)=2, a(n)=0 for n >= 3.
  • A130781 (program): Sequence is identical to its third differences: a(n+3) = 3a(n+2) - 3a(n+1) + 2*a(n), with a(0)=a(1)=1, a(2)=2.
  • A130782 (program): Periodic sequence with period 1, 1, 2, 1, 1.
  • A130784 (program): Period 3: repeat [1, 3, 2].
  • A130785 (program): Sequence identical to its third differences: a(n+3) = 3a(n+2)-3a(n+1)+2a(n), with a(0)=1, a(1)=4, a(2)=9.
  • A130793 (program): Periodic sequence with period 3: 1, 3, 5.
  • A130794 (program): Periodic sequence with period 1,5,3.
  • A130806 (program): Period 6: 1,4,3,-1,-4,-3.
  • A130809 (program): If X_1, …, X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 3-subsets of X containing none of X_i, (i=1,…,n).
  • A130810 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 4-subsets of X containing none of X_i, (i=1,…,n).
  • A130811 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 5-subsets of X containing none of X_i, (i=1,…n).
  • A130812 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 6-subsets of X containing none of X_i, (i=1,…n).
  • A130813 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 7-subsets of X containing none of X_i, (i=1,…n).
  • A130815 (program): Period 6: repeat [1, 5, 4, -1, -5, -4].
  • A130818 (program): Decimal expansion of number whose Engel expansion is the sequence of squares, that is, 1, 4, 9, 16,…
  • A130819 (program): 2n appears 2n-1 times.
  • A130820 (program): Decimal expansion of number whose Engel expansion is given by the sequence: 1,1,2,2,3,3,4,4,…Ceiling[n/2],…
  • A130821 (program): 2n-1 appears 2n times.
  • A130822 (program): Two 1’s, one 2, four 3’s, three 4’s …
  • A130823 (program): Each odd number appears thrice.
  • A130824 (program): a(n) = 2*A004273(n).
  • A130829 (program): 2n+1 appears 2n times.
  • A130840 (program): a(n) = floor((1/16)(16 + 2^n - 8n + 8*n^2)).
  • A130845 (program): a(4n) = a(4n+1) = a(4n+2) = A001477(n), a(4n+3) = A005408(n).
  • A130848 (program): Periodic sequence with period (2, 5, 3, -2, -5, -3).
  • A130851 (program): Catalan numbers A000108(n) modulo 9.
  • A130855 (program): 2n appears 2n+1 times, 2n+1 appears 2n times.
  • A130856 (program): The digital root (A010888) of the Catalan numbers A000108.
  • A130857 (program): a(n) = (n-1)n(n+1)(n+2)(2n+11)/120.
  • A130859 (program): 1729-gonal numbers.
  • A130861 (program): a(n) = (n-1)(2n+5).
  • A130862 (program): a(n) = (n-1)(n+2)(2*n+11)/2.
  • A130863 (program): Ratio of quadruple Sum of k^2-1 to quadruple sum of k made into an integer sequence: (1/6)*(-1 + n)(2 + n)(3 + n)(7 + n).
  • A130869 (program): Partial sums of A130752.
  • A130876 (program): Centered 1729-gonal numbers.
  • A130877 (program): Numbers that are congruent to 0, 5 mod 9.
  • A130881 (program): Numbers n such that n = Sum_digits[(n+k)*abs(n-k)] for some k>=0.
  • A130883 (program): a(n) = 2*n^2 - n + 1.
  • A130884 (program): 3n^3 + 2n^2 + n + 1.
  • A130885 (program): 3n^3 - 2n^2 + n - 1.
  • A130886 (program): 4n^4 + 3n^3 + 2n^2 + n + 1.
  • A130887 (program): Inverse Moebius transform of the Mersenne numbers: a(n) = Sum_(d n (2^n - 1).
  • A130893 (program): Lucas numbers (beginning with 1) mod 10.
  • A130909 (program): Simple periodic sequence (n mod 16).
  • A130910 (program): Sum 0<=k<=n, k mod 16 (Partial sums of A130909).
  • A130917 (program): a(n) is the sum of the digital roots of all of the previous terms.
  • A130974 (program): Period 6: repeat [1, 1, 1, 3, 3, 3].
  • A131015 (program): Period 12: repeat 1, 1, 3, 2, 2, 1, 4, 4, 2, 3, 3, 4.
  • A131017 (program): Period 6 sequence (1, 1, 2, -1, 2, 1).
  • A131026 (program): Periodic sequence (2, 2, 1, 0, 0, 1).
  • A131027 (program): Period 6: repeat [4, 3, 1, 0, 1, 3].
  • A131028 (program): Periodic sequence (7, 4, 1, 1, 4, 7).
  • A131029 (program): Periodic sequence (11, 5, 2, 5, 11, 14).
  • A131030 (program): Period 6: repeat [16, 7, 7, 16, 25, 25].
  • A131037 (program): Sequence A001333 with last digits set to zero.
  • A131040 (program): a(n) = (1/2+1/2isqrt(11))^n + (1/2-1/2isqrt(11))^n, where i=sqrt(-1).
  • A131042 (program): Natural numbers A000027 with 6n+3 and 6n+4 terms swapped.
  • A131051 (program): Row sums of triangle A133805.
  • A131055 (program): 1 followed by repeats of 2*k.
  • A131056 (program): A007318 * A131055.
  • A131060 (program): 3A007318 - 2A000012 as infinite lower triangular matrices.
  • A131061 (program): Triangle read by rows: T(n,k) = 4*binomial(n,k) - 3 for 0 <= k <= n.
  • A131063 (program): Triangle read by rows: T(n,k) = 5*binomial(n,k) - 4 for 0 <= k <= n.
  • A131064 (program): Binomial transform of [1, 1, 5, 5, 5, …].
  • A131065 (program): Triangle read by rows: T(n,k) = 6*binomial(n,k) - 5 for 0 <= k <= n.
  • A131066 (program): Binomial transform of [1, 1, 6, 6, 6, …].
  • A131067 (program): Triangle read by rows: T(n,k) = 7*binomial(n,k) - 6 for 0 <= k <= n.
  • A131068 (program): Binomial transform of [1, 1, 7, 7, 7,…].
  • A131078 (program): Periodic sequence (1, 1, 1, 1, 0, 0, 0, 0).
  • A131079 (program): Periodic sequence (2, 2, 2, 1, 0, 0, 0, 1).
  • A131080 (program): Periodic sequence (4, 4, 3, 1, 0, 0, 1, 3).
  • A131081 (program): Periodic sequence (8, 7, 4, 1, 0, 1, 4, 7).
  • A131082 (program): Periodic sequence (15, 11, 5, 1, 1, 5, 11, 15).
  • A131089 (program): a(n) = Sum_ d n (2 - mu(d)).
  • A131090 (program): First differences of A131666.
  • A131091 (program): Partial sums of A131707.
  • A131098 (program): Partial sums of A151798.
  • A131099 (program): a(n) = n times number of divisors of n of form 3m+1 - n times number of divisors of form 3m+2.
  • A131119 (program): a(n) = (-1)^n * Sum_ i=1..floor(n/2) i * floor(n/(n-i)).
  • A131128 (program): Binomial transform of [1, 1, 5, 1, 5, 1, 5, …].
  • A131130 (program): Binomial transform of [1,1,7,1,7,1,7,1,…].
  • A131132 (program): a(n) = a(n-1) + a(n-2) + 1 if n is a multiple of 6, otherwise a(n) = a(n-1) + a(n-2).
  • A131136 (program): Denominator of (exponential) expansion of log((x/2-1)/(x-1)).
  • A131137 (program): Denominator of (exponential) expansion of log((2*x/3-1)/(x-1)).
  • A131138 (program): a(n)=log_3(A131137(n)).
  • A131174 (program): a(2n) = 2*A000217(n), a(2n+1) = A000217(n).
  • A131176 (program): a(n) = (n^5-n-10)/10.
  • A131179 (program): a(n) = if n mod 2 == 0 then n(n+1)/2, otherwise (n-1)n/2 + 1.
  • A131186 (program): Period 12: repeat 0, 1, 2, 0, 2, 4, 0, 4, 3, 0, 3, 1.
  • A131187 (program): a(n) = the number of positive integers < n that are neither a divisor of n nor a divisor of (n+1).
  • A131189 (program): Numbers n>=0 such that d(n) = (n^1 + 1) (n^2 + 2) … (n^14 + 14) / 14!, e(n) = (n^1 + 1) (n^2 + 2) … (n^15 + 15) / 15!, and f(n) = (n^1 + 1) (n^2 + 2) … (n^16 + 16) / 16! take nonintegral values.
  • A131191 (program): Numbers n>=0 such that d(n) = (n^1 + 1) (n^2 + 2) … (n^22 + 22) / 22!, e(n) = (n^1 + 1) (n^2 + 2) … (n^23 + 23) / 23!, and f(n) = (n^1 + 1) (n^2 + 2) … (n^24 + 24) / 24! take nonintegral values.
  • A131193 (program): Period 6: repeat [0, 1, -3, 3, -1, 0].
  • A131209 (program): Maximal distance between two signed permutations of n elements.
  • A131211 (program): a(n)=(n^5-n-30)/30.
  • A131215 (program): Numbers which are both 11-gonal and centered 11-gonal.
  • A131216 (program): Numbers X such that 99*X^2 - 2178 is a square.
  • A131217 (program): Triangular sequence of a Gray code type made from Pascal’s triangle modulo 2 as b(n,m)=Mod[binomial[n,m],2]:A047999: a(n,m)=Mod[b(n,m)+b(n,m+1),2].
  • A131229 (program): Numbers congruent to 1,7 mod 10.
  • A131234 (program): Starts with 1, then n appears Fibonacci(n-1) times.
  • A131242 (program): Partial sums of A059995: a(n) = sum_ k=0..n floor(k/10).
  • A131259 (program): a(2n)=A000217(n), a(2n+1)=-2*A000217(n).
  • A131269 (program): a(n) = 3a(n-1) - 2a(n-2) - a(n-3) + a(n-4) with n>3, a(0)=1, a(1)=2, a(2)=3, a(3)=6.
  • A131270 (program): Triangle T(n,k) = 2*A046854(n,k) - 1, read by rows.
  • A131282 (program): Period 6: repeat [1, 2, 3, 3, 4, 5].
  • A131290 (program): 1 followed by period 6: repeat [3, 2, 0, -1, 0, 2].
  • A131291 (program): Period 9: repeat [5, 4, 5, 3, 4, 3, 5, 4, 5].
  • A131293 (program): Concatenate a(n-2) and a(n-1) to get a(n); start with a(0)=0, a(1)=1, delete the leading zero. Also: concatenate Fibonacci(n) 1’s.
  • A131294 (program): a(n)=ds_3(a(n-1))+ds_3(a(n-2)), a(0)=0, a(1)=1; where ds_3=digital sum base 3.
  • A131296 (program): a(n) = ds_5(a(n-1))+ds_5(a(n-2)), a(0)=0, a(1)=1; where ds_5=digital sum base 5.
  • A131300 (program): a(n) = 3a(n-1) - 2a(n-2) - a(n-3) + a(n-4) with n>3, a(0)=1, a(1)=2, a(2)=3, a(3)=7.
  • A131301 (program): Regular triangle read by rows: T(n,k) = 3*binomial(floor((n+k)/2),k)-2.
  • A131308 (program): Alternate A001477 and tripled 2*A000027.
  • A131309 (program): Rabbit-like sequence for phi^2.
  • A131326 (program): Row sums of A131325.
  • A131328 (program): Row sums of triangle A131327.
  • A131352 (program): Row sums of triangle A133935.
  • A131355 (program): Partial sums of A065423 plus one.
  • A131358 (program): a(3k) = 0, a(3k+1) = k+1, a(3*k+2) = -k.
  • A131360 (program): a(4n) = a(4n+1) = 0, a(4n+2) = 2n, a(4n+3) = 2n+1.
  • A131369 (program): Period 10: repeat [5, 4, 5, 4, 3, 4, 5, 4, 5, 0].
  • A131370 (program): a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3), a(0) = 3, a(1) = 2, a(2) = 0.
  • A131372 (program): Period 7: repeat [1, -1, 0, 1, 0, -1, 1].
  • A131377 (program): Starting with 1, the sequence a(n) changes from 1 to 0 or back when the next number n is a prime.
  • A131378 (program): Starting with 0, the sequence a(n) changes from 0 to 1 or back when the next number n is a prime.
  • A131379 (program): Period 4: repeat [1, 0, -1, 1].
  • A131380 (program): a(3n) = 2n, a(3n+1) = 2n+2, a(3n+2) = 2n+1.
  • A131381 (program): a(n) = binomial(2*n,n) mod (n+2), with n>=1.
  • A131386 (program): a(n) = (-1)^nn(n-2).
  • A131403 (program): Row sums of triangle A131402.
  • A131405 (program): Row sums of triangle A131404.
  • A131406 (program): 3A128174 - 2A000012(signed).
  • A131410 (program): A127647 * A000012.
  • A131412 (program): a(n) = n*(Fibonacci(n) - 1) + Fibonacci(n + 2) - 1.
  • A131421 (program): Triangle read by rows (n>=1, 1<=k<=n): T(n,k) = 2*(n+k) - 3.
  • A131422 (program): (A000012 * A127773) + (A127773 * A000012) - A000012.
  • A131423 (program): a(n) = n(n+2)(2*n-1)/3. Also, row sums of triangle A131422.
  • A131426 (program): a(n) = 2*prime(n) - 3.
  • A131428 (program): a(n) = 2*C(n) - 1, where C(n) = A000108(n) are the Catalan numbers.
  • A131431 (program): 3n + 1 preceded by n zeros.
  • A131436 (program): Triangle read by rows, (n-1) zeros followed by 2^n - 1.
  • A131437 (program): (A000012 * A131436) + (A131436 * A000012) - A000012.
  • A131438 (program): (2+n)2^n-2-3n.
  • A131439 (program): Inverse binomial transform of A131438 (assuming zero offset in both sequences)
  • A131452 (program): a(3n)=4n, a(3n+1)=4n+2, a(3n+2)=4n+1.
  • A131464 (program): a(n) = 4n^3 - 3n^2 + 2*n - 1.
  • A131465 (program): a(n)=4n^4-3n^3+2n^2-n+1.
  • A131466 (program): a(n) = 5n^4 - 4n^3 + 3n^2 - 2n + 1.
  • A131470 (program): a(n)=smallest number that gives a product with the sum of digits of n written in base 2 greater than n.
  • A131471 (program): a(n)=n^5+n.
  • A131472 (program): a(n) = n^6 + n.
  • A131473 (program): a(n) = n^6 - n.
  • A131474 (program): a(n) = ceiling(n/2)*ceiling(n^2/2).
  • A131475 (program): a(n) = floor(n/2) * floor(n^2/2).
  • A131476 (program): a(n) = floor(n^3/3).
  • A131477 (program): a(n) = ceiling(n^3/3).
  • A131478 (program): a(n) = ceiling(n^4/4).
  • A131479 (program): a(n) = floor(n^4/4).
  • A131491 (program): 2*prime(n)!.
  • A131500 (program): Radii of orbits of planets in solar system, in units of radius of orbit of Mercury, multiplied by 4.
  • A131501 (program): Xm/CV where Xm is a point of maximum error using an approximation method for x^(1/2) which I have found and CV is the population coefficient of variation from my list of error values.
  • A131505 (program): n, -1, n, 2n+2.
  • A131506 (program): 2n+1 appears 2n-1 times.
  • A131507 (program): 2n+1 appears n+1 times.
  • A131508 (program): 2*A000027 (natural numbers) sandwiched by tripled A001477 (nonnegative numbers).
  • A131509 (program): a(n) = (n + 1)(n^2 + 2)(n^3 + 3)/6.
  • A131516 (program): a(n)=1 if n is an odd prime number, otherwise, a(n)=n.
  • A131520 (program): Number of partitions of the graph G_n (defined below) into “strokes”.
  • A131524 (program): Number of possible palindromic rows (or columns) in an n X n crossword puzzle.
  • A131531 (program): Period 6: repeat [0, 0, 1, 0, 0, -1].
  • A131532 (program): Period 6: repeat [0, 0, 0, 0, 1, 1].
  • A131533 (program): Period 6: repeat [0, 0, 0, 0, 1, -1].
  • A131534 (program): Period 3: repeat [1, 2, 1].
  • A131554 (program): Period 5: repeat [1, 1, -1, 1, -1].
  • A131555 (program): Period 6: repeat [0, 0, 1, 1, 2, 2].
  • A131556 (program): Period 6: repeat [1, -2, 1, -1, 2, -1].
  • A131557 (program): Triangular numbers that are the sums of five consecutive triangular numbers.
  • A131561 (program): Period 3: repeat [1, 1, -1].
  • A131572 (program): a(0)=0 and a(1)=1, continued such that absolute values of 2nd differences equal the original sequence.
  • A131575 (program): First differences of A131572.
  • A131577 (program): Zero followed by powers of 2 (cf. A000079).
  • A131579 (program): Period 10: repeat 0, 3, 6, 9, 2, 5, 8, 1, 4, 7.
  • A131588 (program): Interlaces A007583 with A083420.
  • A131598 (program): Period 3: repeat [2, 5, 8].
  • A131607 (program): Pell companion numbers A001333 without last digit.
  • A131640 (program): First differences are periodic: 50, 50, 75, 50, 50, 75, …
  • A131649 (program): Number of distinct improper 2-coloring of edges for odd-order cyclic graphs.
  • A131664 (program): A string of n 1’s repeated n times.
  • A131666 (program): First differences of (A113405 prefixed with a 0).
  • A131668 (program): Smallest number whose sum of digits is 2n+1.
  • A131669 (program): Odd digits followed by positive even digits.
  • A131670 (program): Period 5: repeat [1, 0, -1, 0, 1].
  • A131673 (program): Size of the largest BDD of symmetric Boolean functions of n variables when the sink nodes are counted.
  • A131674 (program): Size of the largest BDD of symmetric Boolean functions of n variables when the sink nodes are not counted.
  • A131707 (program): Period 12: repeat 1, 1, 3, 7, 7, 1, 9, 9, 7, 3, 3, 9 .
  • A131708 (program): A024494 prefixed by a 0.
  • A131711 (program): Period 12: repeat 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1.
  • A131712 (program): Period 4: repeat [1, 3, 7, 9].
  • A131713 (program): Period 3: repeat [1, -2, 1].
  • A131714 (program): Period 6: repeat [1, -2, 2, -1, 2, -2].
  • A131716 (program): Period 6: repeat [0, 1, 2, 5, 8, 9].
  • A131717 (program): Natural numbers A000027 with 6n+4 and 6n+5 terms swapped.
  • A131718 (program): Period 6: repeat [1, 1, 2, 1, 2, 1].
  • A131719 (program): Period 6: repeat [0, 1, 1, 1, 1, 0].
  • A131720 (program): Period 6: repeat [0, 1, -1, 1, -1, 0].
  • A131722 (program): Period 6: repeat [0, 10, 10, 10, 10, 10].
  • A131723 (program): a(2n) = 1-n^2, a(2n+1) = n*(n+1).
  • A131724 (program): Period 6: repeat [1, 9, 7, 13, 11, 9].
  • A131725 (program): Partial sums of A131711.
  • A131726 (program): Pell numbers A000129 with 0 instead of last digit.
  • A131727 (program): Pell numbers A000129 without last digit.
  • A131728 (program): a(4n) = n, a(4n+1) = 2n+1, a(4n+2) = n+1, a(4n+3) = 0.
  • A131729 (program): Period 4: repeat [0, 1, -1, 1].
  • A131731 (program): Period 4: repeat [2, -3, 4, -3].
  • A131732 (program): a(4k) = 2k+1, a(4k+1) = -4k-3, a(4k+2) = 2k+2, a(4*k+3) = 0.
  • A131733 (program): Primes (A000040) - odds (A005408).
  • A131734 (program): Hexaperiodic [0, 1, 0, 1, 0, -1].
  • A131735 (program): Period 6: repeat [0, 0, 1, 1, 1, 1].
  • A131736 (program): Period 6: repeat [0, 0, 1, -1, -1, 1].
  • A131737 (program): Essentially even numbers followed by duplicated odd numbers.
  • A131738 (program): a(0) = 0. a(n) = (n+1)*(-1)^n, n>0 .
  • A131739 (program): a(4n) = a(4n+1) = n, a(4n+2) = 3n+2, a(4n+3) = 3n+3.
  • A131742 (program): a(4n) = a(4n+1) = 0, a(4n+2) = 3n+1, a(4n+3) = 3n+2.
  • A131743 (program): Period 4: repeat [0, 1, 0, 2].
  • A131750 (program): Numbers that are both centered triangular and centered square.
  • A131751 (program): Numbers that are both centered triangular and centered pentagonal.
  • A131755 (program): a(n) = floor of the average of distances between consecutive positive divisors of n. Also, a(n) = floor((n-1)/(d(n)-1)), where d(n) = A000005(n).
  • A131756 (program): Period 3: repeat [2, -1, 3].
  • A131757 (program): Period 10: repeat 3, 3, 3, -7, 3, 3, -7, 3, 3, -7.
  • A131762 (program): Number of 1s in the 1’s complement of the 32-bit binary representation of n.
  • A131768 (program): 2*(A007318 * A097807) - A000012.
  • A131769 (program): Number of connected components in the double Bruhat cells for simple Lie groups of type B_n (or C_n).
  • A131780 (program): Row sums of triangle A131779.
  • A131793 (program): 3 odds, 3 evens.
  • A131800 (program): Period 4: repeat [1, 2, 5, 6].
  • A131804 (program): Antidiagonal sums of triangular array T: T(j,k) = -(k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j.
  • A131805 (program): Row sums of triangular array T: T(j,k) = -(k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j.
  • A131806 (program): Period 4: repeat [0, 2, 4, 6].
  • A131807 (program): Partial sums of A131377.
  • A131808 (program): Partial sums of A131378.
  • A131818 (program): A130296 + A002260 - A000012. Triangle read by rows: row n consists of n, 2, 3, 4,…n.
  • A131820 (program): Row sums of triangle A131819.
  • A131821 (program): Triangle read by rows: row n consists of n followed by (n-2) ones then n.
  • A131833 (program): 2^(n+1)-1+3*n.
  • A131835 (program): Numbers starting with 1.
  • A131843 (program): Triangle read by rows: 2*A131821 - A000012.
  • A131844 (program): 3A131821 - 2A000012.
  • A131849 (program): Cardinality of largest subset of 1,…,n such that the difference between any two elements of the subset is never one less than a prime.
  • A131865 (program): Partial sums of powers of 16.
  • A131870 (program): Period 8: repeat [1, 2, 3, 4, 6, 7, 8, 9].
  • A131874 (program): (7n^2 + 15n + 2) / 2.
  • A131877 (program): a(n) = 14n + 1.
  • A131885 (program): a(n) = 4a(n-1) - 6a(n-2) + 4*a(n-3) for n >= 4 starting with a(0) = 1, a(1) = 2, a(2) = 4, and a(3) = 6.
  • A131895 (program): a(n) = (n + 2)(5n + 1)/2.
  • A131898 (program): a(n) = 2^(n+1) + 2*n - 1.
  • A131912 (program): Row sums of triangle A131911.
  • A131914 (program): 3A002024 - 2A051340.
  • A131922 (program): 2*A002024 - A130296.
  • A131923 (program): Triangle read by rows: T(n,k) = binomial(n,k) + n.
  • A131924 (program): Row sums of triangle A131923.
  • A131925 (program): 2*A002024 - A000012(signed).
  • A131937 (program): a(1)=1; a(2)=4. a(n) = a(n-1) + (n-th positive integer which does not occur in sequence A131938).
  • A131941 (program): Partial sums of ceiling(n^2/2) (A000982).
  • A131949 (program): Row sums of triangle A131948.
  • A131951 (program): 2^n+n*(n+3).
  • A131961 (program): Expansion of f(x, x^2) * f(x^2, x^2) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A131963 (program): Expansion of f(x, x^2) * f(x^4, x^12) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A131964 (program): Expansion of f(x^2, x^10) / f(x, x^3) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A131965 (program): a(n) = 1 + Sum_ i=2..n-1 n*a(i).
  • A131970 (program): 1 followed by 2n 2’s.
  • A131973 (program): Period 8: repeat 121, 242, 363, 484, 605, 726, 847, 968.
  • A131987 (program): Representation of a dense para-sequence.
  • A131991 (program): a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3.
  • A131992 (program): a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3 + prime(n)^4.
  • A131993 (program): 1 + prime(n) + prime(n)^2 + prime(n)^3 + prime(n)^4 + prime(n)^5.
  • A131996 (program): Number of partitions of n into distinct powers of 2 or of 3.
  • A132009 (program): a(1) = 1; for n>=2, a(n) = n-th positive integer which is coprime to the largest prime divisor of n.
  • A132027 (program): a(n) = Product_ k=0..floor(log_3(n)) floor(n/3^k), n>=1.
  • A132028 (program): Product 0<=k<=floor(log_4(n)), floor(n/4^k) , n>=1.
  • A132029 (program): Product 0<=k<=floor(log_5(n)), floor(n/5^k) , n>=1.
  • A132030 (program): a(n) = Product_ k=0..floor(log_6(n)) floor(n/6^k), n>=1.
  • A132031 (program): Product 0<=k<=floor(log_7(n)), floor(n/7^k) , n>=1.
  • A132032 (program): Product 0<=k<=floor(log_8(n)), floor(n/8^k) , n>=1.
  • A132033 (program): Product 0<=k<=floor(log_9(n)), floor(n/9^k) , n>=1.
  • A132044 (program): Triangle T(n,k) = binomial(n, k) - 1 with T(n,0) = T(n,n) = 1, read by rows.
  • A132045 (program): Row sums of triangle A132044.
  • A132046 (program): Triangle read by rows: T(n,0) = T(n,n) = 1, and T(n,k) = 2*binomial(n,k) for 1 <= k <= n - 1.
  • A132047 (program): 3A007318 - 2A103451.
  • A132048 (program): 3*A007318 - A103451 - A000012.
  • A132072 (program): Row sums of triangle A132071.
  • A132074 (program): Row sums of triangle A132073.
  • A132078 (program): Multiply previous term by 6 and reverse.
  • A132079 (program): a(n) = (5^n + 3)/2
  • A132086 (program): Record values in A132085.
  • A132090 (program): a(n) = pi(pi(n)), where pi = A000720.
  • A132106 (program): a(n) = 1 + floor(sqrt(n)) + Sum_ i=1..n floor(n/i).
  • A132109 (program): a(n) = (2^(n+1) + n^2 + n)/2.
  • A132112 (program): a(n) = n(n+1)(11*n+1)/6.
  • A132113 (program): Multiply previous term by 8 and reverse.
  • A132117 (program): Binomial transform of [1, 7, 17, 17, 6, 0, 0, 0,…].
  • A132118 (program): Triangle read by rows: T(n,k) = n(n-1)/2 + 2k - 1.
  • A132119 (program): A002260 + A000027 - A000012 as infinite lower triangular matrices.
  • A132122 (program): a(n) = n * (n+1)^2 * (3n^2 + 4n + 2) / 12.
  • A132123 (program): a(n) = n * (2n + 1) * (6n^2 + 4*n + 1) / 3.
  • A132124 (program): a(n) = n(n+1)(8*n + 1)/6.
  • A132127 (program): a(n) = (n^3 + 3*n - 2)/2.
  • A132128 (program): A051340 + A000027 - A000012.
  • A132140 (program): Numbers containing no zeros in ternary representation and with an initial 1.
  • A132141 (program): Numbers whose ternary representation begins with 1.
  • A132151 (program): Period 8: repeat [0, 1, 0, 0, 0, 0, -1, 0].
  • A132171 (program): 3^n repeated 3^n times.
  • A132173 (program): Maternal generation number of A063882(n).
  • A132188 (program): Number of 3-term geometric progressions with no term exceeding n.
  • A132189 (program): Number of non-constant 3-term geometric progressions with no term exceeding n.
  • A132194 (program): a(n) = 1 if n-th prime is 0 or 2 mod 3, otherwise 0.
  • A132197 (program): 2^n-1 written 2^n-1 times.
  • A132200 (program): Numbers in (4,4)-Pascal triangle .
  • A132208 (program): a(n) = 15n(n+1) + 11.
  • A132209 (program): a(0) = 0 and a(n) = 2n^2 + 2n - 1, for n>=1.
  • A132223 (program): A dense infinitive sequence.
  • A132226 (program): Placement sequence for the dense normalized fractal sequence A132224.
  • A132227 (program): a(n) = 3*prime(n) - 5.
  • A132230 (program): Primes congruent to 1 (mod 30).
  • A132231 (program): Primes congruent to 7 (mod 30).
  • A132232 (program): Primes congruent to 11 (mod 30).
  • A132233 (program): Primes congruent to 13 (mod 30).
  • A132234 (program): Primes congruent to 19 (mod 30).
  • A132235 (program): Primes congruent to 23 (mod 30).
  • A132236 (program): Primes congruent to 29 (mod 30).
  • A132269 (program): Product_ k>=0 (1 + floor(n/2^k)).
  • A132270 (program): a(n) = floor((n^7-1)/(7*n^6)), which is the same as integers repeated 7 times.
  • A132271 (program): Product k>=0, 1+floor(n/10^k) .
  • A132272 (program): Product k>0, 1+floor(n/10^k) .
  • A132292 (program): Integers repeated 8 times: a(n) = floor((n-1)/8).
  • A132295 (program): Sum of the nonsquare numbers not larger than n.
  • A132297 (program): Number of distinct Markov type classes of order 2 possible in binary strings of length n.
  • A132308 (program): 2*3^n - n - 1.
  • A132314 (program): a(n) = n*2^floor((n+1)/2).
  • A132315 (program): Sum of the non-fourth powers less than or equal to n.
  • A132327 (program): Product k>=0, 1+floor(n/3^k) .
  • A132328 (program): a(n) = Product_ k>0 (1+floor(n/3^k)).
  • A132338 (program): Decimal expansion of 1 - 1/phi.
  • A132344 (program): a(n) = n*2^(floor(n/2)).
  • A132345 (program): Number of increasing three-term geometric sequences from the integers 1,2,…,n .
  • A132349 (program): If n is a k-th power with k >= 2 then a(n) = k, otherwise a(n) = 0.
  • A132350 (program): If n > 1 is a k-th power with k >= 2 then a(n) = 0, otherwise a(n) = 1.
  • A132351 (program): Partial sums of A132350.
  • A132352 (program): Partial sums of A132351.
  • A132354 (program): Integers m such that 7*m + 1 is a square.
  • A132355 (program): Numbers of the form 9h^2 + 2h, for h an integer.
  • A132356 (program): a(2k) = k(10k+2), a(2k+1) = 10k^2 + 18k + 8, with k >= 0.
  • A132366 (program): Partial sum of centered tetrahedral numbers A005894.
  • A132367 (program): Period 6: repeat [1, 1, 2, -1, -1, -2].
  • A132369 (program): PrimePi(n)!.
  • A132371 (program): a(n) = n! - Sum_ j=1..n-1 j!.
  • A132380 (program): Period 8: repeat [0, 0, 1, 1, 0, 0, -1, -1].
  • A132383 (program): 4^n written 4^n times.
  • A132397 (program): Second trisection of A024494.
  • A132400 (program): Period 4: repeat [1, 5, 3, 1].
  • A132405 (program): Floor(exp(n)/n^2).
  • A132406 (program): Floor(exp(n)/n^3).
  • A132407 (program): a(n) = ceiling(exp(n)/n).
  • A132408 (program): Ceiling(exp(n)/n^2).
  • A132409 (program): Ceiling(exp(n)/n^3).
  • A132411 (program): a(0) = 0, a(1) = 1 and a(n) = n^2 - 1 with n>=2.
  • A132412 (program): Floor(n^2*exp(n)).
  • A132413 (program): Ceiling(n^2*exp(n)).
  • A132417 (program): a(16j+i) := 8(16j+i) + e_i, for j >= 0, 0 <= i <= 15, where e_0, …, e_15 are 2, -2, -6, -10, -14, -18, -22, -26, -30, -34, -38, -42, -46, -50, -54, 6.
  • A132419 (program): Period 6: repeat [1, 1, -2, -1, -1, 2].
  • A132429 (program): Period 4: repeat [3, 1, -1, -3].
  • A132433 (program): a(1) = 2; for n>=2, a(n) = 8*a(n-1) + 1.
  • A132434 (program): a(n) = A132433(n) - 33.
  • A132440 (program): Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator xDx, iterated Laguerre transforms, associated matrices of the list partition transform and general Euler transformation for sequences.
  • A132442 (program): Triangle, n-th row = first n terms of n-th row of an array formed by A051731 * A127093(transform).
  • A132458 (program): Let df(n,k) = Product_ i=0..k-1 (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2(2n-m)/((m-1)!*m!). Sequence gives P(4,n).
  • A132464 (program): Let df(n,k) = Product_ i=0..k-1 (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2(2n-m)/((m-1)!*m!). Sequence gives P(6,n).
  • A132465 (program): Let df(n,k) = Product_ i=0..k-1 (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2(2n-m)/((m-1)!*m!). Sequence gives P(7,n).
  • A132466 (program): Let df(n,k) = Product_ i=0..k-1 (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2(2n-m)/((m-1)!*m!). Sequence gives P(8,n).
  • A132469 (program): a(n) = (2^(5n)-1)/31.
  • A132477 (program): Row sums of triangle A132476.
  • A132479 (program): Row sums of triangle A132478.
  • A132583 (program): a(n) = n 2’s sandwiched between two 1’s.
  • A132584 (program): a(0)=0, a(1)=4; for n > 1, a(n) = 18*a(n-1) - a(n-2) + 8.
  • A132592 (program): X-values of solutions to the equation X(X + 1) - 8Y^2 = 0.
  • A132593 (program): Nonnegative integer solutions X to the equation: X(X + 1) - 10*Y^2 = 0.
  • A132594 (program): Values X satisfying the equation: X(X + 1) - 7*Y^2 = 0.
  • A132596 (program): X-values of solutions to the equation X(X + 1) - 6Y^2 = 0.
  • A132607 (program): X-values of solutions to the equation X(X + 1) - 11Y^2 = 0.
  • A132635 (program): Number of primes, 0’s, and 1’s in [0, n^2).
  • A132637 (program): Composite number C(n) raised to power C(n).
  • A132644 (program): X-values of solutions to the equation X(X + 1) - 13Y^2 = 0.
  • A132650 (program): Number of divisors of n, d(n) raised to power d(n).
  • A132651 (program): Sum of proper divisors of n, s(n) raised to power s(n), for n > 1.
  • A132652 (program): Sum of divisors of n, Sigma(n) raised to power Sigma(n).
  • A132677 (program): Period 3: repeat [1, 2, -3].
  • A132680 (program): Number of ones in binary representation of odious numbers.
  • A132681 (program): Infinitesimal generator matrix for a diagonally-shifted Pascal matrix, binomial(n+m,k+m), for m=1, related to Laguerre(n,x,m).
  • A132683 (program): a(n) = binomial(2^n + n, n).
  • A132684 (program): a(n) = binomial(2^n + n + 1, n).
  • A132685 (program): a(n) = binomial(2^n + 2*n, n).
  • A132686 (program): a(n) = binomial(2^n + 2*n + 1, n).
  • A132687 (program): a(n) = binomial(2^n + 3*n - 1, n).
  • A132688 (program): a(n) = binomial(2^n + 3*n, n).
  • A132708 (program): Period 6: repeat [4, 2, 1, -4, -2, -1].
  • A132710 (program): Infinitesimal generator for a diagonally-shifted Lah matrix, unsigned A105278, related to n! Laguerre(n,-x,1).
  • A132720 (program): Sequence is identical to its second differences in absolute values.
  • A132723 (program): Binomial transform of A132429.
  • A132727 (program): a(n) = 3 * 2^(n-1) * a(n-1) with a(0) = 1.
  • A132728 (program): Triangle T(n, k) = 4 - 3*(-1)^k, read by rows.
  • A132729 (program): Triangle T(n, k) = 2*binomial(n, k) - 3 with T(n, 0) = T(n, n) = 1, read by rows.
  • A132730 (program): Row sums of triangle A132729.
  • A132731 (program): Triangle T(n,k) = 2 * binomial(n,k) - 2 with T(n,0) = T(n,n) = 1, read by rows.
  • A132732 (program): Row sums of triangle A132731.
  • A132733 (program): Triangle T(n, k) = 4*binomial(n, k) - 5 with T(n, 0) = T(n, n) = 1, read by rows.
  • A132734 (program): Row sums of triangle A132733.
  • A132735 (program): Triangle T(n,k) = binomial(n,k) + 1 with T(n,0) = T(n,n) = 1, read by rows.
  • A132736 (program): Row sums of triangle A132735.
  • A132737 (program): Triangle T(n,k) = 2*binomial(n,k) + 1, read by rows.
  • A132738 (program): Row sums of triangle A132737.
  • A132739 (program): Largest divisor of n not divisible by 5.
  • A132740 (program): Largest divisor of n coprime to 10.
  • A132741 (program): Largest divisor of n having the form 2^i*5^j.
  • A132744 (program): Decimal expansion of Pi/28.
  • A132749 (program): Triangle T(n,k) = binomial(n, k) with T(n, 0) = 2, read by rows.
  • A132750 (program): A132749 * [1, 2, 3, …] = A007318 * A065190.
  • A132751 (program): Triangle T(n, k) = 2/Beta(n-k+1, k) - 1, read by rows.
  • A132752 (program): Triangle T(n, k) = 2*A132749(n, k) - 1, read by rows.
  • A132753 (program): a(n) = 2^(n+1) - n + 1.
  • A132754 (program): a(n) = n*(n + 23)/2.
  • A132755 (program): a(n) = n*(n + 25)/2.
  • A132756 (program): a(n) = n*(n + 27)/2.
  • A132757 (program): a(n) = n*(n+29)/2.
  • A132758 (program): a(n) = n*(n + 31)/2.
  • A132759 (program): a(n) = n*(n+13).
  • A132760 (program): a(n) = n*(n+15).
  • A132761 (program): a(n) = n*(n+17).
  • A132762 (program): a(n) = n*(n + 19).
  • A132763 (program): a(n) = n*(n+21).
  • A132764 (program): a(n) = n*(n+22).
  • A132765 (program): a(n) = n*(n + 23).
  • A132766 (program): a(n) = n*(n+24).
  • A132767 (program): a(n) = n*(n + 25).
  • A132768 (program): a(n) = n*(n + 26).
  • A132769 (program): a(n) = n*(n + 27).
  • A132770 (program): a(n) = n*(n + 28).
  • A132771 (program): a(n) = n*(n + 29).
  • A132772 (program): a(n) = n*(n + 30).
  • A132773 (program): a(n) = n*(n + 31).
  • A132780 (program): a(0)=1. a(n+1)=2*a(n)-A130151(n).
  • A132788 (program): a(n) = 2binomial(2n,n)/(n+1) - n.
  • A132792 (program): The infinitesimal Lah matrix: generator of unsigned A111596.
  • A132798 (program): Period 6: repeat [0, 2, 1, 0, -2, -1].
  • A132804 (program): A trisection of A024495.
  • A132805 (program): A trisection of A024495.
  • A132823 (program): A007318 + 2A103451 - 2A000012.
  • A132824 (program): Row sums of triangle A132823.
  • A132896 (program): Triangle read by rows: T(n,k)=number of prime divisors of C(n,k), counted with multiplicity (0<=k<=n).
  • A132899 (program): Row sums of triangle A132898.
  • A132911 (program): a(n)=(n+1)(2n)!/2^n.
  • A132918 (program): Identity matrix with interpolated zeros.
  • A132920 (program): a(n) = n*Fibonacci(n) + binomial(n, 2).
  • A132922 (program): Row sums of triangle A132921.
  • A132925 (program): a(n) = 2^n - 1 + n*(n-1)/2.
  • A132944 (program): a(n)=Floor[n^(1/3)+n^(1/4)].
  • A132951 (program): Period 6: 1, 3, 1, -1, -3, -1.
  • A132954 (program): Period 6: repeat [1, 2, 4, -1, -2, -4].
  • A132998 (program): a(n) = n^4 - n^3 - n^2.
  • A133012 (program): Even imperfect numbers.
  • A133016 (program): Even imperfect numbers, divided by 2.
  • A133019 (program): Product of n-th prime and n-th prime written backwards.
  • A133022 (program): Product of n-th Fibonacci number and n-th Fibonacci number written backwards.
  • A133037 (program): Squares of members of the Padovan sequence A000931.
  • A133038 (program): Cubes of A000931.
  • A133043 (program): Number of segments needed to draw the spiral of equilateral triangles with side lengths which follow the Padovan sequence.
  • A133044 (program): Area of the spiral of equilateral triangles with side lengths which follow the Padovan sequence, divided by the area of the initial triangle.
  • A133070 (program): a(n) = n^5 - n^3 - n^2.
  • A133071 (program): a(n) = n^5 - n^3 + n^2.
  • A133072 (program): a(n) = n^5 + n^3 - n^2.
  • A133073 (program): a(n) = n^5 + n^3 + n^2.
  • A133080 (program): Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones.
  • A133081 (program): An interpolation operator, companion to A133080.
  • A133082 (program): Triangle read by rows: T(k,m) = dimension of shape space for k labeled points in R^m (1 <= k <= m-1, m >= 2).
  • A133083 (program): A000012 * A133080.
  • A133086 (program): Row sums of triangle A133085.
  • A133090 (program): A133081 * [1,2,3,…].
  • A133092 (program): Row sums of triangle A133091.
  • A133095 (program): Row sums of triangle A133094.
  • A133100 (program): Expansion of f(x, x^4) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A133101 (program): Expansion of f(x^2, x^3) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A133109 (program): A042965 as a diagonalized matrix.
  • A133124 (program): A007318 * [1, 2, 2, 3, 2, 3, 2, 3, 2,…].
  • A133125 (program): A133080 * A000244.
  • A133137 (program): a(1) = 1, a(2) = 2, a(n) = smallest number not the sum of 4th powers of 2 distinct earlier terms.
  • A133140 (program): a(0) = 2, a(n) = 2^n + 2 for n>=1.
  • A133141 (program): Numbers which are both centered pentagonal (A005891) and centered hexagonal numbers (A003215).
  • A133143 (program): Maximal number of mutually nonattacking Super Queens on an n X n board. (a Super Queen is a queen with both queen and knight powers).
  • A133145 (program): Period 4: repeat [1, 2, 4, 8].
  • A133146 (program): Antidiagonal sums of the triangle A133128.
  • A133155 (program): Numbers formed by setting bits representing odd primes, where bit_no = (prime - 1)/2. Setting bit number b is the same as OR-ing with 2^b (i.e., bit numbers start at zero).
  • A133161 (program): Indices of the triangular numbers which are also centered triangular number.
  • A133180 (program): sum[k^6]/sum[k^2], k, 1, A047380(n) ].
  • A133186 (program): Period 4: repeat [1, 2, 1, -4].
  • A133190 (program): a(n) = 2a(n-1) - a(n-2) + 2a(n-3).
  • A133195 (program): Smallest number whose sum of digits is 3n.
  • A133196 (program): n+2 repeated n times.
  • A133201 (program): A133195/3.
  • A133203 (program): a(n) = a(n-1) + 8*n + 4, n > 2.
  • A133221 (program): A001147 with each term repeated.
  • A133223 (program): Sum of digits of primes (A007605), sorted and with duplicates removed.
  • A133224 (program): Let P(A) be the power set of an n-element set A and let B be the Cartesian product of P(A) with itself. Remove (y,x) from B when (x,y) is in B and x <> y and let R35 denote the reduced set B. Then a(n) = the sum of the sizes of the union of x and y for every (x,y) in R35.
  • A133252 (program): Partial sums of A006000.
  • A133256 (program): a(4n+1) = 4n+1, a(4n+2) = 4n+2, a(4n+3) = 4n+4, a(4n+4) = 4n+3.
  • A133257 (program): The number of edges on a piece of paper that has been folded n times (see comments for more precise definition).
  • A133259 (program): a(6n) = 6n+1, a(6n+1) = 6n+2, a(6n+2) = 6n+3, a(6n+3) = 6n+6, a(6n+4) = 6n+5, a(6n+5) = 6n+4.
  • A133263 (program): Binomial transform of (1, 2, 0, 1, -1, 1, -1, 1, …).
  • A133264 (program): Smallest number whose sum of digits is 3n+1.
  • A133265 (program): Diagonal of the A135356 triangle.
  • A133271 (program): Indices of 7-gonal numbers which are also centered 7-gonal numbers.
  • A133272 (program): Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566).
  • A133273 (program): Indices of centered decagonal numbers which are also decagonal numbers.
  • A133274 (program): Numbers which are both 12-gonal and centered 12-gonal numbers.
  • A133275 (program): Numbers X such that 30*X^2-45 is a square.
  • A133280 (program): Triangle formed by: 1 even, 2 odd, 3 even, 4 odd, … starting with zero.
  • A133284 (program): Indices of the 12-gonal numbers which are also centered 12-gonal number or numbers X such that 30X^2-24X+3 is a square.
  • A133292 (program): Period 9: repeat [1, 1, 2, 4, 7, 2, 7, 4, 2].
  • A133294 (program): a(n) = 2a(n-1) + 10a(n-2), a(0)=1, a(1)=1.
  • A133296 (program): Smallest number whose sum of digits is 2n.
  • A133310 (program): a(3n) = 2n+1, a(3n+1) = 2n+2, a(3n+2) = 2n+1.
  • A133337 (program): a(3n) = 0, a(3n+1) = a(3n+2) = 5^n.
  • A133345 (program): a(n)=2a(n-1)+14a(n-2) for n>1, a(0)=1, a(1)=1.
  • A133350 (program): Dimensions of certain Lie algebra (see reference for precise definition).
  • A133355 (program): Dimensions of certain Lie algebra (see reference for precise definition).
  • A133356 (program): a(n)=2a(n-1)+16a(n-2) for n>1, a(0)=1, a(1)=1 .
  • A133363 (program): Numbers n such that 1+Sum[3k, k=1,2,…,n] is prime.
  • A133368 (program): Period 5: 1, 1, 3, 7, 3.
  • A133375 (program): Catalan numbers with digits sorted in increasing order and zeros suppressed.
  • A133383 (program): 10 followed by 2n 9’s.
  • A133384 (program): Numbers with n 0’s between 1 and 2.
  • A133398 (program): Numbers that are not Mersenne primes.
  • A133405 (program): a(n) = 3a(n-1) - a(n-3) + 3a(n-4).
  • A133407 (program): a(n) = a(n-1) + 5*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133409 (program): Zero followed by partial sums of A133405.
  • A133417 (program): a(n) = sqrt(2(P(n)^4 + 16P(n+1)^4 + P(n+2)^4)), where P() = Pell numbers A000129.
  • A133460 (program): 3^n*2^(n^2).
  • A133462 (program): a(n+1)-10a(n)=3(-3, -2, -1, 0, 1, 2, 3, 4, 5 …).
  • A133463 (program): Partial sums of the sequence that starts with 2 and is followed by A111575.
  • A133464 (program): a(3n)=4^n, a(3n+1)=24^n, a(3n+2)=34^n.
  • A133466 (program): Positive integers k for which there is exactly one integer i in 1,2,3,…,k-1 such that i*k is a square.
  • A133467 (program): a(n) = a(n-1) + 6*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133469 (program): a(n) = a(n-1) + 7*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133472 (program): 6 followed by numbers with n-1 0’s between 1 and 5.
  • A133473 (program): 2 followed by numbers with n-1 3’s before 5.
  • A133477 (program): Sum of cubefree divisors of n excluding 1.
  • A133479 (program): a(n) = a(n-1) + 8*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133480 (program): Left 3-step factorial (n,-3)!: a(n) = (-1)^n * A008544(n).
  • A133494 (program): Diagonal of the array of iterated differences of A047848.
  • A133496 (program): a(n) = (29*n)^2.
  • A133499 (program): a(n) = n^7 - n.
  • A133510 (program): Number of primitive H-invariant prime ideals in O_q(M_ 2,n ) generic quantum matrices.
  • A133512 (program): Accept F(1), reject F(1), accept F(2), reject F(2), accept F(3), …,.
  • A133513 (program): Period 6: repeat [0, 1, -3, 0, -1, 3].
  • A133546 (program): Binomial transform of [1,3,5,6,7,8,9,10,11,…] (i.e., positive integers except 2 and 4).
  • A133547 (program): a(n) = sum of squares of first n odd primes.
  • A133548 (program): a(n) = sum of cubes of first n odd primes.
  • A133549 (program): Sum of the fourth powers of the first n odd primes.
  • A133550 (program): Sum of fifth powers of n odd primes.
  • A133558 (program): a(n) = a(n-1) + 9*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133566 (program): Triangle read by rows: (1,1,1,…) on the main diagonal and (0,1,0,1,…) on the subdiagonal.
  • A133572 (program): Row sums of triangle A133571.
  • A133577 (program): a(n) = a(n-1) + 10*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133586 (program): Expansion of x(1+2x)/( (x^2-x-1)*(x^2+x-1) ).
  • A133600 (program): Row sums of triangle A133599.
  • A133610 (program): Partial sums of pyramidal sequence A053616.
  • A133620 (program): Binomial(n+p,n) mod n where p=10.
  • A133622 (program): a(n) = 1 if n is odd, a(n) = n/2+1 if n is even.
  • A133623 (program): Binomial(n+p, n) mod n where p=3.
  • A133624 (program): Binomial(n+p, n) mod n, where p=4.
  • A133625 (program): Binomial(n+p, n) mod n where p=5.
  • A133628 (program): a(1)=1, a(n) = a(n-1) + (p-1)*p^(n/2-1) if n is even, else a(n) = a(n-1) + p^((n-1)/2), where p=4.
  • A133629 (program): a(1)=1, a(n) = a(n-1) + (p-1)*p^(n/2-1) if n is even, otherwise a(n) = a(n-1) + p^((n-1)/2), where p=5.
  • A133631 (program): a(n) = a(n-1) - 4*a(n-2), a(0)=1, a(1)=2.
  • A133632 (program): a(1)=1, a(n)=(p-1)a(n-1), if n is even, else a(n)=pa(n-2), where p=5.
  • A133641 (program): a(n) = 2*L(n) + L(n-1) - n, L(n) = n-th Lucas number of A000032 starting (1,3,4,…). =.
  • A133647 (program): A133566 * A000244.
  • A133648 (program): a(n) = 2*3^n + 3^(n-1) - (n+1).
  • A133649 (program): A007318^(-1) * A133648.
  • A133653 (program): A007318^(-1) * A003261.
  • A133654 (program): a(n) = 2*A000129(n) - 1.
  • A133655 (program): a(n) = 2*A016777(n) + A016777(n-1) - (n+1).
  • A133673 (program): a(n) = nL(n) + (n-1)L(n-1) where L(n) is the Lucas number.
  • A133677 (program): Integers k such that prime(k)(2prime(k)-1)/3 is an integer.
  • A133694 (program): a(n) = (3n^2 + 3n - 4)/2.
  • A133695 (program): a(n) = 2*A008683 - 1.
  • A133752 (program): a(n) = 256^n.
  • A133754 (program): a(n) = n^5 - n^3.
  • A133760 (program): Sum of the number of divisors of the numbers between prime(n) and prime(n+1).
  • A133766 (program): a(n) = (4n+1)(4n+3)(4*n+5).
  • A133767 (program): a(n) = (4n+3)(4n+5)(4*n+7).
  • A133790 (program): A014963*A100994.
  • A133799 (program): a(2) = 1, a(3)=3; for n >= 4, a(n) = (n-2)!*Stirling_2(n,n-1)/2 = n!/4.
  • A133818 (program): a(n) = (8n+3)(8n+5)(8n+7)(8*n+9).
  • A133819 (program): Triangle whose rows are sequences of increasing squares: 1; 1,4; 1,4,9; … .
  • A133820 (program): Triangle whose rows are sequences of increasing cubes: 1; 1,8; 1,8,27; … .
  • A133821 (program): Triangle whose rows are sequences of increasing fourth powers: 1; 1,16; 1,16,81; … .
  • A133823 (program): Triangle whose rows are sequences of increasing and decreasing cubes:1; 1,8,1; 1,8,27,8,1; … .
  • A133824 (program): Triangle whose rows are sequences of increasing and decreasing fourth powers: 1; 1,16,1; 1,16,81,16,1; … .
  • A133825 (program): Triangle whose rows are sequences of increasing and decreasing triangular numbers: 1; 1,3,1; 1,3,6,3,1; … .
  • A133826 (program): Triangle whose rows are sequences of increasing and decreasing tetrahedral numbers: 1; 1,4,1; 1,4,10,4,1; … .
  • A133827 (program): Number of solutions to x + 7 * y = 2 * n in triangular numbers.
  • A133851 (program): Sloping binary representation of powers of 4 (A000302), slope = -1 .
  • A133853 (program): a(n) = (64^n - 1)/63.
  • A133872 (program): Period 4: repeat [1, 1, 0, 0].
  • A133873 (program): n modulo 3 repeated 3 times.
  • A133874 (program): n modulo 4 repeated 4 times.
  • A133875 (program): n modulo 5 repeated 5 times.
  • A133876 (program): n modulo 6 repeated 6 times.
  • A133877 (program): n modulo 7 repeated 7 times.
  • A133878 (program): n modulo 8 repeated 8 times.
  • A133879 (program): n modulo 9 repeated 9 times.
  • A133880 (program): n modulo p repeated p times (where p=10).
  • A133882 (program): a(n) = binomial(n+2,n) mod 2^2.
  • A133883 (program): a(n) = binomial(n+3,n) mod 3^2.
  • A133884 (program): a(n) = binomial(n+4,n) mod 4.
  • A133885 (program): Binomial(n+5,n) mod 5^2.
  • A133886 (program): a(n) = binomial(n+6,n) mod 6.
  • A133887 (program): Binomial(n+7,n) mod 7^2.
  • A133888 (program): Binomial(n+8,n) mod 8.
  • A133889 (program): Binomial(n+9,n) mod 9.
  • A133890 (program): Binomial(n+10,n) mod 10.
  • A133891 (program): a(n) = binomial(n+p,n) mod p, where p=12.
  • A133893 (program): Numbers m such that binomial(m+3,m) mod 3 = 0.
  • A133894 (program): Numbers m such that binomial(m+4,m) mod 4 = 0.
  • A133895 (program): Numbers m such that binomial(m+5,m) mod 5 = 0.
  • A133897 (program): Numbers m such that binomial(m+7,m) mod 7 = 0.
  • A133898 (program): Numbers m such that binomial(m+8,m) mod 8 = 0.
  • A133899 (program): Numbers m such that binomial(m+9,m) mod 9 = 0.
  • A133931 (program): Expansion of x(2-4x^2-x^3)/((1-x)^2*(1-x-x^2)).
  • A133936 (program): Number of times prime powers occur in the columns of tables A133232 and A133233.
  • A133942 (program): a(n) = (-1)^n * n!.
  • A133953 (program): A second integer solution:d=2;h=1; A 4 X 4 vector Markov of a game matrix MA and an anti- game matrix MB such that game_valueMa+game_ValueMB =0 and the score is the sum of the vector out put of the Markov: MA= 0,1 , 1,d ; MB= 1/h,0 ,(2 - d + 1/h + h),h ; Characteristic Polynomial is: -1 + 4 x^2 - 4 x^3 + x^4.
  • A133989 (program): Define fu(1,1) = 0. Then a(n) = fu(1,n) = smallest number t such that an n X 1 strip of n squares can be cut into n squares using p_1, p_2, …, p_t cuts where p_t is a prime number or p_t = 1.
  • A133993 (program): a(n) = a(n-1) + 3a(n-2) - a(n-3) - 2a(n-4), n > 3.
  • A134006 (program): a(n) = 1^n + 3^n + 5^n + 7^n.
  • A134010 (program): n^(initial digit of n).
  • A134011 (program): Period 9: repeat [1, 2, 3, 4, 5, 4, 3, 2, 1].
  • A134012 (program): Period 5: repeat 1, 6, 11, 6, 1.
  • A134017 (program): Period 9: repeat 1, 2, 4, 3, 5, 3, 4, 2, 1.
  • A134021 (program): Length of n in balanced ternary representation.
  • A134022 (program): Number of negative trits in balanced ternary representation of n.
  • A134024 (program): Number of positive trits in balanced ternary representation of n.
  • A134025 (program): Numbers for which the balanced ternary representation is the same length as the ternary representation.
  • A134026 (program): Numbers that are in balanced ternary representation longer than in ternary representation.
  • A134029 (program): Period 9: repeat 3, 2, 4, 1, 5, 1, 4, 2, 3.
  • A134057 (program): a(n) = binomial(2^n-1,2).
  • A134058 (program): Triangle T(n, k) = 2*binomial(n, k) with T(0, 0) = 1, read by rows.
  • A134059 (program): Triangle T(n, k) = 3*binomial(n,k) with T(0, 0) = 1, read by rows.
  • A134060 (program): Triangle T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k), read by rows.
  • A134062 (program): Row sums of triangle A134061.
  • A134063 (program): a(n) = (1/2)*(3^n - 2^(n+1) + 3).
  • A134064 (program): Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements x,y of P(A) for which either 0) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 1) x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x, or 2) x = y.
  • A134067 (program): Row sums of triangle A134066.
  • A134115 (program): Powers of 9 written backwards and sorted.
  • A134119 (program): a(n) = floor(n^2/10) - floor((n-1)^2/10).
  • A134142 (program): List of quadruples: 2(-4)^n, -3(-4)^n, 2(-4^n), 2(-4)^n, n >= 0.
  • A134153 (program): a(n) = 15n^2 + 9n + 1.
  • A134154 (program): a(n) = 15n^2 - 9n + 1.
  • A134155 (program): a(n) = 1 + 21 n + 168 n^2 + 588 n^3 + 1029 n^4.
  • A134156 (program): a(n) = 2*tau(n) - n, where tau(n) is the number of divisors of n (A000005).
  • A134158 (program): a(n) = 1 + 27n + 252n^2 + 882n^3 + 1029n^4.
  • A134159 (program): a(n) = 13 + 165 n + 756 n^2 + 1470 n^3 + 1029 n^4.
  • A134160 (program): a(n) = 163 + 1053n + 2520n^2 + 2646n^3 + 1029n^4.
  • A134161 (program): a(n) = 373 + 1947n + 3780n^2 + 3234n^3 + 1029n^4.
  • A134163 (program): 1 + 12n + 81n^3 + n(105n + 81*n^3)/2.
  • A134169 (program): a(n) = 2^(n-1)*(2^n - 1) + 1.
  • A134171 (program): a(n) = (9/2)(n-1)(n-2)*(n-3).
  • A134172 (program): Expansion of x^2(1+x)(1-x+x^2) / ((1-x)^2*(1+x^2)^2).
  • A134175 (program): a(n) = (32/2)(n-1)(n-2)(n-3)(n-4).
  • A134181 (program): Difference between cumulative prime and odd sums.
  • A134183 (program): A Hankel transform of a Catalan product.
  • A134195 (program): Antidiagonal sums of square array A126885.
  • A134201 (program): Number of rigid hypergroups of order n.
  • A134202 (program): Number of rigid Hv-groups of order n.
  • A134227 (program): Row sums of triangle A134226.
  • A134230 (program): a(n) = (10^n+1)^2-1.
  • A134238 (program): Row sums of triangle A134237.
  • A134249 (program): Triangle read by rows, taken from the lower triangular matrix (M * A000012 + A000012 * M) - A000012; where M = lower triangular matrix with (1,1,1,…) in the main diagonal and the triangular numbers in the subdiagonal and A000012 = (1; 1,1; 1,1,1;…).
  • A134267 (program): a(n) = A090964(n+1) - A090964(n) .
  • A134286 (program): Characteristic sequence for sequence A026905.
  • A134287 (program): Fifth column of triangle A103371 (without leading zeros).
  • A134288 (program): a(n) = binomial(n+7,7)*binomial(n+7,6)/(n+7).
  • A134289 (program): Eighth column (and diagonal) of Narayana triangle A001263.
  • A134290 (program): Ninth column (and diagonal) of Narayana triangle A001263.
  • A134297 (program): a(n) = 107*n.
  • A134298 (program): a(n) = (107*n)^5.
  • A134301 (program): Periodic sequence (0, 2, 6, 2, 0).
  • A134309 (program): Triangle read by rows, where row n consists of n zeros followed by 2^(n-1).
  • A134310 (program): (A000012 * A134309 + A134309 * A000012) - A000012.
  • A134311 (program): Row sums of triangle A134310.
  • A134314 (program): First differences of A134429.
  • A134316 (program): a(n) = index of first derangement of 1..n (n>=2).
  • A134323 (program): a(n) = Legendre(-3, prime(n)).
  • A134327 (program): a(n) = (n^5-n-5)/5.
  • A134341 (program): Numbers whose fifth powers have a partition as a sum of fifth powers of four positive integers.
  • A134342 (program): Accepted inputs by a certain adaptive automaton (number 4258072) with two adaptive functions and unary numbers as input.
  • A134350 (program): Row sums of triangle A134349.
  • A134351 (program): Binomial transform of [1, 5, -1, 5, -1, 5, …]. Inverse binomial transform of A134350.
  • A134353 (program): Row sums of triangle A134352.
  • A134372 (program): a(n) = ((2n)!)^2.
  • A134374 (program): a(n) = ((2n+1)!)^2.
  • A134375 (program): a(n) = (n!)^4.
  • A134391 (program): The sequence A_0, A_1, A_2, A_3, …, where the A_k are defined in A064990.
  • A134393 (program): Row sums of triangle A134392.
  • A134399 (program): Matrix product of Binomial triangle A007318 and triangle with (1, 1, 2, 3, 4, 5,…) in the main diagonal and the rest zeros.
  • A134401 (program): Row sums of triangle A134400.
  • A134402 (program): Triangle read by rows, for n > 0, n zeros followed by n.
  • A134403 (program): Triangle read by rows: row n consists of (n, n, (n+1), (n+2), (n+3),…).
  • A134404 (program): Triangle read by rows in which row n contains Fib(0), …, Fib(n-1), Fib(n), Fib(n-1), …, Fib(0).
  • A134405 (program): -1 before list of quadruples -2n-1, 2n+2, -2n, 2n+1.
  • A134418 (program): Row sums of triangle A134417.
  • A134421 (program): Partial sums of A134021.
  • A134429 (program): Array read by rows: row n lists 4 terms: k, m, k, m where k = 8n+3 and m = -8n -5.
  • A134430 (program): Period 4: repeat [1, -2, -2, 1].
  • A134432 (program): Sum of entries in all the arrangements of the set 1,2,…,n (to n=0 there corresponds the empty set).
  • A134437 (program): Number of cells in the 2nd rows of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A134441 (program): Last two digits of primes of form 4n+1 (A002144), excluding 5. Leading 0’s omitted.
  • A134442 (program): Last two digits of primes of form 4n+3 (A002145). Leading 0’s omitted.
  • A134444 (program): (A000012 * A128174 + A128174 * A000012) - A000012.
  • A134449 (program): Sum of even products minus sum of odd products of different pairs of numbers from 1 to n.
  • A134451 (program): Ternary digital root of n.
  • A134464 (program): (A127648 * A000012 + A000012 * A127773) - A000012.
  • A134465 (program): Row sums of triangle A134464.
  • A134467 (program): a(n) = n(n+1) - A000120(n), where A000120(n) = number of 1’s in binary expansion of n.
  • A134478 (program): Triangle read by rows, T(0,0) = 1; n-th row = (n+1) terms of n, n+1, n+2…
  • A134479 (program): Row sums of triangle A134478.
  • A134481 (program): Row sums of triangle A134480.
  • A134482 (program): Triangle read by rows: row n consists of n followed by the numbers n through 2n-2.
  • A134483 (program): Triangle read by rows: T(n,k)=2n+k-2; 1<=k<=n.
  • A134488 (program): a(0)=1. a(n) = n + d(a(n-1)), where d(m) is the number of positive divisors of m.
  • A134489 (program): a(n) = Fibonacci(5*n + 2).
  • A134490 (program): a(n) = Fibonacci(5n + 3).
  • A134491 (program): Fibonacci(5n+4).
  • A134492 (program): a(n) = Fibonacci(6*n).
  • A134493 (program): a(n) = Fibonacci(6*n+1).
  • A134494 (program): a(n) = Fibonacci(6n+2).
  • A134495 (program): a(n) = Fibonacci(6n + 3).
  • A134496 (program): Numbers that are not lunar pseudoprimes.
  • A134497 (program): a(n) = Fibonacci(6n+5).
  • A134498 (program): a(n) = Fibonacci(7n).
  • A134499 (program): a(n) = Fibonacci(7*n+1).
  • A134500 (program): a(n) = Fibonacci(7n + 2).
  • A134501 (program): a(n) = Fibonacci(7n + 3).
  • A134502 (program): a(n) = Fibonacci(7n + 4).
  • A134503 (program): a(n) = Fibonacci(7n + 5).
  • A134504 (program): a(n) = Fibonacci(7n + 6).
  • A134507 (program): Number of rectangles in a pyramid built with squares. The squares counted in A092498 are excluded.
  • A134519 (program): Numbers remaining when the natural numbers (A000027) are arranged into a triangle and only the beginning and end terms of each row are retained.
  • A134522 (program): a(n) = 2^n + ceiling(n/2).
  • A134538 (program): a(n) = 5*n^2 - 1.
  • A134547 (program): a(n)=5n^2+20n+4.
  • A134567 (program): a(n) = least m such that -mtau < ntau , where denotes fractional part and tau = (1 + sqrt(5))/2.
  • A134582 (program): a(n) = (2*n)^2 - 4.
  • A134591 (program): a(n) is n reflected in n-th prime: distance between a(n) and p(n) equals distance between p(n) and n.
  • A134593 (program): a(n) = 5n^2 + 10n + 1. Coefficients of the rational part of (1 + sqrt(n))^5.
  • A134594 (program): a(n) = n^2 + 10*n + 5: coefficients of the irrational part of (1 + sqrt(n))^5.
  • A134632 (program): 5n^5 + 3n^3 - 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.
  • A134633 (program): 5n^5 + 3n^3 + 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.
  • A134638 (program): Row sums of triangle A134637.
  • A134660 (program): Number of odd coefficients in (1 + x + x^2 + x^3)^n.
  • A134667 (program): Period 6: repeat [0, 1, 0, 0, 0, -1].
  • A134668 (program): Period 6: repeat [1, -1, 0, 0, -1, 1].
  • A134681 (program): Number of digits of all the divisors of n.
  • A134683 (program): Expansion of 1+x(2+3x)/(1-4*x^2).
  • A134684 (program): n^(n+9).
  • A134693 (program): a(n)=A133806(n)+A133806(n+6).
  • A134751 (program): Hankel transform of expansion of (1/(1-x^2))c(x/(1-x^2)), where c(x) is the g.f. of A000108.
  • A134752 (program): a(n) = 3^(2*n-1) + 2.
  • A134758 (program): a(n) = A000984(n) + n.
  • A134759 (program): a(n) = 2*A000984(n) - (n+1)
  • A134760 (program): a(n) = 2*A000984(n) - 1.
  • A134761 (program): A007318^(-2) * A134760.
  • A134762 (program): a(n) = 3*A000984(n) - 2.
  • A134770 (program): a(n) = 4*A000984(n) - 3.
  • A134804 (program): Remainder of triangular number A000217(n) modulo 9.
  • A134816 (program): Padovan’s spiral numbers.
  • A134824 (program): Generated by reverse of Schroeder II o.g.f.
  • A134828 (program): Numerator of moments of Chebyshev U- (or S-) polynomials.
  • A134859 (program): Wythoff AAA numbers.
  • A134860 (program): Wythoff AAB numbers; also, Fib101 numbers: those n for which the Zeckendorf expansion A014417(n) ends with 1,0,1.
  • A134861 (program): Wythoff BAA numbers.
  • A134862 (program): Wythoff ABB numbers.
  • A134863 (program): Wythoff BAB numbers.
  • A134864 (program): Wythoff BBB numbers.
  • A134868 (program): A103451 * A002260.
  • A134869 (program): Row sums of triangle A134868.
  • A134871 (program): a(1) = 1, a(n) = tau(n) + n - 2 for n > 1.
  • A134875 (program): a(n)=the smallest sum of two nontrivial divisors of n, if any, whose product equals n; otherwise, a(n)=n.
  • A134889 (program): a(n)=the largest sum of two nontrivial divisors of n, if any, whose product equals n; otherwise, a(n)=n.
  • A134914 (program): Ceiling(n^(1/3)).
  • A134917 (program): a(n) = ceiling(n^(4/3)).
  • A134918 (program): Ceiling(n^(5/3)).
  • A134919 (program): Floor(n^(5/3)).
  • A134927 (program): a(0)=a(1)=1; a(n) = 3*(a(n-1) + a(n-2)).
  • A134931 (program): a(n) = (5*3^n-3)/2.
  • A134934 (program): a(n) = (14*n+1)^2.
  • A134943 (program): Decimal expansion of (golden ratio divided by 3 = phi/3 = (1 + sqrt(5))/6).
  • A134944 (program): Decimal expansion of (1 + sqrt(5))/8, the golden ratio divided by 4.
  • A134945 (program): Decimal expansion of 1 + sqrt(5).
  • A134946 (program): Decimal expansion of (golden ratio divided by 6 = phi/6 = (1 + sqrt(5))/12).
  • A134960 (program): a(n) = n*453060.
  • A134965 (program): a(1)=3, a(n) = a(n-1) + 7 + 2*mod(n-1, 2) for n>=2.
  • A134967 (program): List of quadruples: [-2n-1, 2n+2, -2n-1, 2n+2].
  • A134972 (program): Decimal expansion of 2 divided by golden ratio = 2/phi = 4/(1 + sqrt(5)) = 2*(-1 + phi).
  • A134973 (program): Decimal expansion of 3/phi = 6/(1 + sqrt(5)).
  • A134974 (program): Decimal expansion of 4(-1 + phi) = 4A094214, where the golden ratio phi = A001622.
  • A134976 (program): Decimal expansion of (6 divided by golden ratio = 6/phi = 12/(1 + sqrt(5))).
  • A134977 (program): Period 6: repeat [1, 4, 2, 3, 0, 2].
  • A134986 (program): a(n) = smallest integer m not equal to n such that n = (floor(n^2/m) + m)/2.
  • A134990 (program): Interleave two arithmetic progressions 8,10,12,14,… and 15,13,11,9,… of differences +2 and -2 respectively.
  • A134999 (program): Triangle-shaped numbers.
  • A135013 (program): Partial sums of A000265.
  • A135022 (program): Define a sequence of binary words by w(1)=10 and w(n+1)=w(n)w(n)Reverse[w(n)]. Sequence gives the limiting word w(infinity).
  • A135032 (program): a(n) = 6a(n-1) + 4a(n-2).
  • A135033 (program): Period 5: repeat 2,4,6,8,0.
  • A135034 (program): Positive integers n repeated 2n-1 times, with a leading a(0) = 0. Also: ceiling of square root of n.
  • A135036 (program): Sums of the products of n consecutive pairs of numbers.
  • A135037 (program): Sums of the products of n consecutive triples of numbers.
  • A135038 (program): Sums of the products of n consecutive quadruples of numbers.
  • A135042 (program): Binomial transform of [1, 1, 2, 0, -2, 4, -6, 8, -10, 12,…].
  • A135051 (program): Pyramid game person numbers that have integer solutions.
  • A135061 (program): a(n) = minimum (floor(n^3/m) + m) for any integer m >= 1.
  • A135064 (program): Numbers n such that the quintic polynomial x^5 - 10nx^2 - 24*n has Galois group A_5 over rationals.
  • A135072 (program): Minimal values of m associated with A135061.
  • A135087 (program): Triangle T(n, k) = 2*A134058(n, k) - 1, read by rows.
  • A135089 (program): Triangle T(n,k) = 5*binomial(n,k) with T(0,0) = 1, read by rows.
  • A135092 (program): Binomial transform of [1, 6, 1, 6, 1, 6, …].
  • A135094 (program): a(n) = 2a(n-1) + 2a(n-2) - 4*a(n-3) with n>2, a(0)=0, a(1)=1, a(2)=3.
  • A135095 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^2 if n is even.
  • A135098 (program): First differences of A135094.
  • A135099 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^3 if n is even.
  • A135124 (program): Numbers such that the digital sums in base 2, base 4 and base 8 are all equal.
  • A135133 (program): a(n) = floor(S2(n)/3) mod 2, where S2(n) denotes the binary weight of n.
  • A135136 (program): a(n) = floor(S2(n)/2) mod 2, where S2(n) is the binary weight of n.
  • A135152 (program): A004736 + A128174 - I, I = Identity matrix.
  • A135153 (program): Repeat Pell numbers A000129.
  • A135169 (program): Period 4: repeat [1, 5, 9, 5].
  • A135171 (program): 3^p - 2^p, where p = prime(n).
  • A135172 (program): a(n) = 3^prime(n) + 2^prime(n).
  • A135177 (program): a(n) = p^2*(p-1), where p = prime(n).
  • A135178 (program): a(n) = p^3 + p^2 where p = prime(n).
  • A135179 (program): p^5 - p^3 - p^2. Exponents are the prime numbers in decreasing order and p is the n-th prime.
  • A135180 (program): a(n) = p^5 - p^3 + p^2, where p = prime(n).
  • A135181 (program): p^5 + p^3 - p^2. Exponents are the prime numbers in decreasing order and p is the n-th prime.
  • A135182 (program): p^5 + p^3 + p^2. Exponents are prime numbers and p = prime(n).
  • A135214 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^4 if n is even.
  • A135215 (program): Maximal number of zero digits in square of number with n digits and without zero digits.
  • A135223 (program): Triangle A000012 * A127648 * A103451, read by rows.
  • A135225 (program): Pascal’s triangle A007318 augmented with a leftmost border column of 1’s.
  • A135231 (program): Row sums of triangle A135230.
  • A135246 (program): Shifted Pell recurrence: a(n) = 2*a(n-2) + a(n-4).
  • A135260 (program): Fibonacci Connell sequence: 1 odd, 1 even, 2 odd, 3 even, 5 odd, 8 even, ….
  • A135262 (program): a(3n)=10^n. a(3n+1)=410^n. a(3n+2)=710^n.
  • A135265 (program): Period 6: repeat [1, 1, 1, 2, 2, 2].
  • A135267 (program): Difference between partial sum of the first n primes and the first n even numbers greater than 0.
  • A135276 (program): a(0)=0, a(1)=1; for n>1, a(n) = a(n-1) + n^0 if n odd, a(n) = a(n-1) + n^1 if n is even.
  • A135278 (program): Triangle read by rows, giving the numbers T(n,m) = binomial(n+1, m+1); or, Pascal’s triangle A007318 with its left-hand edge removed.
  • A135282 (program): Largest k such that 2^k appears in the trajectory of the Collatz 3x+1 sequence started at n.
  • A135287 (program): a(0)=1; for n > 0, a(n) = a(n-1)+n if a(n-1) is odd, else a(n) = a(n-1)/2.
  • A135293 (program): Differences between successive numbers whose sum of digits in base 3 is 2.
  • A135295 (program): a(n) = n^(number of decimal digits of n).
  • A135300 (program): Positive X-values of solutions to the equation 1!X^4 - 2!(X + 1)^3 + 3!(X + 2)^2 - (4^2)(X + 3) + 5^2 = Y^3.
  • A135301 (program): a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^2 if n is even.
  • A135318 (program): a(n) = a(n-2) + 2*a(n-4), with a[0..3] = [1, 1, 1, 2].
  • A135319 (program): a(n) is the first digit after the decimal point in the decimal expansion of log_10(n), i.e., of the Briggsian logarithm of n.
  • A135332 (program): a(1)=1; for n>1, a(n) = a(n-1) + n^0 if n odd, a(n) = a(n-1) + n^3 if n is even.
  • A135342 (program): Number of distinct means of nonempty subsets of 1,…,n .
  • A135344 (program): a(n) = 3a(n-1) - a(n-3) + 3a(n-4).
  • A135351 (program): a(n) = (2^n + 3 - 7(-1)^n + 30^n)/6; or a(0) = 0 and for n > 0, a(n) = A005578(n-1) - (-1)^n.
  • A135352 (program): a(1) = 1, followed by period 5: repeat [1,2,2,1,3].
  • A135358 (program): Numbers n such that 7^n and 7^(n+1) have the same number of decimal digits.
  • A135364 (program): First column of a triangle - see Comments lines.
  • A135370 (program): a(1)=1; then if n even a(n) = n + a(n-1), if n odd a(n) = 2*n + a(n-1).
  • A135374 (program): Mersenne numbers with digits sorted in increasing order and zeros suppressed.
  • A135387 (program): Triangle read by rows, with (2, 1, 0, 0, 0, …) in every column.
  • A135389 (program): Number of walks of length 2*n+2 from origin to (1,1) in a square lattice.
  • A135400 (program): a(n) = (4n^4 - 4n^3 - n^2 + 3*n)/2.
  • A135403 (program): a(n) = 1 + 111110*n.
  • A135405 (program): Sequence where the sum of each pair of consecutive elements is a square.
  • A135407 (program): Partial products of A000032 (Lucas numbers beginning at 2).
  • A135416 (program): a(n) = A036987(n)*(n+1)/2.
  • A135423 (program): a(n) = (5*9^n + 1)/2.
  • A135440 (program): a(n) = a(n-1) + 2a(n-2).
  • A135449 (program): Period 5: repeat 1, 9, -7, 3, 5.
  • A135450 (program): a(n) = 3a(n-1) + 4a(n-2) - a(n-3) + 3a(n-4) + 4a(n-5).
  • A135453 (program): a(n) = 12*n^2.
  • A135466 (program): a(n) = (2*n-8)^2 * 2^(n-3).
  • A135481 (program): a(n) = 2^A007814(n+1) - 1.
  • A135482 (program): a(n) = (Sum_ i=1..n 2^prime(i))/4, where prime(i) denotes i-th prime number.
  • A135483 (program): a(n) = Sum_ i=1..n ( prime(i)*2^(i-2) ), where prime(i) denotes i-th prime number.
  • A135484 (program): a(n) = Sum_ i=1..n i^prime(i), where prime(i) denotes i-th prime number.
  • A135485 (program): a(n) = Sum_ i=1..n) prime(i)^(i-1), where prime(i) denotes i-th prime number.
  • A135491 (program): Number of ways to toss a coin n times and not get a run of four.
  • A135497 (program): a(n) = n^5 - n^2.
  • A135503 (program): a(n) = n*(n^2 - 1)/2.
  • A135509 (program): Nonnegative integers c such that there are nonnegative integers a and b that satisfy a^(1/2) + b^(1/2) = c^(1/2) and a^2 + b = c.
  • A135511 (program): Number of Pierce-Engel hybrid expansions of 3/b, b>=3.
  • A135513 (program): Number of Pierce-Engel hybrid expansions of 4/b, b>=4.
  • A135516 (program): a(0)=1; a(n) = (Product_ i=1..n prime(i)^2) - 1, where prime(i) is the i-th prime.
  • A135517 (program): a(n) = 2^(A091090(n)-1).
  • A135518 (program): Generalized repunits in base 15.
  • A135519 (program): Generalized repunits in base 14.
  • A135520 (program): a(n) = 4*a(n-2).
  • A135521 (program): a(n) = 2^(A091090(n)) - 1.
  • A135522 (program): a(n) = 2a(n-1) + 3a(n-2), with a(0) = 2 and a(1) = 3.
  • A135523 (program): a(n) = A007814(n) + A209229(n).
  • A135528 (program): 1, then repeat 1,0.
  • A135530 (program): a(n) = a(n-1) + 2a(n-2) - 2a(n-3), with a(0)=2, a(1)=1.
  • A135532 (program): a(n) = 2*a(n-1) + a(n-2), with a(0)= -1, a(1)= 3.
  • A135533 (program): Guy Steele’s sequence GS(4,6) (see A135416).
  • A135534 (program): a(1) = 1; for n>=1, a(2n) = A135561(n), a(2n+1) = 0.
  • A135536 (program): a(n) = 8*a(n-2), with a(0) = 7, a(1) = 14.
  • A135537 (program): Period 4: repeat [7, 5, 2, 4].
  • A135540 (program): a(n) = 2^(A000523(n) - A000120(n) + 2) - 1.
  • A135556 (program): Squares of numbers not divisible by 3: a(n) = A001651(n)^2.
  • A135560 (program): a(n) = A007814(n) + A036987(n-1) + 1.
  • A135561 (program): a(n) = 2^A135560(n) - 1.
  • A135569 (program): a(n) = S2(n)*2^n; where S2(n) is digit sum of n, n in binary notation.
  • A135570 (program): a(n) = 1 + Sum_ i=1..n S2(i)*2^i, where S2(n) is digit sum of n, n in binary notation.
  • A135576 (program): Numbers whose binary expansion has only the digit “1” as first, central and final digit.
  • A135577 (program): Numbers that have only the digit “1” as first, central and final digit. For numbers with 5 or more digits the rest of digits are “0”.
  • A135583 (program): a(n) = 4*a(n-1) - 4 for n>0, a(0)=3.
  • A135585 (program): a(n) = Sum_ i=1..n (floor(S2(i)/3) mod 2), where S2(i) = A000120(i).
  • A135600 (program): Angled numbers with an internal digit as the vertex.
  • A135620 (program): a(n) = 2^(prime(n) - 2).
  • A135628 (program): Multiples of 28.
  • A135630 (program): 2^(prime(n) - 2) - 1.
  • A135631 (program): Multiples of 31.
  • A135636 (program): Values of x in positive solutions (x,y,z) to the Diophantine 43x+7y+17z=400.
  • A135639 (program): a(n) = 839*n.
  • A135640 (program): Powers of 839.
  • A135659 (program): a(n) = 24*n + 7.
  • A135668 (program): a(n) = ceiling(n + sqrt(n)).
  • A135671 (program): a(n) = ceiling(n - n^(2/3)).
  • A135672 (program): a(n) = floor(n - n^(2/3)).
  • A135673 (program): Ceiling(n + n^(2/3)).
  • A135674 (program): Floor(n+n^(2/3)).
  • A135675 (program): a(n) = ceiling(n^(4/3) - n).
  • A135676 (program): a(n) = floor(n^(4/3) - n).
  • A135677 (program): a(n) = ceiling(n^(4/3)+n).
  • A135678 (program): Floor(n^(4/3)+n).
  • A135679 (program): a(n) = n if n = 1 or if n is prime. Otherwise, a(n) = 2 if n is even and a(n) = 3 if n is odd.
  • A135680 (program): a(n) = n if n = 1 or if n is prime. Otherwise, n = 4 if n is even and n = 5 if n is odd.
  • A135681 (program): a(n)=n if n=1 or if n=prime. Otherwise, n=4 if n is even and n=1 if n is odd.
  • A135682 (program): a(n)=n if n=1 or if n=prime. Otherwise, n=4 if n is even and n=7 if n is odd.
  • A135683 (program): a(n)=1 if n is a prime number; otherwise, a(n)=n.
  • A135684 (program): a(n)=11 if n is a prime number. Otherwise, a(n)=n.
  • A135694 (program): Period 6: repeat [1, -1, -1, -1, 0, 2].
  • A135695 (program): Period 6: repeat [-1, -1, -2, -2, 3, 3].
  • A135703 (program): a(n) = n(7n-2).
  • A135704 (program): a(n) = 7n^2 + 4n + 1.
  • A135705 (program): a(n) = 10binomial(n,2) + 9n.
  • A135706 (program): a(n) = n(5n-3).
  • A135708 (program): Minimal total number of edges in a polyhex consisting of n hexagonal cells.
  • A135711 (program): Minimal perimeter of a polyhex with n cells.
  • A135712 (program): a(n) = (4n^3 + 11n^2 + 9*n + 2)/2.
  • A135713 (program): a(n) = n(n+1)(4*n+1)/2.
  • A135731 (program): a(1) = 3; thereafter a(n+1) = a(n) + nextprime(a(n)) - prevprime(a(n)).
  • A135732 (program): Distances to next prime associated with A135731.
  • A135757 (program): Central binomial coefficients at triangular positions: a(n) = A000984(n(n+1)/2).
  • A135758 (program): Catalan numbers at triangular positions: a(n) = A000108(n(n+1)/2).
  • A135839 (program): Triangle read by rows: starting with A138174, replace left border with (1, 1, 1, …).
  • A135840 (program): A135839 * A000012 as infinite lower triangular matrices.
  • A135841 (program): A000012 * A135839 as infinite lower triangular matrices.
  • A135849 (program): a(n) is the ratio of the sum of the bends (curvatures) of the circles in the n-th generation of an Apollonian packing to the sum of the bends in the initial four-circle configuration.
  • A135854 (program): a(n) = (n+1)*(2^n+1) for n>0 with a(0)=1.
  • A135859 (program): Row sums of triangle A135858.
  • A135860 (program): a(n) = binomial(n(n+1), n).
  • A135861 (program): a(n) = binomial(n*(n+1),n)/(n+1).
  • A135862 (program): a(n) = binomial(n*(n+1),n)/(n^2+1).
  • A135874 (program): Multiply the positive divisors n in order (starting at 1). a(n) is the smallest such partial product that is >= n.
  • A135875 (program): Multiply the positive divisors n in order (starting at 1). a(n) is the largest such partial product that is <= n.
  • A135908 (program): Clique number of commuting graph of symmetric group S_n.
  • A135913 (program): 2+4*2^n-3^n.
  • A135914 (program): 43^n-22^n-1.
  • A135916 (program): (n^4 - 10n^2 + 15n - 6)/2.
  • A135941 (program): a(n) = floor(n/S2(n)), where S2(n) is the binary weight of n.
  • A135947 (program): a(n)=(floor(3*S2(n)/2)) mod 2, where S2(n) is the binary weight of n.
  • A135962 (program): a(n) = binomial(floor(n*(sqrt(5)+1)/2), n) for n>=0.
  • A135963 (program): a(n) = binomial(floor(n*(sqrt(5)+3)/2), n) for n>=0.
  • A135964 (program): a(n) = binomial(floor(n*sqrt(2)),n) for n>=0.
  • A135966 (program): Triangle, read by rows, where T(n,k) = fibonacci(k(n-k) + 1) for n>=k>=0.
  • A135984 (program): a(n) = 24(prime(n))+7.
  • A135989 (program): a(n) = 6n + 3 + 90floor((6*n+3)/10).
  • A135992 (program): Positive Fibonacci numbers swapped in pairs.
  • A135993 (program): a(0) = 0; a(n) = (floor(n/S2(n))) mod 2 for n >= 1, where S2(n) is the binary weight of n.
  • A135996 (program): Difference between 2^n and the largest factorial <= 2^n.
  • A136004 (program): a(n) = A005811(n) + 4.
  • A136006 (program): a(n) = n^6 - n^3.
  • A136008 (program): a(n) = n^6 - n^2.
  • A136013 (program): a(n) = floor(n/2) + 2*a(floor(n/2)), a(0) = 0.
  • A136016 (program): a(n) = 9*n^2-1.
  • A136017 (program): a(n) = 36n^2 - 1.
  • A136038 (program): a(n) = n^6 - n^4.
  • A136047 (program): a(1)=1, a(n)=a(n-1)+n if n even, a(n)=a(n-1)+ n^2 if n is odd.
  • A136105 (program): Partial sums of A051941.
  • A136107 (program): Number of representations of n as the difference of two positive triangular numbers.
  • A136119 (program): Limiting sequence when we start with the positive integers (A000027) and delete in step n >= 1 the term at position n + a(n).
  • A136157 (program): Triangle by columns, (3, 1, 0, 0, 0,…) in every column.
  • A136169 (program): a(n) = 2*a(n-1) - [(n+1)/3] for n>0 with a(0) = 1.
  • A136185 (program): Number of metacyclic groups of order p^n, prime p >= 3.
  • A136188 (program): Digital roots of the Fermat numbers in A000215(n).
  • A136219 (program): Number of terms in rows of irregular triangle A136218.
  • A136252 (program): a(n) = a(n-1) + 2a(n-2) - 2a(n-3).
  • A136254 (program): Generator for the finite sequence A053016.
  • A136258 (program): a(n) = 2a(n-1) - 2a(n-2), with a(0)=1, a(1)=5.
  • A136264 (program): Expansion of (1+x)^2(x^2-6x+1)/(x-1)^4.
  • A136268 (program): Cyclic p-roots of prime lengths p(n).
  • A136272 (program): Waterbird take-off sequence. Complement of A166021.
  • A136289 (program): Start with three pennies touching each other on a tabletop. In each generation, add pennies subject to the rule that a penny can be placed only when (at least) two pennies are already in position to determine its position; sequence gives number of pennies added at generation n.
  • A136290 (program): a(0)=1, a(1)=3, a(2)=9, a(3)=12, a(4)=15; thereafter a(n) = a(n-1)+a(n-3)-a(n-4).
  • A136293 (program): Linear bound on the genera of Heegaard splittings of closed, orientable 3-manifolds that admit a generalized triangulation with n generalized tetrahedra.
  • A136298 (program): a(n) = 3a(n-1) - 4a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=9.
  • A136302 (program): Transform of A000027 by the T_ 1,1 transformation (see link).
  • A136305 (program): Expansion of g.f. (3 -x +2x^2)/(1 -3x +2*x^2 -x^3).
  • A136313 (program): a(1) = 1; for n>1, a(n) = a(n-1) + 8 mod 22.
  • A136315 (program): Period 10: repeat 1, 2, 3, 6, 5, 0, 7, 4, 9, 8 .
  • A136316 (program): 13 + 12*n - n^2.
  • A136320 (program): Terms of A047241 swapped in pairs.
  • A136324 (program): Interleaving of A002450(n), A002450(n) + 1.
  • A136325 (program): a(n) = 8*a(n-1)-a(n-2) with a(0)=0 and a(1)=3.
  • A136326 (program): a(n) = a(n-1) + 4a(n-2) - 4a(n-3).
  • A136336 (program): a(n) = a(n-1) + 4a(n-2) - 4a(n-3) for n>3.
  • A136362 (program): Numbers n such that P+n is not irreducible, where P = x^8 - 8x^6 + 20x^4 - 16*x^2 + 2.
  • A136376 (program): a(n) = nF(n) + (n-1)F(n-1).
  • A136391 (program): a(n) = nF(n) - (n-1)F(n-1), where the F(j)’s are the Fibonacci numbers (F(0)=0, F(1)=1).
  • A136392 (program): a(n) = 6n^2 - 10n + 5.
  • A136393 (program): a(n) = C(3^n,n).
  • A136395 (program): Binomial transform of [1, 3, 4, 3, 2, 0, 0, 0,…].
  • A136396 (program): a(n) = 1+n(n+1)(n^2-n+12)/12.
  • A136409 (program): a(n) = floor(n*log_3(2)).
  • A136412 (program): a(n) = (5*4^n+1)/3.
  • A136419 (program): a(n) = binomial((n+2)(n+1),(n+1)n).
  • A136423 (program): Floor((x^n - (1-x)^n)/2 +.5) where x = (sqrt(4)+1)/2 = 3/2.
  • A136432 (program): a(n)! is the smallest factorial bigger than n^n.
  • A136437 (program): a(n) = prime(n) - k! where k is the greatest number such that k! <= prime(n).
  • A136442 (program): a(3n) = 1, a(3n-1) = 0 and a(3n+1) = a(n).
  • A136465 (program): Row 0 of square array A136462: a(n) = C(2^(n-1), n) for n>=0.
  • A136466 (program): Row 2 of square array A136462: a(n) = C(3*2^(n-1), n) for n>=0.
  • A136480 (program): Number of trailing equal digits in binary representation of n.
  • A136488 (program): a(n) = 2^n - A005418(n).
  • A136505 (program): a(n) = binomial(2^n + 1, n).
  • A136506 (program): a(n) = binomial(2^n + 2, n).
  • A136516 (program): a(n) = (2^n+1)^n.
  • A136521 (program): Triangle read by rows: (1, 2, 2, 2, …) on the main diagonal and the rest zeros.
  • A136522 (program): a(n) = 1 if n is a palindrome, otherwise 0.
  • A136548 (program): a(n) = max k >= 1 sigma(k) <= n .
  • A136556 (program): a(n) = binomial(2^n - 1, n).
  • A136572 (program): Triangle read by rows: row n consists of n zeros followed by n!.
  • A136574 (program): Row sums of triangle A136573.
  • A136580 (program): Row sums of triangle A136579.
  • A136610 (program): Number of odd digits in Fibonacci numbers.
  • A136616 (program): a(n) = largest m with H(m) - H(n) <= 1, where H(i) = Sum_ j=1 to i 1/j, the i-th harmonic number, H(0) = 0.
  • A136619 (program): a(1) = 1, then repeat period 3: [1, 4, 2].
  • A136655 (program): Product of odd divisors of n.
  • A136687 (program): Number of palindromes in the range [0,n] inclusive.
  • A136690 (program): Final nonzero digit of n! in base 3.
  • A136692 (program): Final nonzero digit of n! in base 5.
  • A136719 (program): Number of labeled directed trees with n nodes.
  • A136724 (program): Numbers divisible by 4 that are not powers of 2.
  • A136725 (program): Primitive dimensions of Hadamard matrices.
  • A136746 (program): G.f.: (z^12+1-z^11-z^10+z^8-z^6+z^5-z^3+z)/((z+1)*(z-1)^2).
  • A136754 (program): Leading digit of n! in base 3.
  • A136755 (program): a(n) = leading digit of n! in base 4.
  • A136756 (program): Leading digit of n! in base 5.
  • A136757 (program): Leading digit of n! in base 6.
  • A136758 (program): a(n) = leading digit of n! in base 7.
  • A136759 (program): a(n) = leading digit of n! in base 8.
  • A136760 (program): a(n) = leading digit of n! in base 9.
  • A136761 (program): a(n) = leading digit of n! in base 11.
  • A136762 (program): Leading digit of n! in base 12.
  • A136763 (program): a(n) = leading digit of n! in base 13.
  • A136764 (program): a(n) = leading digit of n! in base 14.
  • A136765 (program): a(n) = leading digit of n! in base 15.
  • A136766 (program): a(n) = leading digit of n! in base 16.
  • A136767 (program): n! never ends in this many 0’s in base 4.
  • A136768 (program): n! never ends in this many 0’s in base 7.
  • A136771 (program): n! never ends in this many 0’s in base 11.
  • A136775 (program): Number of multiplex juggling sequences of length n, base state <1,1> and hand capacity 2.
  • A136796 (program): Number of labeled marked rooted trees with n nodes.
  • A136797 (program): Number of labeled marked trees with n nodes.
  • A136799 (program): Last term in a sequence of at least 3 consecutive composite integers.
  • A136853 (program): Numbers k such that k and k^2 use only the digits 0, 1, 3 and 9.
  • A136921 (program): Numbers k such that k and k^2 use only the digits 0, 2, 6 and 7.
  • A136926 (program): Numbers k such that k and k^2 use only the digits 0, 2, 7 and 9.
  • A136957 (program): Numbers k such that k and k^2 use only the digits 0, 4, 6 and 9.
  • A136962 (program): Numbers k such that k and k^2 use only the digits 0, 5, 6 and 7.
  • A137120 (program): Numbers k such that k and k^2 use only the digits 3, 4, 5 and 6.
  • A137146 (program): Numbers k such that k and k^2 use only the digits 5, 6, 7 and 8.
  • A137148 (program): a(n) = n*phi(n) for nonprime n.
  • A137149 (program): a(n) = (prime(n)-2)!.
  • A137173 (program): A006516 at positions with even indices, A007582 at positions with odd indices.
  • A137180 (program): Number of palindromes in the range [1,n] inclusive.
  • A137199 (program): a(n)=a(n-1)+3a(n-2)+a(n-3).
  • A137208 (program): a(n) = a(n-1) + 4a(n-2) - 4a(n-3) for n > 2; a(0)=2, a(1)=3, a(2)=6.
  • A137221 (program): a(n) = 5a(n-1) - 9a(n-2) + 8a(n-3) - 4a(n-4).
  • A137224 (program): Mix 4n^2, 1+4n^2, 1+(2n+1)^2, (2n+1)^2 (or A016742, A053755, A069894, A016754).
  • A137228 (program): Minimal total number of edges in a polyiamond consisting of n triangular cells.
  • A137229 (program): Expansion of g.f. x/((1-x)(1-3x+2*x^2-x^3)).
  • A137233 (program): Number of n-digit even numbers.
  • A137234 (program): Expansion of g.f. 1/((1-x)^2(1 - 3x + 2*x^2 - x^3)).
  • A137235 (program): a(n) = (n+1)/2 if n is odd; a(n) = n/2 + 6 if n is even.
  • A137243 (program): Number of coprime pairs (a,b) with -n <= a,b <= n.
  • A137264 (program): Prime number gaps read modulo 3.
  • A137290 (program): Fibonacci(n) mod 30.
  • A137319 (program): Start with the set of natural numbers. Add 1 to every 2nd term, 2 to every 3rd term, 3 to every 4th term, etc.
  • A137325 (program): Number of terms in the Janet periodic table of the elements 32 columns: ordered 14 2’s, 10 4’s, 6 6’s, 2 8’s.
  • A137327 (program): Fermat(n) modulo n.
  • A137331 (program): a(n) = 1 if the binary weight of n is prime, otherwise 0.
  • A137340 (program): a(n) = 2a(n-1) + 3a(n-2), with a(0) = 1, a(1) = 9.
  • A137344 (program): a(n)=4a(n-2). Also 3*A084221.
  • A137345 (program): a(n) = binomial( n(n+1)/2, n) mod n.
  • A137356 (program): a(n) = Sum_ k <= n/2 binomial(n-2k, 3k).
  • A137357 (program): a(n) = Sum_ k <= n/2 binomial(n-2k, 3k+1).
  • A137358 (program): a(n) = Sum_ k <= n/2 binomial(n-2k, 3k+2).
  • A137362 (program): Positions at which the truncated square root of triangular numbers is unique.
  • A137397 (program): Number of distinct palindromic subwords in the binary representation of n.
  • A137399 (program): a(n)=4a(n-4).
  • A137410 (program): a(n) = (5^n - 3) / 2.
  • A137426 (program): a(n)=-a(n-1)+2a(n-3).
  • A137429 (program): a(n) = -2a(n-1) - 2a(n-2), with a(0)=1 and a(1)=-4.
  • A137441 (program): Partial sums of partial sums of PrimePi(k).
  • A137444 (program): a(n) = 2a(n-1) - 2a(n-2) with a(0)=1, a(1)=4.
  • A137445 (program): a(n) = 2a(n-1)-2a(n-2), with a(0)=3 and a(1)=2.
  • A137457 (program): Consider a row of standard dice as a counter. This sequence enumerates the number of changes (one face rotated over an edge to an adjacent face) from n-1 to n.
  • A137458 (program): Prime(core(n)).
  • A137466 (program): 1 concatenated with n 21’s.
  • A137470 (program): Inverse binomial transform of 1, 2, 2, 4, 10, 20, … = A100088.
  • A137480 (program): a(n)=4a(n-2).
  • A137483 (program): a(n+1) = 9*a(n) - 6, a(0) = 2.
  • A137495 (program): A098601(2n)+A098601(2n+1)
  • A137501 (program): The even numbers repeated, with alternating signs.
  • A137505 (program): Inverse binomial transform of A007910.
  • A137508 (program): Successive structures of alkaline earth metals (periodic table elements from 2nd column).
  • A137512 (program): The number of nodes visible from underneath a binary tree, where the nodes are placed such that the innermost of the two sprouting nodes should be underneath the mother.
  • A137517 (program): a(0) = 121; for n>0, a(n) = a(n-1) - n + 1.
  • A137521 (program): Prime numbers concatenated with 45.
  • A137531 (program): a(n) = 3a(n-1) - 2a(n-2) + a(n-3).
  • A137558 (program): A137521(n)/5.
  • A137575 (program): Successive structures central number of Seaborg’s periodic table of the elements (extended to 32 columns) for odd rows.
  • A137584 (program): a(n) = 3a(n-1) - 2a(n-2) + a(n-3), n > 3.
  • A137669 (program): Prime numbers p such that p +- a and p +- b are prime numbers where a and b are distinct positive integers with a < b < p.
  • A137688 (program): 2^A003056: 2^n appears n+1 times.
  • A137693 (program): Numbers n such that 3n^2-n = 6k^2-2k for some integer k>0.
  • A137694 (program): Numbers k such that 6k^2-2k = 3n^2-n for some integer n>0.
  • A137709 (program): Secondary Upper Wythoff Sequence.
  • A137719 (program): Sequence based on the pattern [3n, 3n, 3n, 3n+2, 3n+1, 3n+2].
  • A137727 (program): Final digit of prime(n)*prime(n+1).
  • A137728 (program): Second digit from the end of product of first n primes.
  • A137735 (program): a(0)=1. a(n) = floor(n/b(n)), where b(n) is the largest value among (a(0),a(1),…,a(n-1)).
  • A137742 (program): a(n) = (n-1)(n+4)(n+6)/6 for n>1, a(1)=1.
  • A137780 (program): a(n) = 1 + 2^( prime(n + 1) - prime(n) ).
  • A137797 (program): a(n) = 2( (n+1) mod 5 ) - 2( (n+1) mod 2 ).
  • A137798 (program): Partial sums of A137797.
  • A137803 (program): a(n) = floor(n*(sqrt(2) + 1/2)).
  • A137807 (program): Final digit of prime(n)^2.
  • A137821 (program): Numbers k such that Sum_ j=1..2k Catalan(j) == 0 (mod 3).
  • A137822 (program): First differences of A137821 (numbers such that sum( Catalan(k), k=1..2n) = 0 (mod 3)).
  • A137823 (program): Numbers occurring in A137822 : first differences of numbers n such that 3 sum( Catalan(k), k=1..2n).
  • A137824 (program): Index at which A137823(n) occurs first in A137822 (gaps in numbers m such that 3 sum( Catalan(k), k=1..2m)).
  • A137831 (program): (Prime(n)^2 minus its last digit)/20.
  • A137864 (program): a(n) = n^4 - 10n^3 + 35n^2 - 48n + 23.
  • A137866 (program): a(1)=0. For n >= 2, a(n) = gcd(a(n-1)+1, n).
  • A137882 (program): Number of (directed) Hamiltonian paths in the n-ladder graph.
  • A137883 (program): Number of (directed) Hamiltonian paths in the n-Möbius ladder graph.
  • A137885 (program): Number of directed Hamiltonian paths in the 2n-crossed prism graph.
  • A137893 (program): Fixed point of the morphism 0->100, 1->101, starting from a(1) = 1.
  • A137901 (program): Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value 1.
  • A137913 (program): Rows 2, 4, 6 of Mendeleyev-Seaborg (extended to 32 columns) periodic table elements.
  • A137922 (program): Numbers having exactly two divisors d such that d+1 is not a divisor.
  • A137928 (program): The even principal diagonal of a 2n X 2n square spiral.
  • A137930 (program): The sum of the principal diagonals of an n X n spiral.
  • A137931 (program): Sum of the principal diagonals of a 2n X 2n square spiral.
  • A137932 (program): Terms in an n X n spiral that do not lie on its principal diagonals.
  • A137933 (program): Least common multiple of n^2 and 2.
  • A137934 (program): Period 6: 2,2,2,2,2,0.
  • A137935 (program): a(n) = 5n + 26*floor(n/5).
  • A137936 (program): a(n) = 5*mod(n,5) + floor(n/5).
  • A137937 (program): A137904(n) - A137575(n).
  • A137951 (program): Redundant binary representation (A089591) of n interpreted as ternary number.
  • A137992 (program): A014137 (= partial sums of Catalan numbers A000108) mod 3.
  • A137993 (program): A014138 (= partial sums of Catalan numbers starting with 1,2,5) mod 3.
  • A138010 (program): a(n) is the number of positive divisors of n that divide d(n), where d(n) is the number of positive divisors of n, A000005(n); a(n) also equals d(gcd(n, d(n))).
  • A138015 (program): Triangle read by rows, antidiagonals of an array formed by A000012 * A136579. Replace the term “n” in the correlation triangle A003983 with A003422(n).
  • A138016 (program): Row sums of triangle A138015.
  • A138019 (program): Period 5: repeat 1, 1, 0, -1, -1.
  • A138029 (program): Main diagonal of A138028; the most significant digit of n^(n-1).
  • A138031 (program): a(n) = prime(n)^13.
  • A138032 (program): a(n) = prime(n)^17.
  • A138033 (program): a(n) = max_ 1 <= i <= n-1 min wt(i), wt(n-i) , where wt() = A000120() is the binary weight function; a(1) = 0 by convention.
  • A138034 (program): Expansion of (1+3*x^2)/(1-x+x^2).
  • A138037 (program): a(0) = 0, a(n+1) = n + a(n)/(2 - a(n) mod 2).
  • A138041 (program): a(1) = 1, a(2) = 10; for n>2, a(n+1) = 4a(n) + 6a(n-1). Also a(n) = upper left term in the 2 X 2 matrix [1,3; 3,3].
  • A138055 (program): Period 8: repeat 1, 3, 5, 9, 3, 1, 9, 5.
  • A138070 (program): Triangle read by rows: row n lists the successive digits of A135697(n), the palindromic number formed from the reflected decimal expansion of Pi.
  • A138099 (program): Irregular triangle read by rows: T(n,k) = k + floor(n/2), 1 <= k <= ceiling(n/2).
  • A138100 (program): The atomic numbers read along the odd-indexed rows of the Janet table of the elements.
  • A138102 (program): The number 2k^2 repeated 2k^2 times, k=1 to 4.
  • A138105 (program): Partial sums of non-Fibonacci numbers A001690.
  • A138114 (program): Triangle read by rows: row n lists the first n digits of the decimal expansion of Pi.
  • A138115 (program): Triangle read by rows: row n lists the first n digits of the decimal expansion of e.
  • A138116 (program): Triangle read by rows: row n lists the first n digits of the decimal expansion of golden ratio phi.
  • A138117 (program): Triangle read by rows: row n lists the first 2n-1 prime numbers.
  • A138118 (program): Concatenation of 2n-1 digits 1 and n digits 0.
  • A138127 (program): Multiples of 127.
  • A138128 (program): Powers of 127.
  • A138129 (program): Multiples of 1729, the Hardy-Ramanujan number.
  • A138130 (program): Powers of 1729, the Hardy-Ramanujan number.
  • A138134 (program): a(n) = Sum_ i=0..n Fibonacci(5*i).
  • A138139 (program): Triangle read by rows: row n contains n terms and each column lists the prime numbers A000040.
  • A138143 (program): Triangle read by rows in which row n lists p(1), p(2), …, p(n), p(n-1), …, p(1), where p(i) = i-th prime.
  • A138144 (program): Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1 and infinite 0’s.
  • A138145 (program): Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0’s.
  • A138146 (program): Palindromes with 2n-1 digits formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0’s.
  • A138147 (program): Concatenation of n digits 1 and n digits 0.
  • A138148 (program): Cyclops numbers with binary digits only.
  • A138149 (program): n-th run has length n-th prime, with values 0 and 1 only, starting with 1.
  • A138150 (program): n-th run has length n-th prime, with digits 0 and 1 only, starting with 0.
  • A138179 (program): Wiener index of the prism graph Y_n on 2n nodes.
  • A138181 (program): Largest Fibonacci number not exceeding the n-th prime.
  • A138182 (program): Smallest summand in the Zeckendorf representation of the n-th prime.
  • A138183 (program): Smallest Fibonacci number not less than the n-th prime.
  • A138187 (program): Hankel transform of binomial(2*n+3, n).
  • A138189 (program): Sequence built on pattern (1,-even,-even) beginning 1,-2,-2.
  • A138190 (program): Numerator of (n-1)n(n+1)/12.
  • A138191 (program): Denominator of (n-1)n(n+1)/12.
  • A138219 (program): Integers related to the volume k(n) of a unit hypersphere in n dimensions.
  • A138229 (program): Expansion of (1-x)/(1-2x+6x^2).
  • A138230 (program): Expansion of (1-x)/(1 - 2x + 4x^2).
  • A138233 (program): 2^(2n+1) + 3^(2n+1).
  • A138251 (program): Beatty sequence of the positive root of x^3 - x^2 - 1.
  • A138252 (program): Beatty sequence of the number t satisfying 1/s + 1/t = 1, where s is the positive root of x^3 - x^2 - 1.
  • A138279 (program): Last digit of A136324. After 0, 1, period 4: repeat [1, 2, 5, 6] = A131800.
  • A138287 (program): Palindromic period 10: repeat 0, 2, 8, 4, 6, 6, 4, 8, 2, 0.
  • A138288 (program): a(n) = A054320(n) - A001078(n).
  • A138297 (program): Rows of triangle A138060 converge to this sequence.
  • A138298 (program): First differences of A137976 after having added two leading ones.
  • A138300 (program): Differences of each column for atomic numbers of Mendeleyev-Seaborg 7*32 elements periodic table,first extension,A138096 table.86 terms.Horizontal lecture.
  • A138322 (program): a(n) = 5a(n-1) + 10a(n-2).
  • A138330 (program): Beatty discrepancy (defined in A138253) giving the closeness of the pair (A136497,A136498) to the Beatty pair (A001951,A001952).
  • A138331 (program): a(n) = C(n+5, 5)(n+3)(-1)^(n+1)*16/3.
  • A138332 (program): C(n+7, 7)(n+4)(-1)^(n+1)*16.
  • A138340 (program): Expansion of (1-8x)/(1-4x+16x^2).
  • A138341 (program): Expansion of (1-4x-x^3)/(1-x+x^2)^2.
  • A138342 (program): First differences of A007088.
  • A138357 (program): Floor of sum of the first n^2 square roots.
  • A138364 (program): The number of Motzkin n-paths with exactly one flat step.
  • A138383 (program): If prime(i) = i-th prime, a(n) = prime(n)+1 + prime(n)+2 + … + prime(n+1). a(0) = 3 by convention.
  • A138393 (program): Numbers of form 8k+1 which are not squares.
  • A138395 (program): a(n) = 6a(n-1) - 3a(n-2), a(1) = 1, a(2) = 6.
  • A138401 (program): a(n) = prime(n)^4 - prime(n).
  • A138402 (program): a(n) = (n-th prime)^4-(n-th prime)^2.
  • A138403 (program): a(n) = p^3*(p-1), where p = prime(n).
  • A138404 (program): a(n) = prime(n)^5 - prime(n).
  • A138405 (program): a(n) = prime(n)^5 - prime(n)^2.
  • A138406 (program): a(n) = prime(n)^5 - prime(n)^3.
  • A138407 (program): a(n) = p^4*(p-1), where p = prime(n).
  • A138408 (program): a(n) = prime(n)^6 - prime(n).
  • A138409 (program): a(n) = prime(n)^6 - prime(n)^2.
  • A138410 (program): a(n) = prime(n)^6 - prime(n)^3.
  • A138411 (program): a(n) = prime(n)^6 - prime(n)^4.
  • A138412 (program): a(n) = p^5*(p-1) where p =prime(n).
  • A138416 (program): a(n) = (p^3 - p^2)/2, where p = prime(n).
  • A138417 (program): a(n) = (prime(n)^4 - prime(n))/2.
  • A138418 (program): a(n) = ((n-th prime)^4-(n-th prime)^2)/2.
  • A138419 (program): a(n) = (prime(n)^4 - prime(n)^2)/3.
  • A138420 (program): a(n) = ((prime(n))^4-(prime(n))^2)/4.
  • A138421 (program): a(n) = (prime(n)^4 - prime(n)^2)/6.
  • A138422 (program): a(n) = (prime(n)^4 - prime(n)^2)/12.
  • A138423 (program): a(n) = (prime(n)^4 - prime(n)^3)/2.
  • A138424 (program): a(n) = (prime(n)^5 - prime(n))/2.
  • A138425 (program): a(n) = (prime(n)^5 - prime(n))/3.
  • A138426 (program): a(n) = ((prime(n))^5-prime(n))/5.
  • A138427 (program): a(n) = (prime(n)^5 - prime(n))/6.
  • A138428 (program): a(n) = (prime(n)^5 - prime(n))/10.
  • A138429 (program): a(n) = (prime(n)^5 - prime(n))/15.
  • A138430 (program): (prime(n)^5 - prime(n))/30.
  • A138431 (program): a(n) = ((n-th prime)^5-(n-th prime)^2)/2.
  • A138432 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/2.
  • A138433 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/3.
  • A138434 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/4.
  • A138435 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/6.
  • A138436 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/8.
  • A138437 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/12.
  • A138438 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/24.
  • A138439 (program): a(n) = ((n-th prime)^5-(n-th prime)^4)/2.
  • A138440 (program): a(n) = ((n-th prime)^6-(n-th prime))/2.
  • A138441 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/2.
  • A138442 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/3.
  • A138443 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/4.
  • A138444 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/5.
  • A138445 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/6.
  • A138446 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/10.
  • A138447 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/12.
  • A138448 (program): a(n) = (prime(n)^6-prime(n)^2)/15.
  • A138450 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/30.
  • A138451 (program): a(n) = (prime(n)^6-prime(n)^2)/60.
  • A138452 (program): a(n) = ((n-th prime)^6-(n-th prime)^3))/2.
  • A138453 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/2.
  • A138454 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/3.
  • A138455 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/4.
  • A138456 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/6.
  • A138457 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/8.
  • A138458 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/24.
  • A138459 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/12.
  • A138460 (program): a(n) = ((n-th prime)^6-(n-th prime)^5))/2.
  • A138466 (program): a(1)=1, then for n>=2 a(n)=n-floor((1/2)*a(a(n-1))).
  • A138467 (program): a(1)=1, then for n>=2 a(n) = n - floor((1/3)*a(a(n-1))).
  • A138473 (program): a(n) = Fibonacci(8*n).
  • A138523 (program): a(n) = Sum_ k=1..n (2k-1)!.
  • A138524 (program): a(n) = Sum_ k=1..n (2*k)!.
  • A138525 (program): a(n) = Sum_ k=0..n (2*k)!.
  • A138531 (program): Decimal expansion of 109739369/111111111.
  • A138564 (program): a(1) = 1; a(n) = a(n-1) + (n!)^3.
  • A138585 (program): The sequence is formed by concatenating subsequences S1, S2, … each of finite length. S1 consists of the element 1. The n-th subsequence consist of numbers (n/2)(n/2 - 1)+ 1, …, (n/2)(n/2 + 1) for n even, ((n-1)/2)^2, …, (n-1)/2 * ((n-1)/2 + 2) for n odd.
  • A138589 (program): a(n) = 5^n mod 4^n.
  • A138590 (program): a(n) = Fibonacci(9*n).
  • A138591 (program): Sums of two or more consecutive nonnegative integers.
  • A138611 (program): 6^n mod 4^n.
  • A138616 (program): a(n) = 7^n mod 2^n.
  • A138617 (program): a(n) = 7^n mod 3^n.
  • A138620 (program): Nonnegative integers n such that 12*n-1 is prime.
  • A138622 (program): Nonnegative integers k such that 14*k-1 is prime.
  • A138625 (program): Primes congruent to 12 mod 17.
  • A138626 (program): Nonnegative integers n such that 17*n-5 is prime.
  • A138627 (program): Primes congruent to 10 mod 17.
  • A138628 (program): Positive integers k such that 17*k-7 is prime.
  • A138629 (program): Primes of form 17*n+7.
  • A138630 (program): Nonnegative integers k such that 17*k+7 is prime.
  • A138631 (program): Primes of the form 17*k + 9.
  • A138632 (program): Nonnegative integers k such that 17*k+9 is prime.
  • A138633 (program): Primes of the form 17*k - 9.
  • A138634 (program): Nonnegative integers k such that 17*k-9 is prime.
  • A138636 (program): a(n) = 6 * prime(n).
  • A138638 (program): Primes of form 19*n-1.
  • A138639 (program): Nonnegative integers n such that 19*n-1 is prime.
  • A138640 (program): Primes of form 19*n-2.
  • A138641 (program): Nonnegative integers n such that 19*n-2 is prime.
  • A138642 (program): Primes of form 19*n-3.
  • A138643 (program): Nonnegative integers k such that 19*k-3 is prime.
  • A138648 (program): 7^n mod 5^n.
  • A138649 (program): a(n) = 6^n mod 5^n.
  • A138654 (program): 7^n mod 4^n.
  • A138689 (program): Numbers of the form 26+p^2 (where p is a prime).
  • A138690 (program): Numbers of the form 56+p^2 (where p is a prime).
  • A138691 (program): Numbers of the form 68+p^2 (where p is a prime).
  • A138692 (program): Numbers of the form 86+p^2 (where p is a prime).
  • A138693 (program): Numbers of the form 110 + p^2. (where p is a prime).
  • A138694 (program): Numbers n such that the set 2*n+p^2, p any prime contains exactly one prime.
  • A138709 (program): n-th run has length n-th positive Fibonacci numbers, with digits 0 and 1 only, starting with 1.
  • A138710 (program): n-th run has length n-th positive Fibonacci numbers, with digits 0 and 1 only, starting with 0.
  • A138711 (program): n-th run has length n-th positive triangular number, with digits 0 and 1 only, starting with 1.
  • A138712 (program): n-th run has length n-th positive triangular number, with digits 0 and 1 only, starting with 0.
  • A138714 (program): Add 1, modulo 10, to the decimal expansion of e, A001113.
  • A138718 (program): Group number of the elements of the n-th column of the periodic table of the elements with 18 columns.
  • A138748 (program): a(n) = (n+(n+1)) + (n*(n+1)) + (n^(n+1)).
  • A138750 (program): a(n) = ceiling(n/2) if n == 2 (mod 3), a(n) = 2n otherwise.
  • A138772 (program): Number of entries in the second cycles of all permutations of 1,2,…,n ; each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
  • A138782 (program): a(n) = n(3n-1)*n!/2.
  • A138829 (program): Bisection of imperfect numbers A132999.
  • A138830 (program): Bisection of imperfect numbers A132999.
  • A138836 (program): Non-Mersenne numbers A001348.
  • A138849 (program): a(n) = AlexanderPolynomial[n] defined as Det[Transpose[S]-n S] where S is Kronecker Product of two 2 X 2 Seifert matrices -1, 1 , 0, -1 [X] -1, 1 , 0, -1 = 1, -1, -1, 1 , 0, 1, 0, -1 , 0, 0, 1, -1 , 0, 0, 0, 1 .
  • A138884 (program): Numbers that are not even superperfect numbers.
  • A138885 (program): n-th run has length n-th nonprime number, with digits 0 and 1 only, starting with 1.
  • A138886 (program): n-th run has length n-th nonprime number A018252, with digits 0 and 1 only, starting with 0.
  • A138888 (program): Non-Fermat numbers.
  • A138890 (program): Non-Padovan numbers.
  • A138891 (program): Non-Motzkin numbers.
  • A138894 (program): Expansion of (1+x)/(1-10x+9x^2).
  • A138898 (program): Ratio of (2n-1)! to number of zeros in lower part of Sylvester matrix for polynomial of degree n with all nonzero coefficients.
  • A138902 (program): a(n) = d!, where d is the number of digits in n.
  • A138908 (program): a(n) = d^d, where d is the number of digits in n.
  • A138918 (program): Numbers n such that 18n-1 is prime.
  • A138955 (program): a(n) = 8^n mod 3^n.
  • A138959 (program): a(n) = 8^n mod 5^n.
  • A138964 (program): a(n) = 8^n mod 6^n.
  • A138966 (program): a(n) = n + (smallest composite > n).
  • A138968 (program): Positions of the primes congruent to 1 mod 3 when all primes except 3 are listed in order.
  • A138969 (program): Positions of the primes congruent to 2 mod 3 when all primes except 3 are listed in order.
  • A138970 (program): Positions of the primes congruent to 1 mod 4 when all primes except 2 are listed in order.
  • A138971 (program): Positions of the primes congruent to 3 mod 4 when all primes except 2 are listed in order.
  • A138972 (program): Positions of the primes congruent to 1 mod 6 when all primes except 2 and 3 are listed in order.
  • A138973 (program): a(n) = 8^n mod 7^n.
  • A138977 (program): Number of 2 X n matrices containing a 1 in the top left entry, all entries are integer values and adjacent entries differ by at most 1.
  • A138984 (program): a(n) = Frobenius number for 4 successive numbers = F(n+1,n+2,n+3,n+4).
  • A138985 (program): a(n) = Frobenius number for 5 successive numbers = F(n+1,n+2,n+3,n+4,n+5).
  • A138986 (program): a(n) = Frobenius number for 6 successive numbers = F(n+1,n+2,n+3,n+4,n+5,n+6).
  • A138987 (program): a(n) = Frobenius number for 7 successive numbers = F(n+1,n+2,n+3,n+4,n+5,n+6,n+7).
  • A138988 (program): a(n) = Frobenius number for 8 successive numbers = F(n+1,n+2,n+3,n+4,n+5,n+6,n+7,n+8).
  • A138995 (program): First differences of Frobenius numbers for 4 successive numbers A138984.
  • A138996 (program): First differences of Frobenius numbers for 5 successive numbers A138985.
  • A138997 (program): First differences of Frobenius numbers for 6 successive numbers A138986.
  • A138998 (program): 9^n mod 2^n.
  • A138999 (program): First differences of Frobenius numbers for 8 successive numbers A138988.
  • A139038 (program): Centrally symmetric triangle read by rows: t(n,m) = A000931(m+1) if m <= floor(n/2), A000931(n - m+1) otherwise.
  • A139040 (program): Triangle read by rows: each row is an initial segment of the terms of A000930 followed by its reflection.
  • A139049 (program): a(n) = prime(n) + 6.
  • A139098 (program): a(n) = 8*n^2.
  • A139125 (program): a(0) = 0; a(n) = a(n-1) + binomial( n(n+1)/2, n) mod n.
  • A139130 (program): a(n) = sum k=1 to n d(d(k)), where d(k) = number of divisors of k.
  • A139131 (program): Squarefree kernel of n*(n+1)/2.
  • A139140 (program): For n>=1, a(n) = d(p(n)+1) + d(p(n)+2) + d(p(n)+3) + … + d(p(n+1)), where d(m) is the number of positive divisors of m and p(n) is the n-th prime. a(0) = d(1) + d(2).
  • A139143 (program): This sequence and A139142 are complements. a(1)=2. A139142(1)=1. A139142(n+1) = A139142(n) + sum k=1 to n a(k).
  • A139147 (program): Triangle read by rows: replace A003983(n,k) with F(n).
  • A139149 (program): a(n) = (n!+2)/2.
  • A139150 (program): Natural numbers of the form (n!+3)/3.
  • A139151 (program): (n!+4)/4.
  • A139152 (program): Natural numbers of the form (n!+5)/5.
  • A139153 (program): Natural numbers of the form (n!+6)/6.
  • A139154 (program): Natural numbers of the form (n!+7)/7.
  • A139155 (program): Natural numbers of the form (n!+8)/8.
  • A139156 (program): Natural numbers of the form (n!+9)/9.
  • A139157 (program): Natural numbers of the form (n!+10)/10.
  • A139159 (program): a(n) = prime(n)! + 1.
  • A139160 (program): a(n)=(prime(n)!+2)/2.
  • A139161 (program): a(n)=(prime(n)!+3)/3.
  • A139164 (program): a(n) = (prime(n)!+6)/6.
  • A139172 (program): Natural numbers of the form (n!-2)/2.
  • A139173 (program): a(n) = n!/3 - 1.
  • A139174 (program): a(n) = (n!-4)/4.
  • A139175 (program): a(n) = (n! - 5)/5.
  • A139176 (program): a(n) = (n! - 6)/6.
  • A139177 (program): a(n) = (n! - 7)/7.
  • A139179 (program): Number of non-fourth-powers <= n.
  • A139183 (program): a(n) = (n! - 8)/8.
  • A139184 (program): a(n) = (n! - 9)/9.
  • A139185 (program): a(n) = (n! - 10)/10.
  • A139189 (program): a(n) = prime(n)!-1.
  • A139190 (program): a(n) = (prime(n)!-2)/2.
  • A139191 (program): Natural numbers of the form (prime(n)!-3)/3.
  • A139194 (program): Natural numbers of the form (prime(n)!-6)/6.
  • A139209 (program): Fibonacci bisection minus powers of 2.
  • A139222 (program): a(n) = 30*n - 27.
  • A139245 (program): a(n) = 20*n - 16.
  • A139249 (program): a(n) = 30*n - 24.
  • A139264 (program): a(n) = 70*n - 63.
  • A139267 (program): Twice octagonal numbers: 2n(3*n-2).
  • A139268 (program): Twice nonagonal numbers (or twice 9-gonal numbers): a(n) = n(7n-5).
  • A139270 (program): Twice nonprime numbers.
  • A139271 (program): a(n) = 2n(4*n-3).
  • A139272 (program): a(n) = n(8n-5).
  • A139273 (program): a(n) = n(8n - 3).
  • A139274 (program): a(n) = n(8n-1).
  • A139275 (program): a(n) = n(8n+1).
  • A139276 (program): a(n) = n(8n+3).
  • A139277 (program): a(n) = n(8n+5).
  • A139278 (program): a(n) = n(8n+7).
  • A139279 (program): a(n) = 40*n - 32.
  • A139280 (program): a(n) = 90*n - 81.
  • A139283 (program): Numbers of spots seen on ladybugs.
  • A139286 (program): a(n) = 2^(2*prime(n) - 1).
  • A139287 (program): 2^(2p - 1) - 1, where p is prime.
  • A139288 (program): 2^(2p - 1)/2, where p is prime.
  • A139289 (program): (2^(2p - 1)/2)-1, where p is prime.
  • A139290 (program): 2^(2p - 1)/4, where p is prime.
  • A139291 (program): a(n) = 2^(2p - 3) - 1, where p is the n-th prime.
  • A139292 (program): 2^(2p - 1)/8, where p is prime.
  • A139293 (program): (2^(2p - 1)/8)-1, where p is prime.
  • A139329 (program): a(n) = (factorial of the number of 0’s in the binary expansion of n).
  • A139351 (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 e(n).
  • A139352 (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 o(n).
  • A139374 (program): Digit sum of Lucas numbers.
  • A139391 (program): Next odd term in Collatz trajectory with starting value n.
  • A139398 (program): a(n) = Sum_ k >= 0 binomial(n,5*k).
  • A139399 (program): Number of steps to reach a cycle in Collatz problem.
  • A139413 (program): Triangle read by rows: row n gives the numbers A010888(n*k) for k = 1..n.
  • A139464 (program): n! + 2n - 1.
  • A139477 (program): Number of binary digits in A001109(n).
  • A139482 (program): Binomial transform of [1, 1, 2, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, …].
  • A139483 (program): Numbers n such that 24n+7 is prime.
  • A139486 (program): a(n) = Product_ j=0..n-1 (2^j + 2).
  • A139487 (program): Numbers k such that 8k + 7 is prime.
  • A139488 (program): Binomial transform of [1, 2, 3, 4, 0, 0, 0, …].
  • A139527 (program): Numbers n such that numbers 24n+5 are primes.
  • A139528 (program): Numbers n such that numbers 24n+11 are primes.
  • A139529 (program): Numbers n such that numbers 24n+13 are primes.
  • A139530 (program): Primes of the form 24n+13.
  • A139531 (program): Numbers k such that 24*k + 17 is prime.
  • A139532 (program): Numbers n such that numbers 24n+19 are primes.
  • A139544 (program): Numbers which are not the difference of two squares of positive integers.
  • A139570 (program): 2n(n+3).
  • A139576 (program): a(n) = n(2n+9).
  • A139577 (program): a(n) = n(2n + 11).
  • A139578 (program): a(n) = n(2n+13).
  • A139579 (program): a(n) = 2n^2 + 15n.
  • A139580 (program): a(n) = n(2n+17).
  • A139581 (program): a(n) = n(2n + 19).
  • A139591 (program): A139275(n) followed by 18-gonal number A051870(n+1).
  • A139592 (program): A033585(n) followed by A139271(n+1).
  • A139593 (program): A139276(n) followed by A139272(n+1).
  • A139594 (program): Number of different n X n symmetric matrices with nonnegative entries summing to 4. Also number of symmetric oriented graphs with 4 arcs on n points.
  • A139595 (program): A139277(n) followed by A139273(n+1).
  • A139596 (program): A033587(n) followed by even hexagonal number A014635(n+1).
  • A139597 (program): A139278(n) followed by A139274(n+1).
  • A139598 (program): A035008(n) followed by A139098(n+1).
  • A139606 (program): a(n) = 15*n + 6.
  • A139607 (program): a(n) = 21*n + 7.
  • A139608 (program): a(n) = 28*n + 8.
  • A139609 (program): a(n) = 36*n + 9.
  • A139610 (program): a(n) = 45*n + 10.
  • A139611 (program): 55n + 11.
  • A139612 (program): 66n + 12.
  • A139613 (program): 78n + 13.
  • A139614 (program): a(n) = 91*n + 14.
  • A139615 (program): a(n) = 105*n + 15.
  • A139616 (program): a(n) = 120*n + 16.
  • A139617 (program): a(n) = 136*n + 17.
  • A139618 (program): a(n) = 153*n + 18.
  • A139619 (program): a(n) = 171*n + 19.
  • A139620 (program): a(n) = 190*n + 20.
  • A139624 (program): Table read by rows: T(n,k) is the number of connected directed multigraphs with loops and no vertex of degree 0, with n arcs and k vertices, which are transitive (the existence of a path between two points implies the existence of an arc between those two points).
  • A139626 (program): a(n) = binomial(n+4, 4)*6^n.
  • A139634 (program): 10*2^(n-1) - 9.
  • A139635 (program): Binomial transform of [1, 11, 11, 11,…].
  • A139641 (program): a(n) = binomial(n+4, 4)*7^n.
  • A139672 (program): Convolution of A008619 and A001400.
  • A139693 (program): a(n) is the smallest positive integer m where, for k divides m, minimum( k - m/k ) = n.
  • A139697 (program): Binomial transform of [1, 12, 12, 12,…].
  • A139698 (program): Binomial transform of [1, 25, 25, 25, …].
  • A139700 (program): Binomial transform of [1, 30, 30, 30, …].
  • A139701 (program): Binomial transform of [1, 100, 100, 100, …].
  • A139704 (program): Nearly palindromic numbers: non-palindromes that can be made palindromic by inserting an extra digit.
  • A139716 (program): If k is the largest divisor of n that is <= sqrt(n) then a(n) = n - k^2.
  • A139717 (program): If k is the smallest divisor of n that is >= sqrt(n) then a(n) = k^2 - n.
  • A139729 (program): 9^n mod 4^n.
  • A139730 (program): a(n) = 9^n mod 5^n.
  • A139731 (program): a(n) = 9^n mod 6^n.
  • A139732 (program): a(n) = 9^n mod 7^n.
  • A139733 (program): 9^n mod 8^n.
  • A139734 (program): a(n) = 10^n mod 3^n.
  • A139735 (program): a(n) = 10^n mod 4^n.
  • A139736 (program): a(n) = 10^n mod 6^n.
  • A139737 (program): a(n) = 10^n mod 7^n.
  • A139738 (program): a(n) = 10^n mod 8^n.
  • A139739 (program): a(n) = 10^n mod 9^n.
  • A139740 (program): 11^n - 2^n.
  • A139741 (program): a(n) = 11^n - 3^n.
  • A139742 (program): a(n) = 11^n - 4^n.
  • A139743 (program): a(n) = 11^n - 5^n.
  • A139744 (program): a(n) = 11^n - 6^n.
  • A139745 (program): a(n) = 11^n - 7^n.
  • A139746 (program): a(n) = 11^n - 8^n.
  • A139747 (program): a(n) = 11^n - 9^n.
  • A139756 (program): Binomial transform of A004526.
  • A139757 (program): a(n) = (n+1)*(2n+1)^2.
  • A139760 (program): First quadrisection of A115451.
  • A139763 (program): a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4) with a(n)=n+1 for n<=3.
  • A139764 (program): Smallest term in Zeckendorf representation of n.
  • A139782 (program): Binomial transform of A077947.
  • A139786 (program): a(n) = 7^n mod 6^n.
  • A139788 (program): Period 5: repeat 1, 7, 3, 9, 5.
  • A139790 (program): a(n) = (52^(n+2) - 3n2^n - 2(-1)^n) / 18.
  • A139792 (program): First quadrisection of A139763 (1, 2, 3, 4, 11).
  • A139797 (program): Inverse binomial transform of [0, A133474].
  • A139798 (program): Coefficient of x^5 in (1-x-x^2)^(-n).
  • A139800 (program): a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4).
  • A139806 (program): a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4), a(0)=1, a(1)=3, a(2)=7, a(3)=15.
  • A139814 (program): a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4); a(0)=0,a(1)=1,a(2)=3,a(3)=7.
  • A139817 (program): 2^n - number of digits of 2^n.
  • A139818 (program): Squares of Jacobsthal numbers.
  • A140058 (program): Numbers > 24 that are congruent to 5,6,7,8,9 mod 10.
  • A140062 (program): 101*2^(n-1) - 100.
  • A140063 (program): Binomial transform of [1, 3, 7, 0, 0, 0, …].
  • A140064 (program): a(n) = (9n^2 - 23n + 16)/2.
  • A140065 (program): a(n) = (7n^2 - 17n + 12)/2.
  • A140066 (program): a(n) = (5n^2 - 11n + 8)/2.
  • A140081 (program): Period 4: repeat [0, 1, 1, 2].
  • A140085 (program): Period 8: repeat [0,1,1,2,1,2,2,3].
  • A140090 (program): a(n) = n(3n + 7)/2.
  • A140091 (program): a(n) = 3n(n + 3)/2.
  • A140099 (program): A Beatty sequence: a(n) = [n*(1+t)], where t = tribonacci constant (A058265); complement of A140098.
  • A140106 (program): Number of noncongruent diagonals in a regular n-gon.
  • A140107 (program): a(n) = binomial(n+3, 3)*7^n.
  • A140113 (program): a(1)=1, a(n)=a(n-1)+n if n odd, a(n)=a(n-1)+ n^2 if n is even.
  • A140124 (program): a(n) = degree in N of the number of orbits under S_N of the set of n-tuples of partitions of 1,…,N into n subsets.
  • A140139 (program): Binomial transform of [1, 1, 2, -3, 4, -5, 6, -7,…].
  • A140142 (program): a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^4 if n is even.
  • A140143 (program): a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^5 if n is even.
  • A140144 (program): a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^0 if n is even.
  • A140145 (program): a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^3 if n is even.
  • A140146 (program): a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^4 if n is even.
  • A140147 (program): a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^5 if n is even.
  • A140148 (program): a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^0 if n is even.
  • A140149 (program): a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^3 if n is even.
  • A140150 (program): a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^4 if n is even.
  • A140151 (program): a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^5 if n is even.
  • A140152 (program): a(1)=1, a(n)=a(n-1)+n^3 if n odd, a(n)=a(n-1)+ n^0 if n is even.
  • A140153 (program): a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^1 if n is even.
  • A140154 (program): a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^2 if n is even.
  • A140155 (program): a(1)=1, a(n)=a(n-1)+n^3 if n odd, a(n)=a(n-1)+ n^4 if n is even.
  • A140156 (program): a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^5 if n is even.
  • A140157 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^0 if n is even.
  • A140158 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^1 if n is even.
  • A140159 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^2 if n is even.
  • A140160 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^3 if n is even.
  • A140161 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^5 if n is even.
  • A140162 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^0 if n is even.
  • A140163 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n if n is even.
  • A140164 (program): Binomial transform of [1, 1, 1, 1, -1, -1, 5, -11, 19, -29, 41, …].
  • A140199 (program): a(n) = the number of pairs of (not necessarily distinct) positive integers j and k where j <= n and k <= n such that k+j is prime.
  • A140201 (program): Partial sums of A140081.
  • A140205 (program): Partial sums of A140085.
  • A140208 (program): Floor n*Pi(n)/2.
  • A140210 (program): a(n) = Product_ h == 1 (mod 4) and h n h.
  • A140211 (program): a(n) = Product_ d == 3 (mod 4) and d n d.
  • A140213 (program): Product_ h n and h mod 6 = 1 h; product of divisors of n of the form 6*k + 1.
  • A140214 (program): a(n) = Product_ h == 5 (mod 6) and h n h.
  • A140220 (program): a(n) = binomial(n+7, 7)*5^n.
  • A140226 (program): Binomial transform of [1, 3, 3, 1, 1, -1, 1, -1, 1, …].
  • A140227 (program): Binomial transform of [1, 4, 6, 4, 1, 1, -1, 1, -1, 1,…].
  • A140229 (program): Binomial transform of [1, 3, 3, 1, -2, 3, -4, 5, …].
  • A140230 (program): Binomial transform of [1, 2, -3, -4, 5, 6, -7, -8, 9, 10,…].
  • A140234 (program): Sum of the semiprimes <= n.
  • A140236 (program): Double tetrahedral numbers (or double pyramidal numbers): a(n) = k(k+1)(k+2)/6 where k = n(n+1)(n+2)/6.
  • A140252 (program): Inverse binomial transform of A140420.
  • A140253 (program): a(2n) = 2(24^(n-1)-1) and a(2n-1) = 2*4^(n-1)-1.
  • A140260 (program): Those n for which A140259(n) = A002264(n+11).
  • A140261 (program): The length of Sapro’s necklace at successive years in Werneck’s Black Pearl Necklace problem.
  • A140262 (program): A140260 reduced modulo 9.
  • A140271 (program): Least divisor of n that is > sqrt(n), with a(1) = 1.
  • A140282 (program): Numbers k such that A000330(k) is multiple of 3.
  • A140298 (program): a(0)=1; a(3n+1) = a(3n)+1, a(3n+2) = a(3n+1) + a(3n) (=3*A000244), a(3n+3) = a(3n+2) + a(3n) (=A003462(n+2)).
  • A140299 (program): a(n) = A100626(n+1)/A100626(n).
  • A140300 (program): a(n) = 1024^n.
  • A140303 (program): Triangle T(n,k) = 3^(n-k) read by rows.
  • A140313 (program): First differences of A140298.
  • A140318 (program): Period 18: repeat 0, 1, -1, 1, 0, -1, 1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 0.
  • A140320 (program): a(n) = A137576((3^n-1)/2).
  • A140322 (program): a(n) = -1/6 + (-1)^n/2 + 2*4^n/3.
  • A140323 (program): First differences of A140322.
  • A140325 (program): a(n) = binomial(n+8,8) * 2^n.
  • A140341 (program): The number of bits needed to write the universal code for an Elias delta coding, the simplest asymptotically optimal code.
  • A140345 (program): a(n)=a(n-1)^2-a(n-2)-a(n-3)-a(n-4), a(1)=a(2)=a(3)=a(4)=1.
  • A140346 (program): a(n) = binomial(n+8, 8)*5^n.
  • A140347 (program): Composites of the form ((x+y)/3+2)/(x-y), where x=composite and y=prime.
  • A140353 (program): a(n) = prime(n) + 9.
  • A140354 (program): a(n) = binomial(n+9,9)*2^n.
  • A140356 (program): Triangle T(n,m) read by rows: m! if m <= floor(n/2), and (n-m)! otherwise.
  • A140359 (program): a(n) = 2a(n-1) + a(n-2) - 2a(n-3).
  • A140371 (program): Primes of the form 26k + 7.
  • A140372 (program): Primes of the form 26k + 9.
  • A140373 (program): Primes of the form 26*n+11.
  • A140374 (program): Primes of the form 26k + 15.
  • A140375 (program): Primes of the form 26n+23.
  • A140397 (program): a(n) = floor(3phin) - 3floor(phin) where phi = (1+sqrt(5))/2.
  • A140404 (program): a(n) = binomial(n+5, 5)*7^n.
  • A140405 (program): a(n) = binomial(n+6, 6)*5^n.
  • A140406 (program): a(n) = binomial(n+6, 6)*8^n.
  • A140407 (program): A000225 interleaved with A000051.
  • A140408 (program): Irregular triangle T(n,k) read by rows: n repetitions of -1 followed by (n+1) repetitions of n+1.
  • A140413 (program): a(2n) = A000045(6n) + 1, a(2n+1) = A000045(6n+3) - 1.
  • A140420 (program): Binomial transform of 0, 1, 1, 7, 7, 31, 31, …, zero followed by duplicated A083420.
  • A140426 (program): Number of multi-symmetric Steinhaus matrices of size n.
  • A140427 (program): Arises in relating doubly-even error-correcting codes, graphs and irreducible representations of N-extended supersymmetry.
  • A140429 (program): a(n) = floor(3^(n-1)).
  • A140430 (program): Period 6: repeat [3, 2, 4, 1, 2, 0].
  • A140431 (program): 2*A094555(n).
  • A140434 (program): Number of new visible points created at each step in an n X n grid.
  • A140435 (program): Number of new lattice points created at each step in an n X n grid that are not visible.
  • A140438 (program): Number of letters in word for the number n in Tamil.
  • A140442 (program): Primes congruent to 9 mod 14.
  • A140444 (program): Primes congruent to 1 (mod 14).
  • A140461 (program): Numbers in A008364 but not in A038511.
  • A140462 (program): Turan’s upper bound on the number of triangles of a simplicial complex of dimension two for which every minimal non-face has three vertices.
  • A140466 (program): a(n) = 4*A002088(n).
  • A140472 (program): Chaotic sequence related to A004001: a(n) = a(n - a(n-1)) + a(floor(n/2)).
  • A140475 (program): 1 along with primes greater than 3.
  • A140477 (program): Binomial(127,n).
  • A140479 (program): n^2 - number of digits of n^2.
  • A140482 (program): a(n) = 2*n + tau(n).
  • A140496 (program): a(n) = p - number of digits of p^4, where p = n-th prime.
  • A140500 (program): Period 18: repeat [1, 1, -2, 2, -1, -1, 1, -2, 1, -1, -1, 2, -2, 1, 1, -1, 2, -1].
  • A140504 (program): a(n) = 2^n + 4.
  • A140513 (program): Repeat 2^n n times.
  • A140520 (program): a(n) = binomial(n+9, 9)*5^n.
  • A140524 (program): a(1)=2. For n >=2, a(n) = the least integer >= n that is non-coprime to both n and a(n-1).
  • A140525 (program): a(1)=2. For n >=2, a(n) = the least integer >= a(n-1) that is not coprime to both a(n-1)+1 and a(n-1).
  • A140529 (program): a(n) = 6*4^n - 1.
  • A140531 (program): Concatenate subsequences 0, 1, 2, 4, …, 2^k.
  • A140540 (program): Primes of form 17*n - 3.
  • A140541 (program): Primes of the form 17*k - 1.
  • A140542 (program): Primes of form 17*n - 6.
  • A140543 (program): Primes congruent to 15 mod 17.
  • A140545 (program): Primes of form 17n + 6.
  • A140576 (program): Numbers of the form i*9^j-1 (i=1..8, j >= 0).
  • A140580 (program): a(n) = (n^2)/A048671(n), = n*A014963(n) = A140579 * [1, 2, 3,…].
  • A140584 (program): Row sums of A140583.
  • A140590 (program): Exchange successive pairs of terms of A000051.
  • A140592 (program): a(n) = 2n if A010060(n-1) is 0, and a(n) = 2n+1 if A010060(n-1) is 1.
  • A140649 (program): Triangle whose rows are decreasing powers of 2, followed by 0.
  • A140651 (program): A140579^(-1) * A000290, the squares starting (1, 4, 9, …).
  • A140652 (program): Partial sums of A062968.
  • A140657 (program): Powers of 2 with 3 alternatingly added and subtracted.
  • A140659 (program): a(n) = floor(A140657(n+2)/10).
  • A140660 (program): a(n) = 3*4^n + 1.
  • A140670 (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.
  • A140672 (program): a(n) = n(3n + 13)/2.
  • A140673 (program): a(n) = 3n(n + 5)/2.
  • A140674 (program): a(n) = n(3n + 17)/2.
  • A140675 (program): a(n) = n(3n + 19)/2.
  • A140676 (program): a(n) = n(3n + 4).
  • A140677 (program): a(n) = n(3n + 8).
  • A140678 (program): a(n) = n(3n + 10).
  • A140679 (program): a(n) = n(3n+14).
  • A140680 (program): a(n) = n(3n+16).
  • A140681 (program): a(n) = 3n(n+6).
  • A140683 (program): a(n) = 3(-1)^(n+1)2^n - 1.
  • A140684 (program): A037481 mod 10.
  • A140685 (program): Triangle T(n,k) read by rows: T = 1 if n is odd and k=(n-1)/2; T = 2 otherwise.
  • A140689 (program): a(n) = n(3n + 20).
  • A140701 (program): Product of first n centered triangular numbers.
  • A140710 (program): Number of maximal initial consecutive columns ending at the same level, summed over all deco polyominoes of height n.
  • A140716 (program): Blocky integers, i.e., integers n > 1 such that there is a run of n consecutive integer squares the average of which is a square.
  • A140721 (program): Alternated reading of A000302 and negated A002042.
  • A140724 (program): Period 10: 1, 5, 9, 7, 7, 9, 5, 1, 3, 3 repeated.
  • A140725 (program): Inverse binomial transform of (0 followed by A037481).
  • A140730 (program): a(4n)=5^n, a(4n+1)=25^n, a(4n+2)=35^n, a(4n+3)=4*5^n.
  • A140751 (program): Triangle read by rows, X^n * [1,0,0,0,…] where X = an infinite tridiagonal matrix with (1,0,1,0,1,…) in the main and subdiagonals and (1,1,1,…) in the subsubdiagonal.
  • A140766 (program): a(n) = 6a(n-1) - 6a(n-2).
  • A140777 (program): a(n) = 2*prime(n) - 4.
  • A140780 (program): a(n) = 10*a(n-1) - a(n-2).
  • A140781 (program): a(n) = 10*a(n-1) - a(n-2).
  • A140788 (program): a(n) = 6*4^n + 2.
  • A140801 (program): a(0)=360, a(n)=a(n-1)+720 for n>=1.
  • A140802 (program): a(n) = binomial(n+3, 3)*8^n.
  • A140805 (program): Positive triangular sequence of coefficients inspired by the Belyi transform: x’->(m + n)^(n + m)x^m(1 - x)^n/(m^m*n^n): t(n,m)=Binomial[n, m]^Binomial[n, m].
  • A140807 (program): a(n) is the largest integer such that n^k is palindromic in binary for all nonnegative integers k that are <= a(n).
  • A140811 (program): a(n) = 6*n^2 - 1.
  • A140822 (program): Triangle T(n,m) = binomial(n,gcd(n,m)) read by rows, 0<=m<=n.
  • A140823 (program): Natural numbers which are not perfect fourth powers.
  • A140833 (program): Sum of Fibonacci numbers between F(-n)….F(n), inclusive.
  • A140853 (program): a(n) = prime(prime(n) - 1) - 1, where prime(n) is the n-th prime.
  • A140868 (program): a(n) = floor(floor(nalpha)alpha) where alpha = 1+sqrt(2) = A014176.
  • A140870 (program): 8*P_4(2n), 8 times the Legendre Polynomial of order 4 at 2n.
  • A140899 (program): A140724(n+4). Period 10: repeat 7, 9, 5, 1, 3, 3, 1, 5, 9, 7.
  • A140949 (program): a(n) = number of iterations of k -> k-1/k until we reach a negative number, starting at n.
  • A140960 (program): a(n) = (2(-1)^n - 2^(n+1) + 3n*2^n)/9.
  • A140962 (program): Negative values of the Inverse binomial transform of A045883.
  • A140966 (program): a(n) = (5 + (-2)^n)/3.
  • A140975 (program): Period length 20: repeat 1, 3, 8, 8, 9, 1, 6, 6, 7, 9, 4, 4, 5, 7, 2, 2, 3, 5, 0, 0.
  • A140976 (program): Period length 10: repeat 8, 8, 6, 6, 4, 4, 2, 2, 0, 0.
  • A140978 (program): Repeat (n+1)^2 n times.
  • A140979 (program): Floor(2phifloor(n*phi)) where phi = A001622.
  • A141012 (program): a(0) = 0, a(n) = 13^(n-1) + 1.
  • A141015 (program): a(0) = 0, a(1) = 1, a(2) = 2; for n > 2, a(n) = a(n-1) + 2*a(n-2) + a(n-3).
  • A141022 (program): a(n) = n mod ((sum of digits of n)+1).
  • A141023 (program): a(n) = 2^n - (3-(-1)^n)/2.
  • A141025 (program): a(n) = (2^(2+n)-(-1)^n)/3 - 2*n.
  • A141032 (program): a(n) = 4*(16^n-1)/15.
  • A141042 (program): Product of n and the n-th gap between primes: a(n) = n*A001223(n).
  • A141044 (program): Two 2’s followed by all 1’s.
  • A141046 (program): a(n) = 4*n^4.
  • A141054 (program): Binomial(n+8,8)8^n and 8-idempotent numbers. example: A059300 Triangle of idempotent numbers binomial(n,k)k^(n-k), version 4. A059300 formatted as a triangular array: 1 72 ………..
  • A141060 (program): Fourth quadrisection of Jacobsthal numbers A001045 : a(n)=16a(n-1)-5 .
  • A141083 (program): a(n) = 2^(p - 2)*(2^p - 2), where p = prime(n).
  • A141101 (program): a(n) = prime(2n) - n2.
  • A141104 (program): Lower Even Swappage of Upper Wythoff Sequence.
  • A141105 (program): Upper Even Swappage of Upper Wythoff Sequence.
  • A141106 (program): Lower Odd Swappage of Upper Wythoff Sequence.
  • A141107 (program): Upper Odd Swappage of Upper Wythoff Sequence.
  • A141125 (program): Hankel transform of a transform of Fibonacci numbers.
  • A141134 (program): Hankel transform of C(2n+4,n+4).
  • A141135 (program): Minimal number of unit edges required to construct n regular pentagons when allowing edge-sharing.
  • A141136 (program): p(p(A028815(n)-1)-1)-1, where p(n)=n-th prime.
  • A141138 (program): p(A028815(n)-1)-1, where p(n)=n-th prime.
  • A141169 (program): Triangle of Fibonacci numbers, read by rows: T(n,k) = A000045(k), 0<=k<=n.
  • A141195 (program): Primes of the form 16k+11.
  • A141196 (program): Primes of the form 16k+13.
  • A141212 (program): a(n) = 1, if n == 1,3,4 mod 6; otherwise 0.
  • A141213 (program): Defining A to be the interior angle of a regular polygon, the number of constructible regular polygons such that A is in a field extension = degree 2^n, starting with n=0. This is also the number of values of x such that phi(x)/2 = 2^n (where phi is Euler’s phi function), also starting with n=0.
  • A141214 (program): Defining A to be the interior angle of a regular polygon, the number of constructible regular polygons such that A is in a field extension <= degree 2^n, starting with n=0. This is also the number of values of x such that phi(x)/2 is a power of 2 <= 2^n (where phi is Euler’s phi function), also starting with n=0.
  • A141244 (program): Numerators in the expansion of (1-sqrt(1-x^2))/(1-x).
  • A141259 (program): a(n) == 0,1,3,4,5,7,9,11 mod 12; n>0.
  • A141260 (program): a(n) = 1 if n == 0,1,3,4,5,7,9,11 mod 12, otherwise a(n) = 0.
  • A141291 (program): a(n) = 4a(n-1) + 2n-1
  • A141295 (program): Largest m<=n such that all k with 1<=k<=m are divisors of n or coprime to n.
  • A141310 (program): The odd numbers interlaced with the constant-2 sequence.
  • A141317 (program): a(n) = A000244(n) - A010684(n).
  • A141325 (program): a(n) = A000045(n) + A131531(n+3).
  • A141326 (program): Subsequence of ‘Fermat near misses’ which is generated by a simple formula based on the cubic binomial expansion along with formulas for the corresponding terms in the expression, x^3 + y^3 = z^3 + 1.
  • A141341 (program): Totally Goldbach numbers: Positive integers n such that for all primes p < n-1 with p not dividing n, n-p is prime.
  • A141351 (program): a(n)=C(n)+1-0^n where C(n)=A000108(n).
  • A141354 (program): Expansion of (1-5x-x^2+x^3)/((1+x)(1-x)^3).
  • A141355 (program): The Jacobsthal sequence, dropping each third term.
  • A141364 (program): a(n)=C(n)-1+0^n where C(n)=A000108(n).
  • A141375 (program): Primes of the form x^2+8xy-8y^2 (as well as of the form x^2+10x*y+y^2).
  • A141387 (program): Triangle read by rows: T(n,m) = n + 2m(n - m) (0 <= m <= n).
  • A141397 (program): a(n) = 3*a(n-1) + A001651(n+1).
  • A141407 (program): a(n) = binomial(n+7,7)*6^n.
  • A141413 (program): Inverse binomial transform of A140962.
  • A141419 (program): Triangle read by rows: T(n, k) = A000217(n) - A000217(n - k) with 1 <= k <= n.
  • A141425 (program): Period 6: repeat [1, 2, 4, 5, 7, 8].
  • A141449 (program): A005439 mod 9.
  • A141454 (program): A Legendre symbol type assignment of the modulo ten primes to the polynomial: Expand[(x-1)(x+1)(x-2)(x+2)(x-0)]=4 x - 5 x^3 + x^5; c(n) = If[Mod[n, 10] == 1, 1, If[Mod[n, 10] == 9, -1, If[Mod[n, 10] == 3, 2, If[Mod[n, 10] == 7, -2, 0]]]] such that n is a prime[n].
  • A141468 (program): Zero together with the nonprime numbers A018252.
  • A141475 (program): Number of Turing machines with n states following the standard formalism of the busy beaver problem where the head of a Turing machine either moves to the right or to the left, but none once halted.
  • A141478 (program): Binomial(n+2,3)*4^3.
  • A141480 (program): Binomial(n+2,3)*5^3.
  • A141495 (program): a(n) = 3*a(n-1) for n>2; a(0)=1, a(1)=3, a(2)=7.
  • A141496 (program): a(0)=1; a(1)=5; a(2)=11; a(n)=a(1)*a(n-1).
  • A141499 (program): a(0)=0; a(1)=1; a(n) = triangular number at index 5*2^(n-2)-1.
  • A141518 (program): Period 5: repeat [1, 3, 5, 7, 9].
  • A141523 (program): Expansion of (3-2x-3x^2)/(1-x-x^2-x^3).
  • A141530 (program): a(n) = 4n^3 - 6n^2 + 1.
  • A141531 (program): Inverse binomial transform of A001651.
  • A141534 (program): Derived from the centered polygonal numbers: start with the first triangular number, then the sum of the first square number and the second triangular number, then the sum of first pentagonal number, the second square number and the third triangular number, and so on and so on…
  • A141544 (program): Odd numbers k such that 2k+5 is a prime.
  • A141571 (program): Decimal expansion of 11999/99900.
  • A141583 (program): Squares of tribonacci numbers A000213.
  • A141596 (program): Triangle T(n,k) = 4*binomial(n,k)^2-3, read by rows, 0<=k<=n.
  • A141597 (program): Triangle T(n,k) = 2*binomial(n,k)^2-1, read by rows, 0<=k<=n.
  • A141631 (program): a(n) = 3n^2 - 4n + 3.
  • A141679 (program): Triangle of coefficients of the inverse of A058071.
  • A141683 (program): a(n) = Sum_ k=1..n b(k)*a(n - k) for n >= 1, where b(n) = b(n-2) + b(n-3) for n >= 3 with b(0) = 0 and b(1) = b(2) = 1.
  • A141685 (program): a(1) = 1, a(n) = Sum_ k=1..n (k mod 3) * a(n-k) for n >= 2.
  • A141694 (program): a(n) = 22*n + 12.
  • A141721 (program): A141631(n) mod 10.
  • A141722 (program): a(n) = 8*4^n - 7.
  • A141725 (program): a(n) = 4^(n+1) - 3.
  • A141726 (program): Sawtooth with period length 9: repeat 8, 7, 6, 5, 4, 3, 2, 1, 0.
  • A141742 (program): Starting from the 1 in the first line of triangle A141728 choose one of the three digits below it. Repeat down to the other rows. Sequence gives the numbers in base 10 expressed by the collected digits that cannot be reached following any possible path.
  • A141752 (program): a(n) = Sum_ k=0..n [ Fibonacci(2k-1) + (n-k)*Fibonacci(2k) ].
  • A141759 (program): a(n) = 16n^2 + 32n + 15.
  • A141775 (program): Binomial transform of (1, 2, 0, 1, 2, 0, 1, 2, 0, …).
  • A141834 (program): Sum of the lengths of the cycles at a vertex of the complete graph K_n.
  • A141849 (program): Primes congruent to 1 mod 11.
  • A141850 (program): Primes congruent to 3 mod 11.
  • A141851 (program): Primes congruent to 4 mod 11.
  • A141852 (program): Primes congruent to 5 mod 11.
  • A141853 (program): Primes congruent to 6 mod 11.
  • A141854 (program): Primes congruent to 7 mod 11.
  • A141855 (program): Primes congruent to 8 mod 11.
  • A141856 (program): Primes congruent to 9 mod 11.
  • A141857 (program): Primes congruent to 10 mod 11.
  • A141865 (program): Primes congruent to 13 mod 17.
  • A141872 (program): Primes congruent to 7 mod 19.
  • A141874 (program): Primes congruent to 9 mod 19.
  • A141876 (program): Primes congruent to 11 mod 19.
  • A141877 (program): Primes congruent to 12 mod 19.
  • A141878 (program): Primes congruent to 13 mod 19.
  • A141879 (program): Primes congruent to 14 mod 19.
  • A141881 (program): Primes congruent to 1 mod 20.
  • A141882 (program): Primes congruent to 7 mod 20.
  • A141883 (program): Primes congruent to 9 mod 20.
  • A141884 (program): Primes congruent to 11 mod 20.
  • A141885 (program): Primes congruent to 13 mod 20.
  • A141886 (program): Primes congruent to 17 mod 20.
  • A141889 (program): Primes congruent to 4 mod 21.
  • A141890 (program): Primes congruent to 5 mod 21.
  • A141891 (program): Primes congruent to 8 mod 21.
  • A141892 (program): Primes congruent to 10 mod 21.
  • A141896 (program): Primes congruent to 17 mod 21.
  • A141909 (program): Primes congruent to 4 mod 23.
  • A141910 (program): Primes congruent to 6 mod 23.
  • A141912 (program): Primes congruent to 8 mod 23.
  • A141914 (program): Primes congruent to 10 mod 23.
  • A141915 (program): Primes congruent to 11 mod 23.
  • A141917 (program): Primes congruent to 13 mod 23.
  • A141919 (program): Primes congruent to 15 mod 23.
  • A141921 (program): Primes congruent to 17 mod 23.
  • A141922 (program): Primes congruent to 18 mod 23.
  • A141932 (program): Primes congruent to 7 mod 25.
  • A141933 (program): Primes congruent to 8 mod 25.
  • A141934 (program): Primes congruent to 9 mod 25.
  • A141935 (program): Primes congruent to 11 mod 25.
  • A141937 (program): Primes congruent to 13 mod 25.
  • A141939 (program): Primes congruent to 16 mod 25.
  • A141940 (program): Primes congruent to 17 mod 25.
  • A141941 (program): Primes congruent to 18 mod 25.
  • A141942 (program): Primes congruent to 19 mod 25.
  • A141943 (program): Primes congruent to 21 mod 25.
  • A141952 (program): Primes congruent to 7 mod 27.
  • A141953 (program): Primes congruent to 8 mod 27.
  • A141954 (program): Primes congruent to 10 mod 27.
  • A141955 (program): Primes congruent to 11 mod 27.
  • A141957 (program): Primes congruent to 14 mod 27.
  • A141958 (program): Primes congruent to 16 mod 27.
  • A141959 (program): Primes congruent to 17 mod 27.
  • A141960 (program): Primes congruent to 19 mod 27.
  • A141961 (program): Primes congruent to 20 mod 27.
  • A141962 (program): Primes congruent to 22 mod 27.
  • A141963 (program): Primes congruent to 23 mod 27.
  • A141968 (program): Primes congruent to 9 mod 28.
  • A141970 (program): Primes congruent to 13 mod 28.
  • A141971 (program): Primes congruent to 15 mod 28.
  • A141972 (program): Primes congruent to 17 mod 28.
  • A141973 (program): Primes congruent to 19 mod 28.
  • A141974 (program): Primes congruent to 23 mod 28.
  • A141985 (program): Primes congruent to 9 mod 29.
  • A141986 (program): Primes congruent to 10 mod 29.
  • A141987 (program): Primes congruent to 11 mod 29.
  • A141988 (program): Primes congruent to 12 mod 29.
  • A141989 (program): Primes congruent to 13 mod 29.
  • A141990 (program): Primes congruent to 14 mod 29.
  • A141991 (program): Primes congruent to 15 mod 29.
  • A141992 (program): Primes congruent to 16 mod 29.
  • A141993 (program): Primes congruent to 17 mod 29.
  • A141994 (program): Primes congruent to 18 mod 29.
  • A141995 (program): Primes congruent to 19 mod 29.
  • A141996 (program): Primes congruent to 20 mod 29.
  • A141998 (program): Primes congruent to 22 mod 29.
  • A141999 (program): Primes congruent to 23 mod 29.
  • A142000 (program): Primes congruent to 24 mod 29.
  • A142013 (program): Primes congruent to 9 mod 31.
  • A142014 (program): Primes congruent to 10 mod 31.
  • A142015 (program): Primes congruent to 11 mod 31.
  • A142016 (program): Primes congruent to 12 mod 31.
  • A142020 (program): Primes congruent to 16 mod 31.
  • A142021 (program): Primes congruent to 17 mod 31.
  • A142027 (program): Primes congruent to 23 mod 31.
  • A142038 (program): Primes congruent to 9 mod 32.
  • A142039 (program): Primes congruent to 11 mod 32.
  • A142040 (program): Primes congruent to 13 mod 32.
  • A142044 (program): Primes congruent to 23 mod 32.
  • A142049 (program): Primes congruent to 1 mod 33.
  • A142056 (program): Primes congruent to 13 mod 33.
  • A142057 (program): Primes congruent to 14 mod 33.
  • A142059 (program): Primes congruent to 17 mod 33.
  • A142060 (program): Primes congruent to 19 mod 33.
  • A142061 (program): Primes congruent to 20 mod 33.
  • A142062 (program): Primes congruent to 23 mod 33.
  • A142069 (program): Period length 9: repeat 3, 7, 2, 6, 1, 5, 0, 4, 8 .
  • A142072 (program): Primes congruent to 19 mod 34.
  • A142083 (program): Primes congruent to 11 mod 35.
  • A142085 (program): Primes congruent to 13 mod 35.
  • A142087 (program): Primes congruent to 17 mod 35.
  • A142088 (program): Primes congruent to 18 mod 35.
  • A142089 (program): Primes congruent to 19 mod 35.
  • A142090 (program): Primes congruent to 22 mod 35.
  • A142091 (program): Primes congruent to 23 mod 35.
  • A142092 (program): Primes congruent to 24 mod 35.
  • A142103 (program): Primes congruent to 11 mod 36.
  • A142104 (program): Primes congruent to 13 mod 36.
  • A142105 (program): Primes congruent to 17 mod 36.
  • A142106 (program): Primes congruent to 19 mod 36.
  • A142107 (program): Primes congruent to 23 mod 36.
  • A142108 (program): Primes congruent to 25 mod 36.
  • A142150 (program): The nonnegative integers interleaved with 0’s.
  • A142238 (program): Numerators of continued fraction convergents to sqrt(3/2).
  • A142240 (program): A triangular sequence from the pattern in row sums of Pascal’s triangle A007318, Eulerian numbers A008292 and A060187: Delta_diagonal=m; m= 0,1,2,3,…k .
  • A142241 (program): a(n) = 24*n + 14.
  • A142242 (program): Row sums of A143200.
  • A142245 (program): Expansion of 2x(6 + 5x) / ((1 - x)(1 - x - x^2)).
  • A142248 (program): Odd numbers in A138123.
  • A142333 (program): Primes congruent to 41 mod 45.
  • A142342 (program): a(n) = 10*prime(n).
  • A142354 (program): A triangular sequence “representation” of the modulo 10 Integer field: t(+)(n,m)=Mod[n + m, 10]; t(x)(n,m)=Mod[nm, 10]; t(n,m)=Mod[t(=)(n,m)t(X)(n,m),10].
  • A142463 (program): a(n) = 2n^2 + 2n - 1.
  • A142464 (program): Decimal expansion of 13/36.
  • A142471 (program): a(0) = a(1) = 0; thereafter a(n) = a(n-1)*a(n-2) + 2.
  • A142474 (program): 1 followed by A141015.
  • A142584 (program): a(n) = A014217(n+1) - A115360(n+2).
  • A142588 (program): A trisection of A000129, the Pell numbers.
  • A142590 (program): First trisection of A061037 (Balmer line series of the hydrogen atom).
  • A142599 (program): Second trisection of A061037.
  • A142600 (program): Third trisection of A061037.
  • A142702 (program): Period 4: repeat [5, 2, 5, 8].
  • A142705 (program): Numerator of 1/4 - 1/(2n)^2.
  • A142717 (program): First (leftmost) odd term in the n-th row of triangle A120070.
  • A142719 (program): a(n) = if n < 41 then n^2 - n + 41, otherwise n^2 - 81*n + 1681.
  • A142721 (program): An even-odd sequence: a(n) = n/2 if n is even, or a(n-1) + 2^floor(log_2(n+1)) otherwise.
  • A142880 (program): a(n) = 7*a(n-3) - a(n-6).
  • A142881 (program): a(0) = 0, a(1) = 1, after which, if n=3k: a(n) = 2a(n-1) - a(n-2), if n=3k+1: a(n) = a(n-1) + a(n-2), if n=3k+2: a(n) = 2a(n-1) + a(n-2).
  • A142883 (program): a(n) = A142590(n)/3.
  • A142954 (program): a(n) = 2n+3+3(-1)^n.
  • A142962 (program): Scaled convolution of (n^3)A000984(n) with A000984(n). A000984(n) = binomial(2n,n) (central binomial coefficients).
  • A142964 (program): a(n) = 62^n - 2n - 5.
  • A142974 (program): A007318 * [1, 1, -1, 1, 1, 1,…].
  • A142993 (program): Crystal ball sequence for the lattice C_4.
  • A142994 (program): Crystal ball sequence for the lattice C_5.
  • A143008 (program): Crystal ball sequence for the A2 x A2 lattice.
  • A143012 (program): Numbers of the form (4^p + 2^p + 1)/7, where p > 3 is prime.
  • A143025 (program): Period length 4: repeat [1, 8, 2, 8].
  • A143038 (program): Triangle read by rows, A000012 * A134309 * A000012; where A134309 = an infinite lower triangular matrix with (1, 1, 2, 4, 8, 16,…) in the main diagonal and the rest zeros.
  • A143058 (program): A007318 * [1, 6, 7, 1, 0, 0, 0,…].
  • A143059 (program): A007318 * [1, 10, 25, 15, 1, 0, 0, 0,…].
  • A143075 (program): Polynomial expansion sequence: p(x)=1/(1 - 4x + 5x^2 - 6x^4 + 6x^5 - x^6 - 2x^7 + x^8).
  • A143079 (program): a(n) = ((9+sqrt(9))^n + (9-sqrt(9))^n)/2.
  • A143084 (program): Triangle read by rows: T(n,m) = (n + m)!.
  • A143086 (program): Symmetrical triangle sequence: t(n,m)=If[m < = ( less than or equal) Floor[n/2], 2^(m + 1) - 1, 2^(n - m + 1) - 1].
  • A143088 (program): Triangle T(n,m)=( 2^(m+1)-1 ) * ( 2^(n-m+1)-1 ), read by rows, 0<=m<=n.
  • A143095 (program): (1, 2, 4, 8,…) interleaved with (4, 8, 16, 32,…).
  • A143096 (program): a(n) = 2*a(n-1)-1, with a(1)=1, a(2)=4, a(3)=5.
  • A143097 (program): 3k - 2 interleaved with 3k - 1 and 3*k.
  • A143098 (program): First differences of A143097.
  • A143101 (program): Partial sums of A143097.
  • A143126 (program): a(n) = (1-2n)*2^n.
  • A143127 (program): Sum of k*d(k) over k=1,2,…,n, where d(k) is the number of divisors of k.
  • A143128 (program): a(n) = Sum_ k=1..n k*sigma(k).
  • A143131 (program): Binomial transform of [1, 4, 10, 20, 0, 0, 0,…].
  • A143157 (program): Partial sums of A091512.
  • A143166 (program): a(n) = n(8n^2 + 1)/3.
  • A143182 (program): Triangle T(n,m) = 1 + abs(n-2*m), read by rows, 0<=m<=n.
  • A143200 (program): Triangle read by rows: t(n,m) is -1 if binomial(n, m) is greater than 1 and odd, otherwise t(n,m) = binomial(n, m) mod 2.
  • A143201 (program): Product of distances between prime factors in factorization of n.
  • A143208 (program): a(1)=2; for n>1, a(n) = (4-9n+3n^2)/2.
  • A143214 (program): Gray code applied to Pascal’s triangle: T(n,m)=GrayCode(binomial(n,m)).
  • A143218 (program): Triangle read by rows, A127775 * A000012 * A127775; 1<=k<=n.
  • A143250 (program): Reverse binary expansion of the Fibonacci numbers.
  • A143257 (program): Reverse binary expansion of the factorial numbers.
  • A143259 (program): a(n) = 1 if n is a nonzero square, -1 if n is twice a nonzero square, 0 otherwise.
  • A143261 (program): Triangle read by rows: binary reversed Gray code of binomial(n,m).
  • A143268 (program): a(n) = phi(n)T(n), where phi(n) is Euler’s totient function (A000010) and T(n) = n(n+1)/2 is the n-th triangular number (A000217).
  • A143270 (program): a(n) = n*A002088(n).
  • A143272 (program): a(n) = d(n)*T(n), where d(n) is the number of divisors of n (A000005) and T(n)=n(n+1)/2 are the triangular numbers (A000217).
  • A143274 (program): a(n) = n * A006218(n).
  • A143292 (program): Gray code of prime(n) (decimal representation).
  • A143293 (program): Partial sums of A002110, the primorial numbers.
  • A143299 (program): Number of terms in the Zeckendorf representation of every number in row n of the Wythoff array.
  • A143333 (program): Pascal’s triangle binomial(n,m) read by rows, all even elements replaced by zero.
  • A143348 (program): a(n) = -(-1)^n times sum of divisors of n.
  • A143357 (program): Floor((n-1)!/[n(n+1)]).
  • A143431 (program): Periodic length 8 sequence [1, -1, 1, -1, -1, 1, -1, 1, …].
  • A143432 (program): Ultimately periodic length 4 sequence [ 2, 2, 0, 0, …] with a(0) = a(1) = 1.
  • A143443 (program): a(n) = n * A002321(n).
  • A143462 (program): Expansion of 1/(1 + 4x + 8x^2).
  • A143536 (program): Triangle read by rows, T(n,k) = 1 if n is prime, 0 otherwise.
  • A143538 (program): Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n.
  • A143544 (program): Triangle read by rows, T(n,k) = 2 if n is prime, 1 otherwise; 1<=k<=n.
  • A143545 (program): a(n) = n unless n is a prime, in which case a(n) = 2n.
  • A143579 (program): Permutation of the natural numbers (0,1,2,3,…): Odious numbers (A000069) interleaved with Evil numbers (A001969).
  • A143593 (program): Triangle read by rows, square of an infinite lower triangular matrix with 1’s in the first column and the rest 2’s.
  • A143595 (program): Triangle read by rows, A000012 * (an infinite lower triangular matrix with 1’s in the first column and the rest 2’s); 1<=k<=n.
  • A143607 (program): Numerators of principal and intermediate convergents to 2^(1/2).
  • A143608 (program): A005319 and A002315 interleaved.
  • A143609 (program): Numerators of the upper principal and intermediate convergents to 2^(1/2).
  • A143616 (program): Record values in A010371.
  • A143618 (program): Decimal expansion of 127/216.
  • A143621 (program): a(n) = (-1)^binomial(n,4): Periodic sequence 1,1,1,1,-1,-1,-1,-1,… .
  • A143622 (program): a(n) = (-1)^binomial(n,8): Periodic sequence 1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,… .
  • A143643 (program): Numerators of the lower principal convergents and the lower intermediate convergents to 3^(1/2).
  • A143667 (program): Digits of the infinite Fibonacci word A003849 grouped 2 by 2 and interpreted as a binary value.
  • A143668 (program): Result of the morphing 01->01021212, 02->0102121201, 12->01021201, iterated from ‘01’. Sequence of the Fibonacci word fractal.
  • A143669 (program): a(n) = binomial((n+1)^2, n) / (n+1)^2.
  • A143684 (program): a(0) = a(1) = 0; thereafter a(n) = 2a(n-1)a(n-2) + 1.
  • A143689 (program): a(n) = (3*n^2 - n + 2)/2.
  • A143690 (program): a(n) = A007318 * [1, 6, 14, 9, 0, 0, 0, …].
  • A143698 (program): 12 times hexagonal numbers: 12n(2*n-1).
  • A143712 (program): Numbers with at least two digits in which all digits except the rightmost are even and the rightmost is odd.
  • A143730 (program): a(n) = A141616(n) - A100181(n).
  • A143731 (program): Characteristic function of numbers with at least two distinct prime factors (A024619).
  • A143763 (program): a(n+1) = (a(n)-n)^2, a(1) = 1.
  • A143785 (program): Antidiagonal sums of the triangle A120070.
  • A143795 (program): a(1) = 1, then for n > 1, a(n) = a(n - 1) + 1 for n even, or a(n) = a(n - 1) + 10 for n odd.
  • A143803 (program): a(n) = 2*A001614(n) - 1 where A001614 lists the Connell numbers.
  • A143804 (program): Triangle read by rows, thrice the Connell numbers (A001614) - 2.
  • A143838 (program): Ulam’s spiral (SSW spoke).
  • A143839 (program): Ulam’s spiral (SSE spoke).
  • A143844 (program): Triangle T(n,k) = k^2 read by rows.
  • A143845 (program): See Comments line.
  • A143854 (program): Ulam’s spiral (WSW spoke).
  • A143855 (program): Ulam’s spiral (ESE spoke).
  • A143856 (program): Ulam’s spiral (ENE spoke).
  • A143857 (program): a(n) = n + (n+1)*(n+2)^(n+3).
  • A143859 (program): Ulam’s spiral (WNW spoke).
  • A143860 (program): Ulam’s spiral (NNW spoke).
  • A143861 (program): Ulam’s spiral (NNE spoke).
  • A143901 (program): Rectangular array R by antidiagonals: R(m,n) = floor((m*n+1)/2).
  • A143902 (program): Rectangular array R by antidiagonals: R(m,n) = number of black squares
  • A143918 (program): G.f. A(x) satisfies: A(x) = 1/(1-x)^2 + x^2*A’(x).
  • A143928 (program): 2*p^2, for p an odd prime.
  • A143938 (program): The Wiener index of a benzenoid consisting of a linear chain of n hexagons.
  • A143939 (program): Triangle read by rows: T(n,k) is the number of unordered pairs of vertices at distance k in the cycle C_n (1 <= k <= floor(n/2)).
  • A143941 (program): The Wiener index of a chain of n triangles (i.e., joined like VVV..VV; here V is a triangle!).
  • A143943 (program): The Wiener index of a chain of n squares joined at vertices (i.e., joined like <><><>…<>; here <> is a square!).
  • A143945 (program): Wiener index of the grid P_n x P_n, where P_n is the path graph on n vertices.
  • A143954 (program): Number of peaks in the peak plateaux of all Dyck paths of semilength n.
  • A143956 (program): Triangle read by rows, A000012 * A136521 * A000012; 1<=k<=n.
  • A143959 (program): Final digit of n^(n+1)-(n+1)^n for n>2
  • A143960 (program): a(n) = the n-th positive integer with exactly n zeros and n ones in its binary representation.
  • A143971 (program): Triangle read by rows, (3n-2) subsequences decrescendo
  • A143974 (program): Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark those having x+y=1(mod 3); then R(m,n) is the number of marked unit squares in the rectangle [0,m]x[0,n].
  • A143975 (program): a(n) = floor(n*(n+3)/3).
  • A143976 (program): Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares having x+y=1(mod 3); then R(m,n) is the number of UNmarked squares in the rectangle [0,m]x[0,n].
  • A143977 (program): Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares having x-y =0(mod 3); then R(m,n) is the number of marked squares in the rectangle [0,m] X [0,n].
  • A143978 (program): a(n) = floor(2n(n+1)/3).
  • A143979 (program): Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares having x-y =0(mod 3); then R(m,n) is the number of UNmarked squares in the rectangle [0,m]x[0,n].
  • A143984 (program): a(0) = 0; thereafter, a(n+1) = (a(n) - 2)^2 - n.
  • A143988 (program): Numbers congruent to 5, 13 mod 18.
  • A143996 (program): Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,4), (2,2), (3,3), (4,1); then R(m,n) is the number of marked squares in the rectangle [0,m]x[0,n].
  • A143999 (program): Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,1), (2,3), (3,2), (4,0); then R(m,n) is the number of UNmarked squares in the rectangle [0,m]x[0,n].
  • A144044 (program): a(n) = ((1+sqrt(11))^n-(1-sqrt(11))^n)^2/44.
  • A144065 (program): Values of n such that the expression sqrt(4!*(n+1) + 1) yields an integer.
  • A144075 (program): Duplicate of A008621.
  • A144077 (program): a(n) = z(n^2,n) with z(x,y) = if x>y then z(x-y,y+1) else y.
  • A144083 (program): Triangle read by rows, partial sums from the right an A010892 subsequences decrescendo triangle
  • A144110 (program): Period 6: repeat [2, 2, 2, 1, 1, 1].
  • A144112 (program): Weight array W= w(i,j) of the natural number array A000027.
  • A144124 (program): P_4(2n+1), the Legendre polynomial of order 4 at 2n+1.
  • A144129 (program): ChebyshevT(3, n).
  • A144130 (program): a(n) = ChebyshevT(4, n).
  • A144133 (program): Gegenbauer polynomial C_n^2(3).
  • A144138 (program): Chebyshev polynomial of the second kind U(3,n).
  • A144139 (program): Chebyshev polynomial of the second kind U(4,n).
  • A144193 (program): Square array (5 X 5) read by rows.
  • A144194 (program): Square array (6 X 6) read by rows.
  • A144197 (program): Square array 7 x 7 read by rows.
  • A144204 (program): Array A(k,n) = (n+k-2)*(n-1) - 1 (k >= 1, n >= 1) read by antidiagonals.
  • A144216 (program): C(m,2)+C(n,2), m>=1, n>=1: a rectangular array R read by antidiagonals.
  • A144217 (program): Weight array of A144216: a rectangular array by antidiagonals.
  • A144222 (program): Floor of the volumes of the first sixteen Lobell polyhedra.
  • A144225 (program): Bordered Pascal’s triangle in rectangular format.
  • A144257 (program): Weight array of A086270.
  • A144301 (program): a(0) = a(1) = 1; thereafter a(n) = (2n-3)a(n-1) + a(n-2).
  • A144312 (program): a(n) = 5n(5*n + 1)/2.
  • A144314 (program): a(n) = 3n(6*n + 1).
  • A144328 (program): A002260 preceded by a column of 1’s: a (1, 1, 2, 3, 4, 5,…) crescendo triangle by rows.
  • A144335 (program): Row sums of triangle A144334, binomial transform of [1, 2, 6, 7, 3, 0, 0, 0,…]
  • A144338 (program): Squarefree numbers > 1.
  • A144390 (program): a(n) = 3*n^2 - n - 1.
  • A144391 (program): a(n) = 3*n^2 + n - 1.
  • A144396 (program): The odd numbers greater than 1.
  • A144403 (program): Triangle T(n, k) = binomial(n, k)^2 - binomial(n, k) - 1, read by rows.
  • A144404 (program): Triangle T(n,k) = 3*binomial(n, k)^2 - binomial(n, k) - 1, read by rows.
  • A144410 (program): a(n) = 4(3n+1)(3n+2).
  • A144412 (program): Invert transform of odd nonprime gaps adjusted to be from the set 2,1,0,-1 : b(n)=A067970(n)/2-2; a(n)=Sum[b(n + 1)*a(n - k), k, 1, n ].
  • A144414 (program): a(n) = 2*(4^n - 1)/3 - n.
  • A144429 (program): Starts 1 2 3 then successive terms have differences 1 2 3.
  • A144430 (program): a(n) = 1 + A144429(n).
  • A144433 (program): Multiples of 8 interleaved with the sequence of odd numbers >= 3.
  • A144437 (program): Period 3: repeat [3, 3, 1].
  • A144448 (program): First bisection of A061039.
  • A144449 (program): a(n) = 36n^2 + 60n + 16.
  • A144454 (program): First trisection of A061039.
  • A144459 (program): a(n) = (3n+1)(5*n+1).
  • A144464 (program): Triangle T(n,m) read by rows: T(n,m) = 2^min(m,n-m).
  • A144465 (program): a(n) = 5^n - 2^(n - 1) for n > 0; a(0) = 1.
  • A144468 (program): Final digit of multiples of 7.
  • A144473 (program): A triangle sequence of determinants: a(n)=If[Mod[n, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 0]]]; b(n,m)=If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M= a(m), b(n, m) , a(n), b(n, n) ; t(n,m)=Det[M].
  • A144478 (program): Period 9: repeat 1,0,5,7,6,2,4,3,8.
  • A144479 (program): a(0)=1, a(1)=3, a(n) = 8*a(n-1) - a(n-2).
  • A144481 (program): A078371(n-1) mod 9.
  • A144483 (program): A144481(4n-3).
  • A144485 (program): (3n + 2)*binomial(3n + 1,n).
  • A144489 (program): Partial sums of A087624.
  • A144494 (program): a(n) = 0 if n is prime, otherwise A001222(n).
  • A144519 (program): Triangular numbers n*(n+1)/2 with n prime and n+1 nonprime.
  • A144532 (program): Continued fraction for sqrt(8/9).
  • A144555 (program): a(n) = 14*n^2.
  • A144560 (program): Ten times hexagonal numbers: 10n(2*n-1).
  • A144564 (program): Bisection of A147757.
  • A144570 (program): Nonprime(prime(n)).
  • A144590 (program): Number of ordered ways of writing 2n+1 = i + j, where i is a prime and j is of the form k*(k+1), k > 0.
  • A144595 (program): Christoffel word of slope 4/7.
  • A144596 (program): Christoffel word of slope 2/7.
  • A144597 (program): Christoffel word of slope 3/7.
  • A144598 (program): Christoffel word of slope 5/7.
  • A144599 (program): Christoffel word of slope 6/7.
  • A144600 (program): Christoffel word of slope 2/11.
  • A144601 (program): Christoffel word of slope 3/11.
  • A144602 (program): Christoffel word of slope 4/11.
  • A144603 (program): Christoffel word of slope 5/11.
  • A144604 (program): Christoffel word of slope 6/11.
  • A144605 (program): Christoffel word of slope 7/11.
  • A144606 (program): Christoffel word of slope 8/11.
  • A144607 (program): Christoffel word of slope 9/11.
  • A144608 (program): Christoffel word of slope 10/11.
  • A144609 (program): Sturmian word of slope Pi.
  • A144610 (program): Sturmian word of slope e.
  • A144611 (program): Sturmian word of slope 2-sqrt(2).
  • A144612 (program): Sturmian word of slope (3-sqrt(3))/2.
  • A144613 (program): a(n) = sigma(3n) = A000203(3n).
  • A144614 (program): Sum of divisors of 3*n + 1.
  • A144615 (program): a(n) = A000203(3n+2).
  • A144619 (program): a(n) = 19n + 8.
  • A144640 (program): Row sums from A144562.
  • A144657 (program): a(n) = Sum[Sum[(i+j)!/(i!*j!), i,1,n ], j,1,n ].
  • A144677 (program): Related to enumeration of quantum states (see reference for precise definition).
  • A144678 (program): Related to enumeration of quantum states (see reference for precise definition).
  • A144679 (program): a(n) = [n/5 + 1][n/5 + 2](3n - 10[n/5] + 3)/6, where [.] = floor.
  • A144704 (program): a(n) = 4^n(1-2n).
  • A144706 (program): Central coefficients of Pascal-like triangle A132047.
  • A144707 (program): Diagonal sums of Pascal-like triangle A132047.
  • A144708 (program): a(n)=6^n*(1-4n);
  • A144720 (program): a(0) = 2, a(1) = 3, a(n) = 4 * a(n-1) - a(n-2).
  • A144721 (program): a(0) = 2, a(1) = 5, a(n) = 4 * a(n-1) - a(n-2).
  • A144739 (program): 7-factorial numbers A114799(7n+3): Partial products of A017017(k) = 7k+3, a(0) = 1.
  • A144750 (program): A098777 mod 9.
  • A144751 (program): a(1) = 3, a(n + 1) = 1 + a(n) + least odd prime factor of a(n).
  • A144756 (program): Partial products of successive terms of A017101; a(0)=1 .
  • A144758 (program): Partial products of successive terms of A017197.
  • A144768 (program): a(n) = n! - n^9.
  • A144769 (program): a(n) = floor(prime(n)/3).
  • A144773 (program): 10-fold factorials: Product_ k=0..n-1 (10*k+1).
  • A144786 (program): If n is an oblong number A002378, then a(n)=a(j) where j is the number of oblong numbers in (0,n], otherwise a(n)=n.
  • A144827 (program): Partial products of successive terms of A017029; a(0)=1.
  • A144828 (program): Partial products of successive terms of A017113; a(0)=1.
  • A144829 (program): Partial products of successive terms of A017209; a(0)=1 .
  • A144831 (program): (n+1)^2 - (smallest prime > n^2).
  • A144843 (program): a(n) = (6^n - 2^n)^2 / 16.
  • A144844 (program): a(n) = ((2 + sqrt(2))^n - (2 - sqrt(2))^n)^2/8.
  • A144855 (program): Number of paths from (1,1) to (n,n) in an n X n grid using only the steps +(1,0), -(1,0), +(0,1) and -(0,1) which do not self-intersect and which avoid any point (p,q) satisfying “(p-1)*n + q is prime”.
  • A144864 (program): a(n) = (4*16^(n-1)-1)/3.
  • A144876 (program): Maximal number of distinct polyominoes into which an n X n square can be divided.
  • A144898 (program): Expansion of x/((1-x-x^3)*(1-x)^4).
  • A144916 (program): Integers k for which A144912 attains a new maximal odd value.
  • A144917 (program): a(n) is the maximal odd value attained by A144916(n).
  • A144925 (program): Number of nontrivial divisors of the n-th composite number.
  • A144927 (program): Numbers n such that there exists an integer k with (n+7)^3-n^3=k^2.
  • A144928 (program): Values of k arising in A144927.
  • A144929 (program): Numbers n such that there exists an integer k with (n+1)^3 - n^3 = 7*k^2.
  • A144930 (program): Numbers k arising in A144929.
  • A144945 (program): Number of ways to place 2 queens on an n X n chessboard so that they attack each other.
  • A144965 (program): a(n) = 4n(4*n^2+1).
  • A144968 (program): Number of squares between consecutive cubes.
  • A144971 (program): Integers of the form sum_ i=2521..j i/(i-2520) for any upper limit j.
  • A145004 (program): Values of n at which the number of roots of the function x+n*cos(x) increases.
  • A145005 (program): Values of n at which the number of roots of the function x+n*sin(x) increases.
  • A145011 (program): First differences of A007775.
  • A145018 (program): a(n) = (n^2 - n + 8)/2.
  • A145027 (program): a(n) = a(n-1) + a(n-2) + a(n-3) with a(1) = 2, a(2) = 3, a(3) = 4.
  • A145037 (program): Number of 1’s minus number of 0’s in the binary representation of n.
  • A145051 (program): Numerator of the first convergent to sqrt(n) using the recursion x = (n/x + x)/2.
  • A145052 (program): One-third of the number of n X n nonnegative integer arrays with every 3 X 3 subblock summing to 1.
  • A145064 (program): Reduced numerators of the first convergent to the cube root of n using the recursion x = (2*x+n/x^2)/3.
  • A145066 (program): Partial sums of A002522, starting at n=1.
  • A145067 (program): Zero followed by partial sums of A008865.
  • A145068 (program): Zero followed by partial sums of A059100, starting at n=1.
  • A145069 (program): a(n) = n(n^2 + 3n + 5)/3.
  • A145070 (program): Partial sums of A006127, starting at n=1.
  • A145071 (program): Partial sums of A000051, starting at n=1.
  • A145094 (program): Coefficients in expansion of Eisenstein series q*E’_4.
  • A145095 (program): Coefficients in expansion of Eisenstein series -q*E’_6.
  • A145105 (program): a(n) = n if n is prime or a perfect number, otherwise a(n) = 0.
  • A145109 (program): a(n) = 2n * core(2n).
  • A145126 (program): a(n) = 1 + (6 + (11 + (6 + n)n)n)*n/24.
  • A145127 (program): a(n) = 1 + (144 + (50 + (35 + (10 + n)n)n)n)n/120.
  • A145128 (program): 1 + (1200 + (634 + (225 + (85 + (15 + n)n)n)n)n)*n/720.
  • A145129 (program): 1 + (9960 + (6804 + (2464 + (735 + (175 + (21 + n)n)n)n)n)n)n/5040.
  • A145130 (program): 2 + (89040 + (71868 + (29932 + (8449 + (1960 + (322 + (28 + n)n)n)n)n)n)n)*n/40320.
  • A145131 (program): Expansion of x/((1 - x - x^4)*(1 - x)^2).
  • A145132 (program): Expansion of x/((1 - x - x^4)*(1 - x)^3).
  • A145154 (program): Coefficients in expansion of Eisenstein series E_1.
  • A145172 (program): Number of pentagonal numbers needed to represent n with greedy algorithm.
  • A145216 (program): Self-convolution of (1^3, 2^3, 3^3, 4^3, … ).
  • A145217 (program): a(n) is the self-convolution series of the sum of 4th powers of the first n natural numbers.
  • A145218 (program): a(n) is the self-convolution series of the sum of 5th powers of the first n natural numbers.
  • A145222 (program): a(n) is the number of odd permutations (of an n-set) with exactly 1 fixed point.
  • A145229 (program): Coefficients in expansion of E’_1(q).
  • A145265 (program): A positive integer n is included if there exists a positive integer m such that Sum_ k>=0 floor(n/(m+k)) = n.
  • A145266 (program): A positive integer n is included if there does not exist a positive integer m such that Sum k>=0 floor(n/(m+k)) = n.
  • A145282 (program): a(n) = number of monomials in n-th power of polynomial x^2-x-1
  • A145285 (program): a(n) is the number of monomials in the n-th power of polynomial x^4-x^3-x^2-x-1.
  • A145329 (program): Partial sums of A051442, starting at n=1.
  • A145341 (program): Convert 2n-1 to binary. Reverse its digits. Convert back to decimal to get a(n).
  • A145342 (program): a(n) = (A145341(n) + 1)/2.
  • A145362 (program): Lower triangular array, called S1hat(-1), related to partition number array A145361.
  • A145377 (program): a(n) = A002324(n) mod 2.
  • A145382 (program): Write the n-th prime in binary. Change all 0’s to 1’s and all 1’s to 0’s. a(n) is the decimal equivalent of the result.
  • A145389 (program): Digital roots of triangular numbers.
  • A145393 (program): Number of inequivalent sublattices of index n in square lattice, where two sublattices are considered equivalent if one can be rotated or reflected to give the other, with that rotation or reflection preserving the parent square lattice.
  • A145397 (program): Numbers not of the form 1/6m(m+1)*(m+2), the non-tetrahedral numbers.
  • A145423 (program): Decimal expansion of Sum_ n>=1 (-1)^(n-1)/(n^2-1/4)^2.
  • A145441 (program): Exponents of multipliers 10^a(n) of SI prefixes, in increasing order.
  • A145442 (program): Multipliers of SI prefixes, in increasing order.
  • A145445 (program): a(n) = the smallest square > n-th prime.
  • A145446 (program): a(n) = the smallest cube > n-th prime
  • A145448 (program): a(n) = 12^n*n!.
  • A145516 (program): 11^1,22^2,33^3,44^4,…
  • A145544 (program): 4*(4^n-3^n).
  • A145563 (program): a(0)=0 and a(n+1) = 3*a(n) + 2^(n+2).
  • A145568 (program): Characteristic function of numbers relatively prime to 11.
  • A145569 (program): Multiples of 6 appear in pairs.
  • A145577 (program): A045944 mod 9. Period 9: repeat 0,5,7,6,2,4,3,8,1.
  • A145594 (program): A145593(n) mod 9.
  • A145600 (program): a(n) is the number of walks from (0,0) to (0,1) that remain in the upper half-plane y >= 0 using (2*n - 1) unit steps either up (U), down (D), left (L) or right (R).
  • A145607 (program): Numbers k such that (3(2k + 1)^2 + 2)/5 is a square.
  • A145608 (program): Numbers a(n)=k such that (1/3)(5(2k+1)^2-2) is A057080(n)^2.
  • A145644 (program): Cubefree part of 10^n.
  • A145654 (program): Partial sums of A000918, starting from index 1.
  • A145655 (program): Partial sums of A080674.
  • A145677 (program): Triangle T(n,m) read by rows: T(n,0) =1; T(n,n) =n, n>0; T(n,k) =0, 0<k<n-1 .
  • A145678 (program): a(n) = 441*n^2 - 21.
  • A145693 (program): Numbers X such that there exists Y in N with X^2=21*Y^2+7.
  • A145729 (program): Partial sums of A052379.
  • A145730 (program): Partial sums of A108019.
  • A145737 (program): a(n) = square part of A145609(n).
  • A145756 (program): a(n) = ((2^prime(n+2)-2)/prime(n+2))/3, where n >= 1
  • A145766 (program): Partial sums of A020988.
  • A145801 (program): Number of islands of ones fitting in an n X n array with all ones connected only either two adjacent vertically or two adjacent horizontally.
  • A145806 (program): 1/4 of the number of islands of ones fitting in an n X n array symmetric under 90-degree rotation with all ones connected only either two adjacent vertically or two adjacent horizontally.
  • A145812 (program): Odd positive integers a(n) such that for every odd integer m > 1 there exists a unique representation of m as a sum of the form a(l) + 2a(s).
  • A145813 (program): 1/2 the number of islands of ones fitting in an n X n array symmetric about main diagonal with all ones connected only either three adjacent vertically or three adjacent horizontally.
  • A145816 (program): 1/4 of the number of islands of ones fitting in an n X n array symmetric under 90-degree rotation with all ones connected only either three adjacent vertically or three adjacent horizontally.
  • A145818 (program): Odd positive integers a(n) such that for every integer m == 3 (mod 4) there exists a unique representation of the form m = a(l) + 2*a(s), but there are no such representations for m == 1 (mod 4).
  • A145826 (program): Arises from critical number of finite Abelian groups.
  • A145849 (program): a(n) = A145812(2n-1).
  • A145850 (program): a(n) = A145818(2n-1).
  • A145885 (program): a(n) = (n-1)^2binomial(2n,n)/(2(n+1)).
  • A145886 (program): Number of excedances in all odd permutations of 1,2,…,n with no fixed points.
  • A145889 (program): Number of even entries that are followed by a smaller entry in all permutations of 1,2,…,n .
  • A145909 (program): First 6-fold decimation of A061039. First bisection of A144454.
  • A145910 (program): a(n) = (1 + 3n)(4 + 3*n)/2.
  • A145911 (program): a(n) = A145909(n)/8.
  • A145919 (program): A000332(n) = a(n)(3a(n) - 1)/2.
  • A145920 (program): List of numbers that are both pentagonal (A000326) and binomial coefficients C(n,4) (A000332).
  • A145923 (program): Second bisection of A061041: a(n) = A061041(2n+1) = (2n+1)*(2n+9).
  • A145924 (program): Last digit of A145923(n).
  • A145934 (program): Expansion of 1/(1-x(1-6x)).
  • A145976 (program): Expansion of 1/(1-x(1-7x)).
  • A145978 (program): Expansion of 1/(1-x(1-8x)).
  • A145979 (program): a(n) = (2*n + 4)/gcd(n,4).
  • A145980 (program): a(n) = 29 + 73n + 37n^2.
  • A145995 (program): a(n) = 8 - 12n + 5n^2.
  • A146005 (program): a(n) = n*Lucas(n).
  • A146029 (program): Numbers that can be written from base 2 to base 17 using only the digits 0 to 8 (conjectured to be complete).
  • A146076 (program): Sum of even divisors of n.
  • A146078 (program): Expansion of 1/(1-x(1-9x)).
  • A146079 (program): Period 9: repeat 2,4,8,5,4,5,8,4,2.
  • A146080 (program): Expansion of 1/(1-x(1-10x)).
  • A146081 (program): First differences of A145980.
  • A146082 (program): a(n) = A146081(n) mod 9.
  • A146083 (program): Expansion of 1/(1 - x(1 - 11x)).
  • A146084 (program): Expansion of 1/(1-x(1-12x)).
  • A146085 (program): Positive integers a(n) such that for every integer m == 1 (mod 3), m >= 4, there exists a unique representation of m as a sum of the form a(l) + 3*a(s).
  • A146086 (program): Number of n-digit numbers with each digit odd where the digits 1 and 3 occur an even number of times.
  • A146087 (program): a(n) = 3*A146085(n) - 1.
  • A146091 (program): a(n) = 3*A146085(n) - 2.
  • A146093 (program): Bell numbers (A000110) read mod 3.
  • A146135 (program): Positive integers a(n) such that for every integer m==1(mod 4),m>=5, there exists a unique representation of m as a sum of the form a(l)+4a(s).
  • A146160 (program): Period 4: repeat [1, 4, 1, 16].
  • A146161 (program): a(n) is the number of n X n matrices with entries in 1,2,3 such that all adjacent entries (in the same row or column) differ by 1 or -1.
  • A146179 (program): Digit sums of Cullen numbers.
  • A146205 (program): Number of paths of the simple random walk on condition that the median applied to the partial sums S_0=0, S_1,…,S_n, n odd (n=15 in this example), is equal to half-integer values k+1/2, -[n/2]-1<=k<=[n/2].
  • A146211 (program): Fermat quotient of the n-th prime with base 3.
  • A146298 (program): Difference between the cubes and 2tetrahedral numbers; A000578(n) - 2A000292(n).
  • A146301 (program): a(n) = (8n+3)(8*n+7).
  • A146302 (program): a(n) = (8n+5)(8*n+9).
  • A146306 (program): a(n) = numerator of (n-6)/(2n)
  • A146307 (program): a(n) = denominator of (n-6)/(2n) = denominator of (n+6)/(2n).
  • A146308 (program): a(n) is the smallest k such that the numerator of (k-6)/(2k) equals n.
  • A146312 (program): a(n) = -cos((2 n - 1) arcsin(sqrt(3)))^2 = -1 + cosh((2 n - 1) arcsinh(sqrt(2)))^2.
  • A146313 (program): a(n) = cosh( (2n - 1)arcsinh(sqrt(2)) )^2 = 1 - cos( (2n - 1)arcsin(sqrt(3)) )^2.
  • A146325 (program): Period 3: repeat [1, 4, 1].
  • A146501 (program): Period 6: 4,8,7,5,1,2.
  • A146507 (program): Numbers congruent to 1, 13 mod 42.
  • A146509 (program): Numbers that are congruent to 1, 5 mod 18.
  • A146510 (program): Numbers congruent to 1, 4 mod 15.
  • A146511 (program): Numbers congruent to 5, 17 modulo 66.
  • A146512 (program): Numbers congruent to 1, 3 mod 12.
  • A146523 (program): Binomial transform of A010685.
  • A146528 (program): a(0) = 4; for n >= 1, a(n) = 2^n + 4.
  • A146529 (program): A two level sequence: v(n)=2*(If[n == 0, 0, 2^(n - 1)] + 2); a(n)=If[n == 0, 6, (v[n] + v[n - 1] - 2)].
  • A146533 (program): Catalan transform of A135092.
  • A146534 (program): 4C(2n,n)-30^n.
  • A146535 (program): Numerator of (2*n-1)/3.
  • A146541 (program): Binomial transform of A010688.
  • A146559 (program): Expansion of (1-x)/(1 - 2x + 2x^2).
  • A146564 (program): a(n) is the number of solutions of the equation k*n/(k-n) = c. k,c integers.
  • A146761 (program): Period 6: repeat [0, 0, 6, 6, 3, 3].
  • A146762 (program): Numbers in A061039 ending with 0.
  • A146763 (program): Rank of terms ending in 0 in A061039.
  • A146880 (program): A symmetrical triangle sequence of coefficients : p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 2])x^m(1 + x^(n - 2*m)), m, 1, n - 1 ]].
  • A146882 (program): a(n) = 5*(4^(n+1)-1)/3.
  • A146883 (program): a(n) = 6 * Sum_ m=0..n 5^m.
  • A146884 (program): Sum of power terms sequence: a(n)=Sum[7*6^m, m, 0, n ].
  • A146885 (program): Sum of power terms sequence: a(n)=Sum[8*7^m, m, 0, n ].
  • A146951 (program): Rank of terms of A061047 ending in with 0.
  • A146963 (program): a(n) = ((3 + sqrt(7))^n + (3 - sqrt(7))^n)/2.
  • A146975 (program): First quintisection of A061043: A061043(5n).
  • A146977 (program): a(n) = Sum_ k=1..prime(n) binomial(2k,k).
  • A146983 (program): a(n) = A002531(n)*A002531(n+1).
  • A146994 (program): a(n) = (n+1)^2/4 + (floor((n+5)/6) - 1/4) * ((n+1) mod 2).
  • A147296 (program): n(9n+2).
  • A147513 (program): Numbers such that the n-th and (n+1)st terms are the successors of prime numbers and primes themselves and n+1 > n.
  • A147534 (program): a(n) is congruent to (1,1,2) mod 3.
  • A147536 (program): A counting vertex substitution vector matrix Markov 2x2 with characteristic polynomial:12 - 7 x + x=^2
  • A147537 (program): Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n digits 0.
  • A147538 (program): Numbers whose binary representation is the concatenation of n 1’s and 2n-1 digits 0.
  • A147560 (program): a(n) = 4*A046162(n+1).
  • A147562 (program): Number of “ON” cells at n-th stage in the “Ulam-Warburton” two-dimensional cellular automaton.
  • A147568 (program): a(n) = 2*A000695(n)+3.
  • A147582 (program): First differences of A147562.
  • A147585 (program): a(1) = 1; a(n) = (7n-9)a(n-1) for n > 1.
  • A147587 (program): a(n) = 14*n + 7.
  • A147589 (program): Concatenation of 2n-1 digits 1 and n-1 digits 0.
  • A147590 (program): Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n-1 digits 0.
  • A147594 (program): a(1)=1, a(n)= sigma_0 (n+a(n-1)).
  • A147595 (program): a(n) is the number whose binary representation is A138144(n).
  • A147596 (program): a(n) is the number whose binary representation is A138145(n).
  • A147597 (program): a(n) is the number whose binary representation is A138146(n).
  • A147600 (program): Expansion of 1/(1 - 3*x^2 + x^4).
  • A147601 (program): First differences of A132355.
  • A147609 (program): A000290(n-1) - A065893(n)
  • A147610 (program): a(n) = 3^(wt(n-1)-1), where wt() = A000120().
  • A147612 (program): If n is a Jacobsthal number then 1 else 0.
  • A147613 (program): Numbers that are not Jacobsthal numbers.
  • A147615 (program): 13, 13+4!, 13+4!+5!, 13+4!+5!+6!, …
  • A147623 (program): The 3rd Witt transform of A040000.
  • A147625 (program): Octo-factorial numbers(4).
  • A147626 (program): Octo-factorial numbers(5).
  • A147629 (program): 9-factorial numbers (4).
  • A147630 (program): a(1) = 1; for n>1, a(n) = Product_ k = 1..n-1 (9k - 3).
  • A147631 (program): 9-factorial numbers (6).
  • A147648 (program): Number of distinct even superperfect numbers dividing n.
  • A147651 (program): First trisection of A028560.
  • A147656 (program): The arithmetic mean of the n-th and (n+1)-st cubes, rounded down.
  • A147661 (program): a(n) = squarefree part of n^n.
  • A147666 (program): List of triples (0, 6n+1, 6n+5) for n = 0, 1, 2, …
  • A147674 (program): Period 9:repeat 81,27,9,27,27,9,27,81,9.
  • A147675 (program): Divide by 2, multiply by 4, repeat.
  • A147677 (program): Subtract 5, add 8, repeat.
  • A147678 (program): Double, add 0, double, add 1, double, add 2, double, add 3, etc.
  • A147685 (program): Squares and centered square numbers interleaved.
  • A147704 (program): Diagonal sums of Riordan array ((1-2x)/(1 - 3x + x^2),x(1-x)/(1 - 3x + x^2)).
  • A147722 (program): Row sums of Riordan array ((1-3x)/(1-4x+x^2), x(1-x)/(1-4x+x^2)).
  • A147748 (program): Row sums of Riordan array ((1-3x+x^2)/(1-4x+3x^2), x(1-2x)/(1-4x+3x^2)).
  • A147753 (program): Number of maximum-size subsets of 1,2,3,…,n whose geometric means are an integer.
  • A147754 (program): Terms of this sequence are equal to gcd between two polynomials P1(n)=(512n^4+1024n^3+712n^2+194n+15) and P2(n)=(120n^2+151n+47) which are used in the BBP formula
  • A147758 (program): Numbers whose binary representation is a palindrome formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1.
  • A147788 (program): a(n) = floor(2*(3/2)^n).
  • A147795 (program): If n=A000695(k_n)+2*A000695(l_n), then a(n) is the number of nonnegative integers m<n such that k_m differs from k_n and l_m differs from l_n.
  • A147806 (program): Partial sums of A147809(n) = tau(n^2 + 1)/2 - 1.
  • A147807 (program): Partial sums of A147810(n) = tau(n^2 + 1)/2.
  • A147809 (program): Half the number of proper divisors (> 1) of n^2 + 1, i.e., tau(n^2 + 1)/2 - 1.
  • A147810 (program): Half the number of divisors of n^2+1.
  • A147818 (program): Period 4: repeat [5, 9, 9, 5].
  • A147832 (program): Numbers congruent (0,2) mod 14.
  • A147837 (program): a(n)=7a(n-1)-5a(n-2), a(0)=1, a(1)=5 .
  • A147838 (program): a(n)=8a(n-1)-6a(n-2), a(0)=1, a(1)=6 .
  • A147839 (program): a(n)=9a(n-1)-7a(n-2), a(0)=1, a(1)=7 .
  • A147840 (program): a(n)=10a(n-1)-8a(n-2), a(0)=1, a(1)=8 .
  • A147841 (program): a(n) = 11a(n-1) - 9a(n-2) with a(0)=1, a(1)=9.
  • A147845 (program): Odd positive integers a(n) such that for every odd integer m>=7 there exists a unique representation of the form m=a(p)+2a(q)+4a(r)
  • A147846 (program): Triangular numbers n*(n+1)/2 with n or n+1 prime.
  • A147849 (program): Smallest triangular number > n-th prime
  • A147874 (program): a(n) = (5n-7)(n-1).
  • A147875 (program): Second heptagonal numbers: a(n) = n(5n+3)/2.
  • A147965 (program): a(n) is the difference between n and the n-th gap between primes.
  • A147967 (program): Product of n and n-th gap between primes.
  • A147973 (program): a(n) = -2n^2 + 12n - 14.
  • A147974 (program): a(n) = n^3-((n-1)^3+(n-2)^3+(n-3)^3).
  • A147991 (program): Sequence S such that 1 is in S and if x is in S, then 3x-1 and 3x+1 are in S.
  • A147992 (program): Sequence S such that 1 is in S and if x is in S, then 4x-1 and 4x+1 are in S.
  • A147997 (program): Number of nonnegative even integers <= Fibonacci(n).