List of integer sequences with links to LODA programs.

  • A050140 (program): a(n) = 2floor(nphi)-n, where phi = (1+sqrt(5))/2.
  • A050141 (program): a(n) = 2floor((n+1)phi) - 2floor(nphi) - 1 where phi = (1 + sqrt(5))/2 is the golden ratio.
  • A050185 (program): T(2n+7,n), array T as in A051168; a count of Lyndon words.
  • A050187 (program): a(n) = n * floor((n-1)/2).
  • A050188 (program): T(n,3), array T as in A050186; a count of aperiodic binary words.
  • A050189 (program): T(n,4), array T as in A050186; a count of aperiodic binary words.
  • A050190 (program): T(n,5), array T as in A050186; a count of aperiodic binary words.
  • A050206 (program): Smallest denominator in unit fraction representation of triangle of numbers 1/2, 1/3, 2/3, 1/4, 2/4, … as computed with greedy algorithm.
  • A050228 (program): a(n) is the number of subsequences s(k) of 1,2,3,…n such that s(k+1)-s(k) is 1 or 3.
  • A050250 (program): Number of nonzero palindromes less than 10^n.
  • A050271 (program): Numbers n such that n = floor(sqrt(n)*ceiling(sqrt(n))).
  • A050292 (program): a(2n) = 2n - a(n), a(2n+1) = 2n + 1 - a(n) (for n >= 0).
  • A050294 (program): Maximum cardinality of a 3-fold-free subset of 1, 2, …, n .
  • A050297 (program): Number of scalars which can be constructed from the Riemann tensor and metric tensor in n dimensions.
  • A050399 (program): Least k such that n = A009195(k) (= gcd(phi(k), k)).
  • A050403 (program): Partial sums of A051877.
  • A050404 (program): Partial sums of A051878.
  • A050405 (program): Partial sums of A051879.
  • A050406 (program): Partial sums of A051880.
  • A050407 (program): a(n) = n(n^2 - 6n + 11)/6.
  • A050408 (program): a(n) = (117n^2 - 99n + 2)/2.
  • A050409 (program): Truncated square pyramid numbers: a(n) = Sum_ k = n..2*n k^2.
  • A050410 (program): Truncated square pyramid numbers: a(n) = Sum_ k = n..2*n-1 k^2.
  • A050435 (program): a(n) = composite(composite(n)), where composite = A002808, composite numbers.
  • A050436 (program): Third-order composites.
  • A050438 (program): Fourth-order composites.
  • A050439 (program): Fifth-order composites.
  • A050440 (program): Sixth-order composites.
  • A050441 (program): Partial sums of A051865.
  • A050442 (program): Octahedral torus number: a(n) = n^2+2sum(k^2,k=1..n-1)-2(floor((n+1)/2)^2+2*sum(k^2,k=1..floor((n+1)/2)-1))+(1-(-1)^n)/2.
  • A050449 (program): a(n) = Sum_ d n, d=1 mod 4 d.
  • A050450 (program): Sum_ d n, d=1 mod 4 d^2.
  • A050452 (program): a(n) = Sum_ d n, d=3 mod 4 d.
  • A050457 (program): a(n) = Sum_ d divides n, d==1 mod 4 d - Sum_ d divides n, d==3 mod 4 d.
  • A050464 (program): a(n) = Sum_ d divides n, n/d=3 mod 4 d.
  • A050482 (program): Sum of remainders when n-th prime is divided by all preceding integers.
  • A050483 (program): Partial sums of A051947.
  • A050484 (program): Partial sums of A051946.
  • A050486 (program): a(n) = binomial(n+6,6)*(2n+7)/7.
  • A050487 (program): Geometric Connell sequence: start with 1; then next two numbers == 2 mod 3; next four == 3 mod 3; next eight == 1 mod 3; etc.
  • A050488 (program): a(n) = 3(2^n-1) - 2n.
  • A050492 (program): Thickened cube numbers: n(n^2+(n-1)^2)+(n-1)2n(n-1).
  • A050493 (program): a(n) = sum of binary digits of n-th triangular number.
  • A050494 (program): Partial sums of A051923.
  • A050506 (program): Nearest integer to log(Fibonacci(n)).
  • A050508 (program): Golden rectangle numbers: n * A007067(n).
  • A050509 (program): House numbers (version 2): a(n) = (n+1)^3 + (n+1)*Sum_ i=0..n i.
  • A050514 (program): Cards left over after dealing evenly to n people.
  • A050518 (program): An arithmetic progression of at least 6 terms having the same value of phi starts at these numbers.
  • A050519 (program): Increments of arithmetic progression of at least 6 terms having the same value of phi in A050518.
  • A050533 (program): Thickened pyramidal numbers: a(n) = sum(4i(i-1)+1, i=1..n) + 2(n+1)n.
  • A050534 (program): Tritriangular numbers: a(n) = binomial(binomial(n,2),2) = n(n+1)(n-1)*(n-2)/8.
  • A050603 (program): A001511 with every term repeated.
  • A050605 (program): Column/row 2 of A050602: a(n) = add3c(n,2).
  • A050621 (program): Smallest n-digit number divisible by 2^n.
  • A050624 (program): Let b(n) = A050623(n) = smallest n-digit number divisible by 3^n; sequence gives b(n)/3^n.
  • A050683 (program): Number of nonzero palindromes of length n.
  • A050685 (program): Number of nonzero palindromes < 10^n and containing at least one digit ‘0’.
  • A050720 (program): Number of nonzero palindromes of length n containing the digit ‘0’.
  • A050763 (program): Numbers k such that the decimal expansion of k^k contains no pair of consecutive equal digits (probably finite).
  • A050815 (program): Number of positive Fibonacci numbers with n decimal digits.
  • A050873 (program): Triangular array T read by rows: T(n,k) = gcd(n,k).
  • A050914 (program): a(n) = n*3^n + 1.
  • A050915 (program): a(n) = n*4^n + 1.
  • A050916 (program): a(n) = n*5^n + 1.
  • A050917 (program): a(n) = n*6^n + 1.
  • A050919 (program): a(n) = n*7^n + 1.
  • A050921 (program): Smallest prime of form n*2^m+1, m >= 0, or 0 if no prime exists.
  • A050982 (program): 5-idempotent numbers.
  • A050988 (program): 6-idempotent numbers.
  • A050989 (program): 7-idempotent numbers.
  • A050997 (program): Fifth powers of primes.
  • A050999 (program): Sum of squares of odd divisors of n.
  • A051000 (program): Sum of cubes of odd divisors of n.
  • A051001 (program): Sum of 4th powers of odd divisors of n.
  • A051002 (program): Sum of 5th powers of odd divisors of n.
  • A051027 (program): a(n) = sigma(sigma(n)) = sum of the divisors of the sum of the divisors of n.
  • A051032 (program): Summatory Rudin-Shapiro sequence for 2^(n-1).
  • A051033 (program): a(n) = binomial(n, floor(n/3)).
  • A051036 (program): a(n) = binomial(n, floor(n/4)).
  • A051039 (program): 4-Stohr sequence.
  • A051040 (program): 5-Stohr sequence.
  • A051049 (program): Number of moves needed to solve an (n+1)-ring baguenaudier if two simultaneous moves of the two end rings are counted as one.
  • A051052 (program): a(n) = binomial(n, floor(n/5)).
  • A051053 (program): a(n) = binomial(n, floor(n/6)).
  • A051062 (program): a(n) = 16*n + 8.
  • A051063 (program): 27n+9 or 27n+18.
  • A051064 (program): 3^a(n) exactly divides 3n. Or, 3-adic valuation of 3n.
  • A051065 (program): a(n) = A004128(n) mod 2.
  • A051066 (program): Partial sums of A051065.
  • A051067 (program): A051066 read mod 2.
  • A051068 (program): Partial sums of A014578.
  • A051069 (program): A051068 read mod 2.
  • A051102 (program): Floor of exp(n-th prime).
  • A051109 (program): Hyperinflation sequence for banknotes.
  • A051119 (program): n/p^k, where p = largest prime dividing n and p^k = highest power of p dividing n.
  • A051123 (program): a(n) = Fibonacci(n) OR Fibonacci(n+1).
  • A051124 (program): a(n) = Fibonacci(n) XOR Fibonacci(n+1).
  • A051125 (program): Table T(n,k) = max n,k read by antidiagonals (n >= 1, k >= 1).
  • A051126 (program): Table T(n,k) = n mod k read by antidiagonals (n >= 1, k >= 1).
  • A051127 (program): Table T(n,k) = k mod n read by antidiagonals (n >= 1, k >= 1).
  • A051133 (program): a(n) = binomial(2n,n)n(2n+1)/2.
  • A051162 (program): Triangle T(n,k) = n+k, n >= 0, 0 <= k <= n.
  • A051170 (program): T(n,5), array T as in A051168; a count of Lyndon words; aperiodic necklaces with 5 black beads and n-5 white beads.
  • A051172 (program): T(n,7), array T as in A051168; a count of Lyndon words; aperiodic necklaces with 7 black beads and n-7 white beads.
  • A051176 (program): If n mod 3 = 0 then n/3 else n.
  • A051188 (program): Sept-factorial numbers.
  • A051189 (program): Octo-factorial numbers.
  • A051190 (program): a(n) = Product_ k=1..n-1 gcd(k,n).
  • A051192 (program): T(n,7), array T as in A050186; a count of aperiodic binary words.
  • A051194 (program): Triangular array T read by rows: T(n,k) = number of positive integers that divide both n and k.
  • A051201 (program): Sum of elements of the set [ n/k ] : 1 <= k <= n .
  • A051232 (program): 9-factorial numbers.
  • A051262 (program): 10-factorial numbers.
  • A051263 (program): Expansion of 1/((1-x)(1-x^3)^2(1-x^5)).
  • A051274 (program): Expansion of (1+x^4)/((1-x^2)*(1-x^3)).
  • A051275 (program): Expansion of (1+x^2)/((1-x^2)*(1-x^3)).
  • A051329 (program): A generalized Thue-Morse sequence.
  • A051336 (program): Number of arithmetic progressions in 1,2,3,…,n , including trivial arithmetic progressions of lengths 1 and 2.
  • A051340 (program): A simple 2-dimensional array, read by antidiagonals: T[i,j] = 1 for j>0, T[i,0] = i+1; i,j = 0,1,2,3,…
  • A051349 (program): Sum of first n nonprimes.
  • A051350 (program): Sum of digit-sums of first n nonprimes.
  • A051351 (program): a(n) = a(n-1) + sum of digits of n-th prime.
  • A051398 (program): a(n) = -(n-3)a(n-1)+2(n-2)^2.
  • A051403 (program): a(n) = (n+2)*(a(n-1)-a(n-2)).
  • A051405 (program): a(n) = (3^n+1)*(3^(n+1)+1)/4.
  • A051406 (program): a(n) = (3^n+1) * (3^(n+1)+1) / 8.
  • A051407 (program): a(n) = 3^n*(3^(n+1)+1)/2.
  • A051417 (program): Quotients of consecutive values of lcm 1, 3, 5 …,2n-1 or A025547(n+1)/A025547(n).
  • A051431 (program): a(n) = (n+10)!/10!.
  • A051437 (program): Number of undirected walks of length n+1 on an oriented triangle, visiting n+2 vertices, with n “corners”; the symmetry group is C3. Walks are not self-avoiding.
  • A051442 (program): a(n) = n^(n+1)+(n+1)^n.
  • A051443 (program): a(n) = n^(n+1)*(n+1)^n.
  • A051462 (program): Molien series for group G_ 1,2 ^ 8 of order 1536.
  • A051489 (program): a(n) = n^(n+2) + (n+2)^n.
  • A051490 (program): a(n) = n^(n+2)*(n+2)^n.
  • A051494 (program): Expansion of (1 - x + x^2 + x^3)/(1 - x^2)^3.
  • A051500 (program): a(n) = (3^n+1)^2/4.
  • A051503 (program): a(n) = min n, floor(100/n) .
  • A051515 (program): (Terms in A014738)/4.
  • A051543 (program): Quotients of consecutive values of lcm of first n triangular numbers (A000217).
  • A051577 (program): a(n) = (2*n + 3)!!/3 = A001147(n+2)/3.
  • A051578 (program): a(n) = (2*n+4)!!/4!!, related to A000165 (even double factorials).
  • A051579 (program): a(n) = (2*n+5)!!/5!!, related to A001147 (odd double factorials).
  • A051580 (program): a(n) = (2*n+6)!!/6!!, related to A000165 (even double factorials).
  • A051581 (program): a(n) = (2*n+7)!!/7!!, related to A001147 (odd double factorials).
  • A051582 (program): a(n) = (2*n+8)!!/8!!, related to A000165 (even double factorials).
  • A051583 (program): a(n) = (2*n+9)!!/9!!, related to A001147 (odd double factorials).
  • A051596 (program): Numerical values or Gematriahs of Hebrew letters aleph, bet, …, tav .
  • A051604 (program): a(n) = (3*n+4)!!!/4!!!
  • A051605 (program): a(n) = (3*n+5)!!!/5!!!.
  • A051606 (program): a(n) = (3n+6)!!!/6!!!, related to A032031 ((3n)!!! triple factorials).
  • A051607 (program): a(n) = (3n+7)!!!/7!!!, related to A007559(n+1) ((3n+1)!!! triple factorials).
  • A051608 (program): a(n) = (3n+8)!!!/8!!!, related to A008544(n+1) ((3n+2)!!! triple factorials).
  • A051609 (program): a(n) = (3n+9)!!!/9!!!, related to A032031 ((3n)!!! triple factorials).
  • A051612 (program): a(n) = sigma(n) - phi(n).
  • A051617 (program): a(n) = (4n+5)(!^4)/5(!^4), related to A007696(n+1) ((4n+1)(!^4) quartic, or 4-factorials).
  • A051618 (program): a(n) = (4*n+6)(!^4)/6(!^4).
  • A051619 (program): a(n) = (4n+7)(!^4)/7(!^4), related to A034176(n+1) ((4n+3)(!^4) quartic, or 4-factorials).
  • A051620 (program): a(n) = (4n+8)(!^4)/8(!^4), related to A034177(n+1) ((4n+4)(!^4) quartic, or 4-factorials).
  • A051621 (program): a(n) = (4n+9)(!^4)/9(!^4), related to A007696(n+1) ((4n+1)(!^4) quartic, or 4-factorials).
  • A051622 (program): a(n) = (4n+10)(!^4)/10(!^4), related to A000407 ((4n+2)(!^4) quartic, or 4-factorials).
  • A051624 (program): 12-gonal (or dodecagonal) numbers: a(n) = n(5n-4).
  • A051628 (program): Number of digits in decimal expansion of 1/n before the periodic part begins.
  • A051633 (program): a(n) = 5*2^n - 2.
  • A051662 (program): House numbers: a(n) = (n+1)^3 + Sum_ i=1..n i^2.
  • A051667 (program): a(n) = 62^n - 4n - 6.
  • A051669 (program): 112^n - 4n - 10.
  • A051673 (program): Cubic star numbers: a(n) = n^3 + 4*Sum_ i=0..n-1 i^2.
  • A051677 (program): Tetrahedron-tree numbers: a(n)=sum(b(m),m=1..n), b(m)=1, 1,3, 1,3,6, 1,3,6,10,…, 1,2,…,i*(i+1)2.
  • A051678 (program): Square-pyramid-tree numbers: a(n) = sum(b(m),m=1..n), b(m) = 1^2, 1^2,2^2, 1^2,2^2,3^2,.. = (A002260)^2.
  • A051679 (program): Total number of even entries in first n rows of Pascal’s triangle (the zeroth and first rows being 1; 1,1).
  • A051682 (program): 11-gonal (or hendecagonal) numbers: a(n) = n(9n-7)/2.
  • A051683 (program): Triangle read by rows: T(n,k) = n!*k.
  • A051684 (program): Auxiliary sequence for calculation of number of even permutations of degree n and order exactly 2.
  • A051687 (program): a(n) = (5n+6)(!^5)/6, related to A008548 ((5n+1)(!^5) quintic, or 5-factorials).
  • A051688 (program): a(n) = (5n+7)(!^5)/7(!^5), related to A034323 ((5n+2)(!^5) quintic, or 5-factorials).
  • A051689 (program): a(n) = (5n+8)(!^5)/8(!^5), related to A034300 ((5n+3)(!^5) quintic, or 5-factorials).
  • A051690 (program): a(n) = (5n+9)(!^5)/9(!^5), related to A034301 ((5n+2)(!^5) quintic, or 5-factorials).
  • A051691 (program): a(n) = (5n+10)(!^5)/10(!^5), related to A052562 ((5n)(!^5) quintic, or 5-factorials).
  • A051696 (program): Greatest common divisor of n! and n^n.
  • A051711 (program): a(0) = 1; for n > 0, a(n) = n!*4^n/2.
  • A051712 (program): Numerator of b(n)-b(n+1), where b(n) = n/((n+1)(n+2)) = A026741/A045896.
  • A051724 (program): Numerator of n/12.
  • A051725 (program): Denominator of n/12.
  • A051731 (program): Triangle read by rows: T(n,k) = 1 if k divides n, T(n,k) = 0 otherwise (for n >= 1 and 1 <= k <= n).
  • A051740 (program): Partial sums of A007584.
  • A051743 (program): a(n) = (1/24)n(n + 5)*(n^2 + n + 6).
  • A051744 (program): a(n) = n(n+1)(n^2+5*n+18)/24.
  • A051745 (program): a(n) = n(n^4 + 10n^3 + 35n^2 + 50n + 144)/120.
  • A051746 (program): a(n) = n(n+7)(n+1)(n^2+2n+12)/120.
  • A051747 (program): a(n) = n(n+1)(n+2)(n^2+7n+32)/120.
  • A051754 (program): Consider problem of placing N queens on an n X n board so that each queen attacks precisely 1 other. Sequence gives maximal number of queens.
  • A051755 (program): Consider problem of placing N queens on an n X n board so that each queen attacks precisely 2 others. Sequence gives maximal number of queens.
  • A051789 (program): C(n)*(C(n)-1)/2, where C(n) are the Catalan numbers (A000108).
  • A051790 (program): a(n) = C(n)(C(n)-1)(C(n)-2)/6, where C(n) are the Catalan numbers (A000108).
  • A051797 (program): Partial sums of A007585.
  • A051798 (program): a(n) = (n+1)(n+2)(n+3)*(9n+4)/24.
  • A051799 (program): Partial sums of A007587.
  • A051801 (program): Product of the nonzero digits of n.
  • A051830 (program): Fibonacci(Pn+1) mod Pn, where Pn is the n-th prime.
  • A051834 (program): Fibonacci(Pn-1) mod Pn, where Pn is the n-th prime.
  • A051836 (program): a(n) = n(n+1)(n+2)(n+3)(3*n+2)/120.
  • A051837 (program): Rank of Demjanenko matrix mod n-th prime.
  • A051843 (program): Partial sums of A002419.
  • A051846 (program): Digits 1..n in strict descending order n..1 interpreted in base n+1.
  • A051865 (program): 13-gonal (or tridecagonal) numbers: a(n) = n(11n - 9)/2.
  • A051866 (program): 14-gonal (or tetradecagonal) numbers: a(n) = n(6n-5).
  • A051867 (program): 15-gonal (or pentadecagonal) numbers: n(13n-11)/2.
  • A051868 (program): 16-gonal (or hexadecagonal) numbers: a(n) = n(7n-6).
  • A051869 (program): 17-gonal (or heptadecagonal) numbers: n(15n-13)/2.
  • A051870 (program): 18-gonal (or octadecagonal) numbers: a(n) = n(8n-7).
  • A051871 (program): 19-gonal (or enneadecagonal) numbers: n(17n-15)/2.
  • A051872 (program): 20-gonal (or icosagonal) numbers: a(n) = n(9n-8).
  • A051873 (program): 21-gonal numbers: a(n) = n*(19n - 17)/2.
  • A051874 (program): 22-gonal numbers: a(n) = n(10n-9).
  • A051875 (program): 23-gonal numbers: a(n) = n(21n-19)/2.
  • A051876 (program): 24-gonal numbers: a(n) = n(11n-10).
  • A051877 (program): Partial sums of A051740.
  • A051878 (program): Partial sums of A051797.
  • A051879 (program): Partial sums of A051798.
  • A051880 (program): a(n) = binomial(n+4,4)(2n+1).
  • A051885 (program): Smallest number whose sum of digits is n.
  • A051890 (program): a(n) = 2*(n^2 - n + 1).
  • A051893 (program): a(n) = Sum_ i=1..n-1 i^2*a(i), a(1) = 1.
  • A051895 (program): Partial sums of second pentagonal numbers with even index (A049453).
  • A051903 (program): Maximal exponent in prime factorization of n.
  • A051920 (program): a(n) = binomial(n, floor(n/2)) + 1.
  • A051923 (program): Partial sums of A051836.
  • A051924 (program): a(n) = binomial(2n,n) - binomial(2n-2,n-1); or (3n-2)*C(n-1), where C = Catalan numbers (A000108).
  • A051925 (program): a(n) = n(2n+5)*(n-1)/6.
  • A051927 (program): Number of independent vertex sets in the n-prism graph Y_n = K_2 X C_n (n > 2).
  • A051936 (program): Truncated triangular numbers: a(n) = n*(n+1)/2 - 9.
  • A051937 (program): Truncated triangular pyramid numbers: a(n) = Sum_ k=4..n k*(k+1)/2-9.
  • A051938 (program): Truncated triangular numbers: a(n) = n*(n+1)/2 - 18.
  • A051939 (program): Truncated triangular pyramid numbers: a(n) = (n-5)(n^2+8n-66)/6.
  • A051940 (program): Truncated triangular numbers: n(n+1)/2 - 3t*(t+1)/2 with t=4.
  • A051941 (program): Truncated triangular pyramid numbers: a(n) = (n-7)(n^2 + 10n - 108)/6, n >= 8.
  • A051942 (program): a(n) = n*(n+1)/2 - 45.
  • A051943 (program): Truncated triangular pyramid numbers: a(n) = Sum_ k=9..n (k*(k+1)/2 - 45).
  • A051946 (program): Expansion of g.f.: (1+4*x)/(1-x)^7.
  • A051947 (program): Partial sums of A034263.
  • A051950 (program): Differences between values of tau(n) (A000005): a(n) = tau(n)-tau(n-1).
  • A051953 (program): Cototient(n) := n - phi(n).
  • A051958 (program): a(n) = 2 a(n-1) + 24 a(n-2), a(0)=0, a(1)=1.
  • A051959 (program): Expansion of (1+6x)/( (1-2x-x^2)(1-x)^2).
  • A051960 (program): a(n) = C(n)*(3n+2) where C(n) = Catalan numbers = A000108.
  • A052008 (program): a(n) = ‘n with digits sorted in ascending order’ + ‘n with digits sorted in descending order’.
  • A052036 (program): Smallest number that must be added to n to make or keep n palindromic.
  • A052038 (program): First nonzero digit in expansion of 1/n.
  • A052126 (program): a(1) = 1; for n>1, a(n)=n/(largest prime dividing n).
  • A052144 (program): A000172(n)^2.
  • A052145 (program): a(n) = (2n-1)*(2n-1)!/n.
  • A052146 (program): a(n) = floor((sqrt(1+8*n)-3)/2).
  • A052147 (program): a(n) = prime(n) + 2.
  • A052149 (program): Nonsquare rectangles on an n X n board.
  • A052150 (program): Partial sums of A000340, second partial sums of A003462.
  • A052153 (program): Rhombi (in 3 different orientations) in a rhombus with 60-degree acute angles.
  • A052156 (program): Number of compositions of n into 2*j-1 kinds of j’s for all j>=1.
  • A052161 (program): Partial sums of A014825, second partial sums of A002450.
  • A052181 (program): Partial sums of A050483.
  • A052182 (program): Determinant of n X n matrix whose rows are cyclic permutations of 1..n.
  • A052183 (program): A second-order recursive sequence.
  • A052200 (program): Number of n-state, 2-symbol, d+ in LEFT, RIGHT , 5-tuple (q, s, q+, s+, d+) (halting or not) Turing machines.
  • A052203 (program): a(n) = (4n+1)*binomial(4n,n)/(3n+1).
  • A052206 (program): Partial sums of A050405.
  • A052209 (program): b(n)b(2n), b(n) = A001353(n+1).
  • A052225 (program): (n+1)!*(n+3)-3.
  • A052226 (program): Partial sums of A050404.
  • A052244 (program): Partial sums of A014827.
  • A052245 (program): Expansion of 10x / ((1 - x) * (1 - 10x)^2) in powers of x.
  • A052254 (program): Partial sums of A050406.
  • A052255 (program): Partial sums of A050484.
  • A052262 (program): Partial sums of A014824.
  • A052268 (program): First differences of 10^n (A011557).
  • A052288 (program): First differences of the average of two consecutive primes (A024675).
  • A052343 (program): Number of ways to write n as the unordered sum of two triangular numbers (zero allowed).
  • A052369 (program): Largest prime factor of n, where n runs through composite numbers.
  • A052379 (program): Number of integers from 1 to 10^(n+1)-1 that lack 0 and 1 as a digit.
  • A052380 (program): a(n) = D is the smallest distance (D) between 2 non-overlapping prime twins differing by d=2n; these twins are [p,p+d] or [p+D,p+D+d] and p > 3.
  • A052386 (program): Number of integers from 1 to 10^n-1 that lack 0 as a digit.
  • A052409 (program): a(n) = largest integer power m for which a representation of the form n = k^m exists (for some k).
  • A052410 (program): Write n = m^k with m, k integers, k >= 1, then a(n) is the smallest possible choice for m.
  • A052423 (program): Highest common factor of nonzero digits of n.
  • A052449 (program): a(n) = 1 + Product_ k=1..n Fibonacci(k).
  • A052453 (program): Number of nonisomorphic (3,n) cage graphs.
  • A052459 (program): a(n) = n(2n^2 + 1)*(n^2 + 1)/6.
  • A052460 (program): 3-magic series constant.
  • A052462 (program): a(n) is the minimal positive integral solution k to 24*k == 1 (mod 5^n).
  • A052463 (program): a(n) is the smallest nonnegative solution k to 24k == 1 (mod 7^(2n-2)).
  • A052468 (program): Numerators in the Taylor series for arccosh(x) - log(2*x).
  • A052472 (program): Number of independent components for a Weyl tensor in n dimensions.
  • A052473 (program): a(n) = binomial(2*n-5,n-2) + 2.
  • A052481 (program): a(n) = 2^n*(binomial(n,2) + 1).
  • A052482 (program): a(n) = 2^(n-2)*binomial(n+1,2).
  • A052502 (program): Number of permutations sigma of [3n] without fixed points such that sigma^3 = Id.
  • A052510 (program): Number of labeled planar binary trees with 2n-1 elements (external nodes or internal nodes).
  • A052511 (program): Prime(n) - 1 - A006218(n).
  • A052515 (program): Number of ordered pairs of complementary subsets of an n-set with both subsets of cardinality at least 2.
  • A052516 (program): Number of pairs of sets of cardinality at least 3.
  • A052520 (program): Number of pairs of sequences of cardinality at least 2.
  • A052521 (program): Number of pairs of sequences of cardinality at least 3.
  • A052528 (program): Expansion of (1 - x)/(1 - 2x - 2x^2 + 2*x^3).
  • A052529 (program): Expansion of (1-x)^3/(1 - 4x + 3x^2 - x^3).
  • A052530 (program): a(n) = 4*a(n-1) - a(n-2), with a(0) = 0, a(1) = 2.
  • A052531 (program): If n is even then 2^n+1 otherwise 2^n.
  • A052533 (program): Expansion of (1-x)/(1-x-3*x^2).
  • A052534 (program): Expansion of (1-x)(1+x)/(1-2x-x^2+x^3).
  • A052535 (program): Expansion of (1-x)(1+x)/(1-x-2x^2+x^4).
  • A052536 (program): Number of compositions of n when parts 1 and 2 are of two kinds.
  • A052539 (program): a(n) = 4^n + 1.
  • A052542 (program): a(n) = 2*a(n-1) + a(n-2), with a(0) = 1, a(1) = 2, a(2) = 4.
  • A052544 (program): Expansion of (1-x)^2/(1 - 4x + 3x^2 - x^3).
  • A052545 (program): Expansion of (1-x)^2/(1-3*x+x^3).
  • A052547 (program): Expansion of (1-x)/(1-x-2*x^2+x^3).
  • A052548 (program): a(n) = 2^n + 2.
  • A052549 (program): a(n) = 5*2^(n-1) - 1, n>0, with a(0)=1.
  • A052551 (program): Expansion of 1/((1 - x)(1 - 2x^2)).
  • A052552 (program): a(2n+1) = 1, a(2n) = 2a(2n-2) - 1.
  • A052553 (program): Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by antidiagonals.
  • A052558 (program): a(n) = n! ((-1)^n + 2n + 3)/4.
  • A052560 (program): a(n) = 3*n!.
  • A052561 (program): a(n) = (1 + 2^n) * n!.
  • A052562 (program): a(n) = 5^n * n!.
  • A052563 (program): E.g.f.: (1-x)/(1-3*x).
  • A052564 (program): Expansion of e.g.f. x(1-x)/(1-2x).
  • A052565 (program): E.g.f. (1+x^3-x^4)/(1-x).
  • A052566 (program): E.g.f.: (2 + x)/(1 - x^2).
  • A052567 (program): E.g.f.: (1-x)^2/(1-3*x+x^2).
  • A052568 (program): E.g.f.: (1-x)/(1-3*x+x^2).
  • A052569 (program): E.g.f. 1/((1-x)(1-x^3)).
  • A052570 (program): E.g.f.: x/(1-4*x).
  • A052571 (program): E.g.f. x^3/(1-x)^2.
  • A052572 (program): E.g.f. (1+2x-2x^2)/(1-x)^2.
  • A052573 (program): (1+3^n)*n!.
  • A052574 (program): E.g.f. (1-2x)/(1-3x+x^2).
  • A052576 (program): E.g.f. (1+x^2-2x^3)/(1-2x).
  • A052578 (program): a(0) = 0, a(n) = 4*n! for n > 0.
  • A052582 (program): a(n) = 2nn!.
  • A052584 (program): E.g.f. (2-4x+x^2)/((1-x)(1-2x)).
  • A052587 (program): E.g.f. x^2(1-x)/(1-2x).
  • A052589 (program): a(n) = (2^n - 1)*n!.
  • A052590 (program): E.g.f. (1-x)/(1-4x+2x^2).
  • A052591 (program): E.g.f. x/((1-x)(1-x^2)).
  • A052592 (program): E.g.f. (1-x)/(1-4x).
  • A052596 (program): E.g.f. (1+x^4-x^5)/(1-x).
  • A052609 (program): a(n) = (2n - 2)n!.
  • A052612 (program): E.g.f. x*(2+x)/(1-x^2).
  • A052614 (program): E.g.f. 1/((1-x)(1-x^4)).
  • A052616 (program): E.g.f. (3+2x)/(1-x^2).
  • A052618 (program): Expansion of e.g.f. 1/((1-x)^2*(1-x^2)).
  • A052619 (program): E.g.f. 3x^3/(1-x).
  • A052624 (program): E.g.f. (1+x^2-2x^3+x^4)/(1-x)^2.
  • A052626 (program): (2^n+2)*n!.
  • A052628 (program): E.g.f. (2+x^3-x^4)/(1-x).
  • A052633 (program): E.g.f. x^2*(1+x-x^2)/(1-x)^2.
  • A052637 (program): E.g.f. 3x(1+x-x^2)/(1-x).
  • A052642 (program): E.g.f. x^2*(2+x-x^2)/(1-x).
  • A052644 (program): E.g.f. (1+3x-3x^2)/(1-x)^2.
  • A052645 (program): E.g.f. 2x^2(1+x-x^2)/(1-x).
  • A052648 (program): Expansion of e.g.f. 5*x/(1-x).
  • A052649 (program): E.g.f. (2+x-x^2)/(1-x)^2.
  • A052652 (program): E.g.f. x^4/(1-2x).
  • A052655 (program): a(2) = 6, otherwise a(n) = n*n!.
  • A052656 (program): E.g.f. x*(1+2x-4x^2)/(1-2x).
  • A052657 (program): E.g.f. x^2/((1-x)^2*(1+x)).
  • A052659 (program): E.g.f. (1-2x)(1-x)/(1-4x+2x^2).
  • A052665 (program): a(0)=0, for n >= 1, a(n) = ((2^(n-1)-1)*n!.
  • A052670 (program): E.g.f. x^2/(1-4x).
  • A052671 (program): E.g.f. x^3*(1-x)/(1-2x).
  • A052673 (program): a(n) = 3nn!.
  • A052675 (program): E.g.f. (1-x)/(1-5x).
  • A052676 (program): E.g.f. 3x/(1 - 2x).
  • A052677 (program): E.g.f. (1-x)/(1-4x+x^2).
  • A052678 (program): E.g.f. x^3/(1-3x).
  • A052680 (program): E.g.f. (1-2x)/(1-4x+2x^2).
  • A052683 (program): E.g.f. 2x^4/(1-x).
  • A052686 (program): E.g.f. x^2*(1+3x-3x^2)/(1-x).
  • A052687 (program): E.g.f. (1+x-x^3)/((1-x)(1-x^2)).
  • A052688 (program): E.g.f. x/((1-x)(1-x^3)).
  • A052689 (program): E.g.f. (1+x-x^2)/((1-x)(1-x^2)).
  • A052695 (program): E.g.f. (2-5x)/((1-4x)(1-x)).
  • A052698 (program): E.g.f. x/((1-x)(1-3x)).
  • A052700 (program): E.g.f. x*(1-x)/(1-3x).
  • A052701 (program): a(0) = 0; for n >= 1, a(n) = 2^(n-1)*C(n-1), where C(n) = A000108(n) Catalan numbers, n>0.
  • A052712 (program): E.g.f. (1+4x-sqrt(1-8x))/8.
  • A052713 (program): E.g.f. (1-sqrt(1-8*x))/2.
  • A052714 (program): a(n) = 2^(n-1) * n! * Catalan(n-1) for n > 0 with a(0) = 0.
  • A052718 (program): E.g.f. 1 - x - sqrt(1-4*x).
  • A052719 (program): E.g.f. (1-2xsqrt(1-4x)) *(1-sqrt(1-4x))/4.
  • A052746 (program): a(0) = 0; a(n) = (2*n)^(n-1), n > 0.
  • A052747 (program): a(0) = a(1) = a(2) = 0; a(n) = n!/(n-2) for n > 2.
  • A052749 (program): 2n*S2(n-1,2).
  • A052750 (program): a(n) = (2*n + 1)^(n - 1).
  • A052752 (program): a(n) = (3*n+1)^(n-1).
  • A052756 (program): E.g.f.: (-1/3)LambertW(-3x).
  • A052759 (program): E.g.f.: x^3*log(1/(1-x)).
  • A052760 (program): Expansion of e.g.f.: x^2*(exp(x)-1)^2.
  • A052762 (program): Products of 4 consecutive integers: a(n) = n(n-1)(n-2)*(n-3).
  • A052764 (program): E.g.f.: -1/4LambertW(-4x).
  • A052768 (program): A simple grammar.
  • A052771 (program): E.g.f.: x^3*exp(x)^2.
  • A052774 (program): a(n) = (4*n+1)^(n-1).
  • A052780 (program): Expansion of e.g.f. x^2exp(4x).
  • A052782 (program): a(n) = (5*n+1)^(n-1).
  • A052787 (program): A simple grammar. Product of 5 consecutive integers.
  • A052789 (program): Expansion of e.g.f. -(1/5)LambertW(-5x).
  • A052791 (program): 3^(n-3)n(n-1)*(n-2).
  • A052794 (program): E.g.f.: -x^5*log(1-x).
  • A052796 (program): E.g.f.: x^4*exp(x)^2.
  • A052800 (program): E.g.f.: x^5*exp(x)-x^5.
  • A052849 (program): a(0) = 0; a(n+1) = 2*n! (n >= 0).
  • A052867 (program): E.g.f.: log(-(-1+x)^2/(-1+2*x)).
  • A052898 (program): 2*n! + 1.
  • A052899 (program): Expansion of g.f.: ( 1-2x ) / ((x-1)(4x^2+2x-1)).
  • A052901 (program): Periodic with period 3: a(3n)=3, a(3n+1)=a(3n+2)=2.
  • A052905 (program): a(n) = (n^2 + 7*n + 2)/2.
  • A052906 (program): Expansion of (1-x^2)/(1-3*x-x^2).
  • A052909 (program): Expansion of (1+x-x^2)/((1-x)(1-3x)).
  • A052910 (program): Expansion of 1 + 2/(1-2*x-x^3).
  • A052913 (program): a(n+2) = 5a(n+1) - 2a(n), with a(0) = 1, a(1) = 4.
  • A052919 (program): a(n) = 1 + 2*3^(n-1) with a(0)=2.
  • A052921 (program): Expansion of (1 - x)/(1 - 3x + 2x^2 - x^3).
  • A052923 (program): Expansion of (1-x)/(1 - x - 4*x^2).
  • A052924 (program): Expansion of g.f.: (1-x)/(1 - 3*x - x^2).
  • A052925 (program): Expansion of (2-6x+4x^2-x^3)/((1-x)(1-3x+x^2)).
  • A052928 (program): The even numbers repeated.
  • A052929 (program): Expansion of (2-3x-x^2)/((1-x^2)(1-3*x)).
  • A052934 (program): Expansion of (1-x)/(1-6*x).
  • A052935 (program): Expansion of (2-2x-x^3)/((1-2x)*(1-x^3)).
  • A052936 (program): Expansion of (1-x)(1-2x)/(1-5x+5x^2).
  • A052937 (program): Expansion of (2-3x-x^2)/((1-x)(1-2*x-x^2)).
  • A052938 (program): Expansion of (1 + 2x - 2x^2)/( (1+x)*(1-x)^2 ).
  • A052940 (program): a(0) = 1; a(n) = 3*2^n - 1, for n > 0.
  • A052942 (program): Expansion of 1/((1+x)(1-2x+2x^2-2x^3)).
  • A052944 (program): a(n) = 2^n + n - 1.
  • A052945 (program): Number of compositions of n when each odd part can be of two kinds.
  • A052947 (program): Expansion of 1/(1-x^2-2*x^3).
  • A052948 (program): Expansion of g.f.: (1-2x)/(1-3x+2*x^3).
  • A052949 (program): Expansion of (2-4x+x^3)/((1-x)(1-2*x-x^2+x^3)).
  • A052950 (program): Expansion of (2-3x-x^2+x^3)/((1-x)(1+x)(1-2x)).
  • A052951 (program): Expansion of (1 + x - 2x^2)/(1 - 2x)^2.
  • A052952 (program): a(n) = Fibonacci(n+2) - (1-(-1)^n)/2.
  • A052953 (program): Expansion of 2(1-x-x^2)/((1-x)(1+x)(1-2x)).
  • A052954 (program): Expansion of (2-x-x^2-x^3)/((1-x)*(1-x^2-x^3)).
  • A052955 (program): a(2n) = 22^n - 1, a(2n+1) = 32^n - 1.
  • A052956 (program): a(n) = 2^n + Fibonacci(n+1).
  • A052957 (program): Expansion of 2(1-x-x^2)/((1-2x)(1-2x^2)).
  • A052959 (program): a(2n) = a(2n-1)+a(2n-2), a(2n+1) = a(2n)+a(2n-1)-1, a(0)=2, a(1)=1.
  • A052961 (program): Expansion of (1 - 3x) / (1 - 5x + 3*x^2).
  • A052963 (program): a(0)=1, a(1)=2, a(2)=5, a(n) = 3*a(n+2) - a(n+3).
  • A052968 (program): a(n) = 1 + 2^(n-1) + n for n > 0, a(0) = 2.
  • A052969 (program): Expansion of (1-x)/(1-x-2x^2+x^4).
  • A052970 (program): Expansion of (1-2x)/(1-2x-2x^2+2x^3).
  • A052975 (program): Expansion of (1-2x)(1-x)/(1-5x+6x^2-x^3).
  • A052980 (program): Expansion of (1 - x)/(1 - 2*x - x^3).
  • A052984 (program): a(n) = 5a(n-1) - 2a(n-2) for n>1, with a(0) = 1, a(1) = 3.
  • A052986 (program): Expansion of ( 1-2x ) / ( (x-1)(2x^2+3x-1) ).
  • A052987 (program): Expansion of (1-2x^2)/(1-2x-2x^2+2x^3).
  • A052991 (program): Expansion of (1-x-x^2)/(1-3x-x^2).
  • A052992 (program): Expansion of 1/((1 - x)(1 - 2x)(1 + 2x)).
  • A052993 (program): a(n) = a(n-1) + 3a(n-2) - 3a(n-3), with a(0)=a(1)=1, a(2)=4.
  • A052994 (program): Expansion of 2x(1-x)/(1-2x-x^2+x^3).
  • A052995 (program): Expansion of 2x(1 - x)/(1 - 3*x + x^2).
  • A052996 (program): G.f.: (1+x^2-x^3)/((1-x)(1-2*x)).
  • A052997 (program): Expansion of (1+x-x^3)/((1-2x)(1-x^2)).
  • A053000 (program): (Smallest prime > n^2) - n^2.
  • A053001 (program): Largest prime < n^2.
  • A053024 (program): a(n) = n*p where p is the next prime >= n.
  • A053044 (program): a(n) is the number of iterations of the Euler totient function to reach 1, starting at n!.
  • A053061 (program): a(n) is the decimal concatenation of n and n^2.
  • A053088 (program): a(n) = 3a(n-2) + 2a(n-3) for n > 2, a(0)=1, a(1)=0, a(2)=3.
  • A053100 (program): a(n) = ((6n+7)(!^6))/7, related to A008542 ((6n+1)(!^6) sextic, or 6-factorials).
  • A053101 (program): a(n) = ((6n+8)(!^6))/8(!^6), related to A034689 (((6n+2)(!^6))/2 sextic, or 6-factorials).
  • A053102 (program): a(n) = ((6n+9)(!^6))/9(!^6), related to A034723 (((6n+3)(!^6))/3 sextic, or 6-factorials).
  • A053103 (program): a(n) = ((6n+10)(!^6))/10(!^6), related to A034724 (((6n+4)(!^6))/4 sextic, or 6-factorials).
  • A053104 (program): a(n) = ((7n+8)(!^7))/8, related to A045754 ((7n+1)(!^7) sept-, or 7-factorials).
  • A053105 (program): a(n) = ((7n+9)(!^7))/9(!^7), related to A034829 (((7n+2)(!^7))/2 sept-, or 7-factorials).
  • A053106 (program): a(n) = ((7n+10)(!^7))/10(1^7), related to A034830 (((7n+3)(!^7))/3 sept-, or 7-factorials).
  • A053107 (program): Expansion of 1/(1-8*x)^8.
  • A053108 (program): Expansion of 1/(1 - 9*x)^9.
  • A053109 (program): Expansion of 1/(1-10*x)^10.
  • A053110 (program): Expansion of (-1 + 1/(1-7x)^7)/(49x); related to A036226.
  • A053111 (program): Expansion of (-1 + 1/(1-8x)^8)/(64x); related to A053107.
  • A053112 (program): Expansion of (-1 + 1/(1-9x)^9)/(81x); related to A053108.
  • A053113 (program): Expansion of (-1 + 1/(1-10x)^10)/(100x); related to A053109.
  • A053114 (program): a(n) = ((8n+9)(!^8))/9, related to A045755 ((8n+1)(!^8) octo- or 8-factorials).
  • A053115 (program): a(n) = ((8n+10)(!^8))/20, related to A034908 ((8n+2)(!^8) octo- or 8-factorials).
  • A053116 (program): a(n) = ((9n+10)(!^9))/10, related to A045756 ((9n+1)(!^9) 9-factorials).
  • A053126 (program): Binomial coefficients binomial(2*n-3,4).
  • A053127 (program): Binomial coefficients C(2*n-4,5).
  • A053128 (program): Binomial coefficients C(2*n-5,6).
  • A053129 (program): Binomial coefficients C(2*n-6,7).
  • A053130 (program): Binomial coefficients C(2*n-7,8).
  • A053131 (program): Binomial coefficients C(2*n-8,9).
  • A053132 (program): One half of binomial coefficients C(2*n-4,5).
  • A053133 (program): One half of binomial coefficients binomial(2*n-8,9).
  • A053134 (program): Binomial coefficients C(2*n+4,4).
  • A053135 (program): Binomial coefficients C(2*n+6,6).
  • A053136 (program): Binomial coefficients C(2*n+7,7).
  • A053137 (program): Binomial coefficients C(2*n+8,8).
  • A053138 (program): Binomial coefficients C(2*n+9,9).
  • A053139 (program): a(n) = phi(n) - mu(n).
  • A053141 (program): a(0)=0, a(1)=2 then a(n) = a(n-2) + 2sqrt(8a(n-1)^2 + 8*a(n-1) + 1).
  • A053142 (program): a(n) = A053141(n)/2.
  • A053143 (program): Smallest square divisible by n.
  • A053152 (program): Number of 2-element intersecting families whose union is an n-element set.
  • A053154 (program): Number of 2-element intersecting families (with not necessary distinct sets) of an n-element set.
  • A053156 (program): Number of 2-element intersecting families (with not necessary distinct sets) whose union is an n-element set.
  • A053158 (program): Sum of n and its cototient function value (A051953).
  • A053164 (program): 4th root of largest 4th power dividing n.
  • A053186 (program): Square excess of n: difference between n and largest square <= n.
  • A053187 (program): Square nearest to n.
  • A053188 (program): Distance from n to nearest square.
  • A053191 (program): a(n) = n^2 * phi(n).
  • A053192 (program): a(n) is the cototient of n^3.
  • A053193 (program): Cototient of odd numbers.
  • A053196 (program): Cototients of even numbers.
  • A053200 (program): Binomial coefficients C(n,k) reduced modulo n, read by rows; T(0,0)=0 by convention.
  • A053208 (program): Row sums of A053207.
  • A053209 (program): Row sums of A051598.
  • A053210 (program): Row sums of A051599.
  • A053214 (program): Central binomial coefficients (A000984) read mod 2n, with a(0)=1.
  • A053220 (program): a(n) = (3*n-1) * 2^(n-2).
  • A053221 (program): Row sums of triangle A053218.
  • A053222 (program): First differences of sigma(n).
  • A053246 (program): First differences of chowla(n).
  • A053297 (program): Row sums of array T in A053199.
  • A053307 (program): Number of nonnegative integer 2 X 2 matrices with sum of elements equal to n, under row and column permutations.
  • A053310 (program): a(n) = (n+3)*binomial(n+8, 8)/3.
  • A053311 (program): Partial sums of A000285.
  • A053347 (program): a(n) = binomial(n+7, 7)*(n+4)/4.
  • A053367 (program): Partial sums of A050494.
  • A053381 (program): Maximal number of linearly independent smooth nowhere-zero vector fields on a (2n+1)-sphere.
  • A053384 (program): A053398(4, n).
  • A053386 (program): A053398(6, n).
  • A053387 (program): A053398(7, n).
  • A053388 (program): A053398(8, n).
  • A053399 (program): A053398(3, n).
  • A053404 (program): Expansion of 1/((1+3x)(1-4*x)).
  • A053405 (program): Definition: A kara B = C, where C is the least nonnegative integer such that: C * B >= A and C * (B-1) < A. Sequence gives smallest a such that n kara a is undefined.
  • A053408 (program): Numbers n such that A003266(n) + 1 is prime.
  • A053410 (program): a(1) = 0, a(2) = 16, a(2n+1) = 10a(2n) - a(2n-1), a(2n) = 10a(2n-1) - a(2n-2) + 16.
  • A053422 (program): n times (n 1’s): a(n) = n*(10^n - 1)/9.
  • A053428 (program): a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=1.
  • A053430 (program): a(n) = (6^(n+1) - (-5)^(n+1))/11.
  • A053436 (program): a(n) = n+1 + ceiling(n/2)(ceiling(n/2)-1)(ceiling(n/2)+1)/6.
  • A053438 (program): Expansion of (1+x+2x^3)/((1-x)(1-x^2)).
  • A053439 (program): Expansion of (1+x+2x^3)/((1-x)(1-x^2)^2).
  • A053455 (program): a(n) = ((8^n) - (-6)^n)/14.
  • A053464 (program): a(n) = n*5^(n-1).
  • A053469 (program): a(n) = n*6^(n-1).
  • A053470 (program): a(n) is the cototient of n (A051953) iterated twice.
  • A053475 (program): 1 + the number of iterations of A051953 (Euler-cototient) function needed to reach 0, starting at n.
  • A053477 (program): Sum of iterates of divisor number function A000005.
  • A053478 (program): Sum of iterates when phi, A000010, is iterated until fixed point 1.
  • A053480 (program): Sum of values when cototient function A051953 is iterated until fixed point is reached.
  • A053486 (program): E.g.f.: exp(3x)/(1-x).
  • A053487 (program): E.g.f.: exp(4x)/(1-x).
  • A053506 (program): a(n) = (n-1)*n^(n-2).
  • A053507 (program): a(n) = binomial(n-1,2)*n^(n-3).
  • A053524 (program): a(n) = (6^n - (-2)^n)/8.
  • A053526 (program): Number of bipartite graphs with 3 edges on nodes 1..n .
  • A053535 (program): Expansion of 1/((1+3x)(1-9*x)).
  • A053539 (program): a(n) = n * 8^(n-1).
  • A053540 (program): a(n) = n*9^(n-1).
  • A053541 (program): a(n) = n*10^(n-1).
  • A053542 (program): Distance from n-th composite number (A002808) to next prime.
  • A053545 (program): Comparisons needed for Batcher’s sorting algorithm applied to 2^n items.
  • A053565 (program): a(n) = 2^(n-1)(3n-4).
  • A053566 (program): Expansion of (11x-2)/(1-3x)^2.
  • A053574 (program): Exponent of 2 in phi(n) where phi(n) = A000010(n).
  • A053575 (program): Odd part of phi(n): a(n) = A000265(A000010(n)).
  • A053581 (program): First differences of the Poly-Bernoulli numbers B_n^(k) with k=-2 (A027649).
  • A053585 (program): If n = p_1^e_1 * … * p_k^e_k, p_1 < … < p_k primes, then a(n) = p_k^e_k.
  • A053589 (program): Greatest primorial number (A002110) which divides n.
  • A053599 (program): Number of nonempty subsequences s(k) of 1..n such that the difference sequence is palindromic.
  • A053602 (program): a(n) = a(n-1) - (-1)^n*a(n-2), a(0)=0, a(1)=1.
  • A053606 (program): a(n) = (Fibonacci(6*n+3) - 2)/4.
  • A053610 (program): Number of positive squares needed to sum to n using the greedy algorithm.
  • A053615 (program): Pyramidal sequence: distance to nearest product of two consecutive integers (promic or heteromecic numbers).
  • A053616 (program): Pyramidal sequence: distance to nearest triangular number.
  • A053618 (program): a(n) = ceiling(binomial(n,4)/n).
  • A053625 (program): Product of 6 consecutive integers.
  • A053637 (program): a(n) = ceiling(2^(n-1)/n).
  • A053638 (program): a(n) = ceiling(2^n/n).
  • A053639 (program): a(n) = ceiling(2^(n+1)/n).
  • A053641 (program): Rotate one binary digit to the right, calculate, then rotate one binary digit to the left.
  • A053643 (program): a(n) = ceiling(binomial(n,6)/n).
  • A053644 (program): Most significant bit of n, msb(n); largest power of 2 less than or equal to n; write n in binary and change all but the first digit to zero.
  • A053645 (program): Distance to largest power of 2 less than or equal to n; write n in binary, change the first digit to zero, and convert back to decimal.
  • A053646 (program): Distance to nearest power of 2.
  • A053650 (program): Cototient function of n^2.
  • A053654 (program): Multiples of 123456789.
  • A053666 (program): Product of digits of n-th prime.
  • A053667 (program): Product of digits of n^2.
  • A053668 (program): Product of digits of n^3.
  • A053669 (program): Smallest prime not dividing n.
  • A053692 (program): Number of self-conjugate 4-core partitions of n.
  • A053698 (program): a(n) = n^3 + n^2 + n + 1.
  • A053699 (program): a(n) = n^4 + n^3 + n^2 + n + 1.
  • A053700 (program): a(n) = 111111 in base n.
  • A053715 (program): a(n) = n-th triangular number (the sum of the first n integers) in base n.
  • A053716 (program): a(n) = 1111111 in base n.
  • A053717 (program): a(n) = n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.
  • A053730 (program): a(n) = 2^(n-2)*(n^2 - n + 4).
  • A053731 (program): a(n) = ceiling(binomial(n,8)/n).
  • A053733 (program): a(n) = ceiling(binomial(n,9)/n).
  • A053735 (program): Sum of digits of (n written in base 3).
  • A053737 (program): Sum of digits of (n written in base 4).
  • A053738 (program): If k is in sequence then 2k and 2k+1 are not (and 1 is in the sequence); numbers with an odd number of digits in binary.
  • A053739 (program): Partial sums of A014166.
  • A053741 (program): Sum of even numbers in range 10n to 10n+9.
  • A053742 (program): Sum of odd numbers in range 10n to 10n+9.
  • A053743 (program): Sum of numbers in range 10n to 10n+9.
  • A053754 (program): If k is in the sequence then 2k and 2k+1 are not (and 0 is in the sequence); when written in binary k has an even number of bits (0 has 0 digits).
  • A053755 (program): a(n) = 4*n^2 + 1.
  • A053763 (program): a(n) = 2^(n^2 - n).
  • A053764 (program): a(n) = 3^(n^2 - n).
  • A053767 (program): Sum of first n composite numbers.
  • A053793 (program): n^2+n modulo 7.
  • A053794 (program): a(n) = (n^2 + n) modulo 8.
  • A053796 (program): a(n) = (n^2+n) modulo 5.
  • A053798 (program): Number of basis partitions of n+16 with Durfee square size 4.
  • A053799 (program): Number of basis partitions of n+9 with Durfee square size 3.
  • A053800 (program): Number of basis partitions of n+25 with Durfee square size 5.
  • A053807 (program): a(n) = Sum_ k=1..n, n mod k = 1 k^2.
  • A053808 (program): Partial sums of A001891.
  • A053809 (program): Second partial sums of A001891.
  • A053815 (program): Floor(n / (sum of proper divisors of n)).
  • A053817 (program): a(0)=1, a(n) = n*(a(n-1) + n).
  • A053824 (program): Sum of digits of (n written in base 5).
  • A053827 (program): Sum of digits of (n written in base 6).
  • A053828 (program): Sum of digits of (n written in base 7).
  • A053829 (program): Sum of digits of (n written in base 8).
  • A053830 (program): Sum of digits of (n written in base 9).
  • A053831 (program): Sum of digits of n written in base 11.
  • A053833 (program): Sum of digits of n written in base 13.
  • A053834 (program): Sum of digits of n written in base 14.
  • A053835 (program): Sum of digits of n written in base 15.
  • A053836 (program): Sum of digits of n written in base 16.
  • A053837 (program): Sum of digits of n modulo 10.
  • A053838 (program): a(n) = (sum of digits of n written in base 3) modulo 3.
  • A053839 (program): a(n) = (sum of digits of n written in base 4) modulo 4.
  • A053840 (program): (Sum of digits of n written in base 5) modulo 5.
  • A053841 (program): (Sum of digits of n written in base 6) modulo 6.
  • A053842 (program): (Sum of digits of n written in base 7) modulo 7.
  • A053843 (program): (Sum of digits of n written in base 8) modulo 8.
  • A053844 (program): (Sum of digits of n written in base 9) modulo 9.
  • A053866 (program): Parity of A000203(n), the sum of the divisors of n; a(n) = 1 when n is a square or twice a square, 0 otherwise.
  • A053867 (program): Parity of sum of divisors of n less than n.
  • A053879 (program): a(n) = n^2 mod 7.
  • A054000 (program): a(n) = 2*n^2 - 2.
  • A054008 (program): n read modulo (number of divisors of n).
  • A054013 (program): Chowla function of n read modulo n.
  • A054024 (program): Sum of the divisors of n reduced modulo n.
  • A054025 (program): Sum of divisors of n read modulo (number of divisors of n).
  • A054027 (program): Numbers that do not divide their sum of divisors.
  • A054042 (program): Decimal expansion of 1 - 1/sqrt(10).
  • A054054 (program): Smallest digit of n.
  • A054055 (program): Largest digit of n.
  • A054066 (program): Position of n-th 1 in A054065.
  • A054071 (program): Position of 1 in the permutation of 1,2,…,n obtained by ordering the fractional parts h*sqrt(2) for h=1,2,…,n.
  • A054074 (program): Position of n-th 1 in A054073.
  • A054087 (program): s(3n-2), s=A054086; also a bisection of A003511.
  • A054088 (program): a(n) = A054086(3n); also a bisection of A003511.
  • A054091 (program): Row sums of A054090.
  • A054092 (program): T(n,n), array T as in A054090.
  • A054096 (program): T(n,2), array T as in A054090.
  • A054107 (program): T(n,n-3), array T as in A054106.
  • A054108 (program): a(n)=(-1)^(n+1)sum(k=0,n+1,(-1)^kbinomial(2*k,k)).
  • A054111 (program): Row sums of array T as in A054110.
  • A054113 (program): T(2n,n), array T as in A054110.
  • A054114 (program): T(2n+1,n), array T as in A054110.
  • A054116 (program): T(n,n-1), array T as in A054115.
  • A054117 (program): T(n,n-2), array T as in A054115.
  • A054121 (program): T(n,n-3), array T as in A054120.
  • A054127 (program): a(1) = 2; a(n) = 9*2^(n-2) - n - 2, n>1.
  • A054135 (program): T(n,1), array T as in A054134.
  • A054145 (program): Row sums of array T as in A054144.
  • A054146 (program): a(n) = A054145(n)/2.
  • A054147 (program): a(n) = T(2n,n), array T as in A054144.
  • A054204 (program): Integers expressible as sums of distinct even-subscripted Fibonacci numbers.
  • A054243 (program): Number of partitions of n into distinct positive parts <= n, where parts are combined by XOR.
  • A054249 (program): Alternately subtract and add 1 to digits in decimal expansion of Pi.
  • A054254 (program): a(n) is n plus the minimum of the a(i)*a(n-i) of the previous i=1..n-1.
  • A054265 (program): Sum of composite numbers between successive primes.
  • A054271 (program): Difference between prime(n)^2 and the previous prime.
  • A054275 (program): Susceptibility series H_2 for 2-dimensional Ising model (divided by 2).
  • A054318 (program): a(n)-th star number (A003154) is a square.
  • A054320 (program): Expansion of g.f.: (1 + x)/(1 - 10*x + x^2).
  • A054322 (program): Fourth unsigned column of Lanczos triangle A053125 (decreasing powers).
  • A054323 (program): Fifth column of Lanczos triangle A053125 (decreasing powers).
  • A054324 (program): Sixth unsigned column of Lanczos triangle A053125 (decreasing powers).
  • A054325 (program): Seventh column of Lanczos triangle A053125 (decreasing powers).
  • A054326 (program): Eighth unsigned column of Lanczos triangle A053125 (decreasing powers).
  • A054327 (program): Ninth column of Lanczos triangle A053125 (decreasing powers).
  • A054328 (program): Tenth unsigned column of Lanczos triangle A053125 (decreasing powers).
  • A054329 (program): One quarter of fourth unsigned column of Lanczos’ triangle A053125.
  • A054330 (program): One half of sixth unsigned column of Lanczos’ triangle A053125.
  • A054331 (program): One eighth of eighth unsigned column of Lanczos’ triangle A053125.
  • A054332 (program): One half of tenth unsigned column of Lanczos triangle A053125 (decreasing powers).
  • A054333 (program): 1/256 of tenth unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted).
  • A054334 (program): 1/512 of 11th unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted).
  • A054337 (program): 7-fold convolution of A000302 (powers of 4).
  • A054338 (program): 8-fold convolution of A000302 (powers of 4).
  • A054339 (program): 9-fold convolution of A000302 (powers of 4).
  • A054340 (program): 10-fold convolution of A000302 (powers of 4).
  • A054347 (program): Partial sums of A000201.
  • A054401 (program): 5^n-4^n-1.
  • A054405 (program): Row sums of array T as in A055215.
  • A054406 (program): Beatty sequence for (3+sqrt 3)/2; complement of A022838.
  • A054410 (program): Susceptibility series H_3 for 2-dimensional Ising model (divided by 2).
  • A054414 (program): a(n) = 1 + floor(n/(1-log(2)/log(3))).
  • A054429 (program): Simple self-inverse permutation of natural numbers: List each block of 2^n numbers (from 2^n to 2^(n+1) - 1) in reverse order.
  • A054444 (program): Even-indexed terms of A001629(n), n >= 2, (Fibonacci convolution).
  • A054447 (program): Row sums of triangle A054446 (partial row sums triangle of Fibonacci convolution triangle).
  • A054451 (program): Third column of triangle A054450 (partial row sums of unsigned Chebyshev triangle A049310).
  • A054452 (program): Partial sums of A027941(n-1) with a(-1) = 0.
  • A054459 (program): A001333(n), n >= 1, convolved with itself.
  • A054477 (program): A Pellian-related sequence.
  • A054485 (program): Expansion of (1+3x)/(1-4x+x^2).
  • A054486 (program): Expansion of (1+2x)/(1-3x+x^2).
  • A054487 (program): a(n) = (3n+4)binomial(n+7, 7)/4.
  • A054488 (program): Expansion of (1+2x)/(1-6x+x^2).
  • A054489 (program): Expansion of (1+4x)/(1-6x+x^2).
  • A054490 (program): Expansion of (1+5x)/(1-6x+x^2).
  • A054491 (program): a(n) = 4*a(n-1) - a(n-2), a(0)=1, a(1)=6.
  • A054492 (program): a(n) = 3*a(n-1) - a(n-2), a(0)=1, a(1)=6.
  • A054493 (program): A Pellian-related recursive sequence.
  • A054498 (program): Number of symmetric nonnegative integer 8 X 8 matrices with sum of elements equal to 4*n, under action of dihedral group D_4.
  • A054516 (program): Equivalent of the Kurepa hypothesis for left factorial.
  • A054519 (program): Number of increasing arithmetic progressions of nonnegative integers ending in n, including those of length 1 or 2.
  • A054521 (program): Triangle T(n,k): T(n,k) = 1 if gcd(n, k) = 1, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).
  • A054526 (program): Triangle T(n,k): T(n,k) = phi(k) (n >= 1, 1 <= k <= n).
  • A054527 (program): Triangle read by rows: T(n,k) = Moebius mu(k) (n >= 1, 1<=k<=n).
  • A054541 (program): Sum of first n terms equals n-th prime.
  • A054546 (program): First differences of nonprimes (including 0 and 1, A002808).
  • A054552 (program): a(n) = 4n^2 - 3n + 1.
  • A054554 (program): a(n) = 4n^2 - 10n + 7.
  • A054556 (program): a(n) = 4n^2 - 9n + 6.
  • A054559 (program): Number of labeled pure 2-complexes on n nodes (0-simplexes) with 5 2-simplexes and 8 1-simplexes.
  • A054563 (program): a(n) = n(n^2 - 1)(n + 2)(n^2 + 4n + 6)/72.
  • A054567 (program): a(n) = 4n^2 - 7n + 4.
  • A054569 (program): a(n) = 4n^2 - 6n + 3.
  • A054576 (program): Largest proper factor of the largest proper factor of n.
  • A054577 (program): A Catalan-like sequence.
  • A054579 (program): n^2+n modulo 17.
  • A054580 (program): n^2 modulo 17.
  • A054585 (program): Sum_ d=1..n phi(d)*mu(d).
  • A054586 (program): Sum_ d 2n+1 phi(d)*mu(d).
  • A054602 (program): a(n) = Sum_ d 3 phi(d)*n^(3/d).
  • A054603 (program): a(n) = Sum_ d 4 phi(d)*n^(4/d).
  • A054604 (program): a(n) = Sum_ d 5 phi(d)*n^(5/d).
  • A054605 (program): a(n) = Sum_ d 6 phi(d)*n^(6/d).
  • A054606 (program): a(n) = Sum_ d 7 phi(d)*n^(7/d).
  • A054607 (program): a(n) = Sum_ d 8 phi(d)*n^(8/d).
  • A054608 (program): a(n) = Sum_ d 9 phi(d)*n^(9/d).
  • A054620 (program): Number of ways to color vertices of a pentagon using <= n colors, allowing only rotations.
  • A054621 (program): Number of ways to color vertices of a heptagon using <= n colors, allowing only rotations.
  • A054622 (program): Number of ways to color vertices of an octagon using <= n colors, allowing only rotations.
  • A054623 (program): Number of ways to color vertices of a 9-gon using <= n colors, allowing only rotations.
  • A054644 (program): Number of labeled pure 2-complexes on n nodes with 3 2-simplexes.
  • A054650 (program): Nearest integer to 2^(n-1)/n.
  • A054668 (program): Number of distinct non-extendable sequences X= x(1),x(2),…,x(k) where x(1)=1, the x(i)’s are distinct elements of 1,…,n with x(i)-x(i+1) =1 or 2, for i=1,2,…,k.
  • A054683 (program): Numbers n such that sum of digits is even.
  • A054684 (program): Sum of digits is odd.
  • A054688 (program): Number of nonnegative integer n X n matrices with sum of elements equal to n; polynomial symmetric functions of matrix of order n.
  • A054725 (program): a(1)=1; a(n)= sum(p \ n, a(p-1)), where sum is over all primes p that divide n, with multiplicity.
  • A054763 (program): Residues of consecutive prime differences modulo 6.
  • A054770 (program): Numbers that are not the sum of distinct Lucas numbers 1,3,4,7,11 … (A000204).
  • A054776 (program): a(n) = 3n(3n-1)(3*n-2).
  • A054777 (program): a(n) = 4n(4n-1)(4n-2)(4*n-3).
  • A054778 (program): 5n(5n-1)(5n-2)(5n-3)(5n-4).
  • A054779 (program): 6n(6n-1)(6n-2)(6n-3)(6n-4)*(6n-5).
  • A054783 (program): (n^2)-th Fibonacci number.
  • A054785 (program): a(n) = sigma(2n) - sigma(n), where sigma is the sum of divisors of n, A000203.
  • A054843 (program): Number of sequences of consecutive nonnegative integers (including sequences of length 1) that sum to n.
  • A054844 (program): Number of ways to write n as the sum of any number of consecutive integers (including the trivial one-term sum n = n).
  • A054849 (program): a(n) = 2^(n-5)*binomial(n,5). Number of 5D hypercubes in an n-dimensional hypercube.
  • A054851 (program): a(n) = 2^(n-7)*binomial(n,7). Number of 7D hypercubes in an n-dimensional hypercube.
  • A054861 (program): Highest power of 3 dividing n!.
  • A054868 (program): Sum of bits of sum of bits of n: a(n) = wt(wt(n)).
  • A054878 (program): Number of closed walks of length n along the edges of a tetrahedron based at a vertex.
  • A054879 (program): Closed walks of length 2n along the edges of a cube based at a vertex.
  • A054880 (program): a(n) = 3*(9^n - 1)/4.
  • A054881 (program): Number of walks of length n along the edges of an octahedron starting and ending at a vertex and also ( with a(0)=0 ) between two opposite vertices.
  • A054886 (program): Layer counting sequence for hyperbolic tessellation by cuspidal triangles of angles (Pi/3,Pi/3,0) (this is the classical modular tessellation).
  • A054888 (program): Layer counting sequence for hyperbolic tessellation by regular pentagons of angle Pi/2.
  • A054890 (program): Layer counting sequence for hyperbolic tessellation by regular heptagons of angle Pi/3.
  • A054893 (program): Floor[n/4] + floor[n/16] + floor[n/64] + floor[n/256] + ….
  • A054895 (program): a(n) = Sum_ k>0 floor(n/6^k).
  • A054896 (program): a(n) = Sum_ k>0 floor(n/7^k).
  • A054897 (program): a(n) = Sum_ k>0 floor(n/8^k).
  • A054898 (program): a(n) = Sum_ k>0 floor(n/9^k).
  • A054899 (program): a(n) = Sum_ k>0 floor(n/10^k).
  • A054900 (program): (n) = floor(n/16) + floor(n/256) + floor(n/4096) + floor(n/65536) + ….
  • A054925 (program): a(n) = ceiling(n*(n-1)/4).
  • A054961 (program): Maximal number of binary vectors of length n such that the unions (or bitwise ORs) of any 2 distinct vectors are all distinct.
  • A054963 (program): Number of cells in the first column of all directed column-convex polyominoes of area n+1.
  • A054965 (program): Beatty sequence for log_3(10), i.e., for 1/log_10(3); so largest exponent of 3 which produces an n-digit decimal number.
  • A054966 (program): Numbers that are congruent to 0, 1, 8 mod 9.
  • A054967 (program): Numbers that are congruent to 0, 1, 9 mod 10.
  • A054968 (program): 3*Fibonacci(n) - 11.
  • A054974 (program): Number of nonnegative integer 2 X 2 matrices with no zero rows or columns and with sum of elements equal to n, up to row and column permutation.
  • A054977 (program): a(0)=2, a(n)=1, n >= 1.
  • A054995 (program): A version of Josephus problem: a(n) is the surviving integer under the following elimination process. Arrange 1,2,3,…,n in a circle, increasing clockwise. Starting with i=1, delete the integer two places clockwise from i. Repeat, counting two places from the next undeleted integer, until only one integer remains.
  • A055003 (program): a(n) = prime(prime(n)-1).
  • A055010 (program): a(0) = 0; for n > 0, a(n) = 3*2^(n-1) - 1.
  • A055012 (program): Sum of cubes of the digits of n written in base 10.
  • A055013 (program): Sum of 4th powers of digits of n.
  • A055014 (program): Sum of 5th powers of digits of n.
  • A055015 (program): Sum of 6th powers of digits of n.
  • A055034 (program): a(1) = 1, a(n) = phi(2*n)/2 for n>1.
  • A055037 (program): Number of numbers <= n with an even number of prime factors (counted with multiplicity).
  • A055038 (program): Number of numbers <= n with an odd number of prime factors (counted with multiplicity).
  • A055067 (program): Product of numbers < n which do not divide n (or 1 if no such numbers exist).
  • A055076 (program): Multiplicity of Max gcd(d, n/d) when d runs over divisors of n.
  • A055081 (program): Number of positive integers whose harmonic mean with n is a positive integer.
  • A055086 (program): n appears 1+[n/2] times.
  • A055087 (program): Integers 0..n then 0..n then 0..n+1 then 0..n+1 etc.
  • A055099 (program): Expansion of g.f.: (1 + x)/(1 - 3x - 2x^2).
  • A055112 (program): a(n) = n(n+1)(2*n+1).
  • A055131 (program): Those composite s for which A055095[s] = 2.
  • A055142 (program): E.g.f.: exp(x)*sqrt(1-2x).
  • A055156 (program): Powers of 3 which are not powers of 3^3.
  • A055214 (program): a(0) = 1; a(n) = 2na(n-1) - 1 for n >= 1.
  • A055223 (program): One-fourth the digital sum of base 5 representations of 2^n.
  • A055225 (program): a(n) = Sum_ k divides n (n/k)^k.
  • A055231 (program): Powerfree part of n: product of primes that divide n only once.
  • A055232 (program): Expansion of (1+2x+3x^2)/((1-x)^3*(1-x^2)).
  • A055235 (program): Sums of two powers of 3.
  • A055236 (program): Sums of two powers of 4.
  • A055246 (program): At step number k >= 1 the 2^(k-1) open intervals that are erased from [0,1] in the Cantor middle-third set construction are I(k,n) = (a(n)/3^k, (1+a(n))/3^k), n=1..2^(k-1).
  • A055247 (program): Related to A055246 and A005836. Used for boundaries of open intervals which have to be erased in the Cantor middle third set construction.
  • A055250 (program): Seventh column of triangle A055249.
  • A055254 (program): Number of odd digits in 2^n.
  • A055257 (program): Sums of two powers of 6.
  • A055258 (program): Sums of two powers of 7.
  • A055259 (program): Sums of two powers of 8.
  • A055260 (program): Sums of two powers of 9.
  • A055261 (program): Sums of two powers of 16.
  • A055264 (program): Possible values of A055263; numbers equal to 0, 1, 3 or 6 modulo 9.
  • A055267 (program): a(n) = 3*a(n-1) - a(n-2) with a(0)=1, a(1)=7.
  • A055268 (program): a(n) = (11n + 4)C(n+3, 3)/4.
  • A055269 (program): a(n) = 4*a(n-1) - a(n-2) + 3 with a(0)=1, a(1)=7.
  • A055270 (program): a(n) = 7*a(n-1) + (-1)^n * binomial(2,2-n) with a(-1)=0.
  • A055271 (program): a(n) = 5*a(n-1) - a(n-2) with a(0)=1, a(1)=7.
  • A055272 (program): First differences of 7^n (A000420).
  • A055273 (program): a(n) = 3*a(n-1) - a(n-2) with a(0) = 1, a(1) = 8.
  • A055274 (program): First differences of 8^n (A001018).
  • A055275 (program): First differences of 9^n (A001019).
  • A055276 (program): First differences of 11^n (A001020).
  • A055278 (program): Number of rooted trees with n nodes and 3 leaves.
  • A055315 (program): Number of labeled trees with n nodes and 3 leaves.
  • A055328 (program): Number of rooted identity trees with n nodes and 3 leaves.
  • A055341 (program): Number of mobiles (circular rooted trees) with n nodes and 3 leaves.
  • A055364 (program): Number of asymmetric mobiles (circular rooted trees) with n nodes and 3 leaves.
  • A055377 (program): a(n) = largest prime <= n/2.
  • A055389 (program): a(0) = 1, then twice the Fibonacci sequence.
  • A055396 (program): Smallest prime dividing n is a(n)-th prime (a(1)=0).
  • A055400 (program): Cube excess: difference between n and largest cube <= n.
  • A055401 (program): Number of positive cubes needed to sum to n using the greedy algorithm.
  • A055417 (program): Number of points in N^n of norm <= 2.
  • A055426 (program): Number of points in Z^n of norm <= 2.
  • A055436 (program): a(n) = concatenation of n^2 and n.
  • A055437 (program): a(n) = 10*n^2+n.
  • A055438 (program): a(n) = 100*n^2 + n.
  • A055457 (program): 5^a(n) exactly divides 5n. Or, 5-adic valuation of 5n.
  • A055461 (program): Square decrescendo subsequences: triangle T(n,k) = (n-k)^2, n >= 1, 0 <= k < n.
  • A055473 (program): Powers of ten written in base 2.
  • A055475 (program): Powers of ten written in base 4.
  • A055476 (program): Powers of ten written in base 5.
  • A055483 (program): a(n) = GCD of n and the reverse of n.
  • A055491 (program): Smallest square divisible by n divided by largest square which divides n.
  • A055495 (program): Numbers n such that there exists a pair of mutually orthogonal Latin squares of order n.
  • A055497 (program): a(-1) = 4, a(0) = 5; thereafter a(n) = 4 + (Product_ k=1..n prime(k))^2.
  • A055504 (program): n(n-1)(n-2)(n-3)(n-4)(2n-1)/72.
  • A055522 (program): Largest area of a Pythagorean triangle with n as length of one of the three sides (in fact as a leg).
  • A055523 (program): Longest other leg of a Pythagorean triangle with n as length of a leg.
  • A055524 (program): Longest other side of a Pythagorean triangle with n as length of one of the three sides (in fact n is a leg and a(n) the hypotenuse).
  • A055541 (program): Total number of leaves (nodes of vertex degree 1) in all labeled trees with n nodes.
  • A055554 (program): An arithmetic progression each term of which is followed by at least 4 nonsquarefree consecutive integers.
  • A055555 (program): a(n) = n!*(n!+1)/2.
  • A055562 (program): a(n) = least number greater than a(n-1) not the sum of an earlier pair of consecutive terms, a(0) = 2.
  • A055565 (program): Sum of digits of n^4.
  • A055566 (program): Sum of digits of n^5.
  • A055567 (program): Sum of digits of n^6.
  • A055569 (program): Sum of digits of a(n)^3 is greater than or equal to a(n).
  • A055580 (program): Björner-Welker sequence: 2^n*(n^2 + n + 2) - 1.
  • A055581 (program): Fifth column of triangle A055252.
  • A055582 (program): Sixth column of triangle A055252.
  • A055585 (program): Second column of triangle A055584.
  • A055586 (program): Sixth column of triangle A055584.
  • A055588 (program): a(n) = 3*a(n-1) - a(n-2) - 1 with a(0) = 1 and a(1) = 2.
  • A055601 (program): Number of n X n binary matrices with no zero rows.
  • A055602 (program): Number of n X n binary matrices with no 0 rows or columns and with n+1 1’s.
  • A055607 (program): a(2n+1) = n^2 - 1 + A002620(n), a(2n) = a(2n-1) + n.
  • A055610 (program): A companion sequence to A011896.
  • A055615 (program): a(n) = n*moebius(n) (cf. A008683).
  • A055631 (program): Sum of Euler’s totient function phi of distinct primes dividing n.
  • A055636 (program): Partial sums of A144494.
  • A055640 (program): Number of nonzero digits in decimal expansion of n.
  • A055642 (program): Number of digits in decimal expansion of n.
  • A055646 (program): Integers in base 15 with each base 15 digit represented by 2 decimal digits.
  • A055647 (program): Integers in base 14 with each base 14 digit represented by 2 decimal digits.
  • A055658 (program): Number of (3,n)-partitions of a chain of length n^2.
  • A055659 (program): Number of (2,n)-partitions of a chain of length n^3.
  • A055660 (program): Number of (2,2; n,n)-partitions of a chain of length n^2 + n.
  • A055669 (program): Number of prime Hurwitz quaternions of norm prime(n).
  • A055670 (program): a(n) = prime(n) - (-1)^prime(n).
  • A055671 (program): Number of prime Hurwitz quaternions of norm n.
  • A055672 (program): Number of right-inequivalent prime Hurwitz quaternions of norm n.
  • A055679 (program): Number of distinct prime factors of phi(n!).
  • A055684 (program): Number of different n-pointed stars.
  • A055734 (program): Number of distinct primes dividing phi(n).
  • A055770 (program): Largest factorial number which divides n.
  • A055775 (program): a(n) = floor(n^n / n!).
  • A055789 (program): a(n) = binomial(n, round(sqrt(n))).
  • A055792 (program): a(n) and floor(a(n)/2) are both squares; i.e., squares which remain squares when written in base 2 and last digit is removed.
  • A055795 (program): a(n) = binomial(n,4) + binomial(n,2).
  • A055796 (program): T(2n+3,n), array T as in A055794.
  • A055797 (program): T(2n+4,n), array T as in A055794.
  • A055798 (program): T(2n+5,n), array T as in A055794.
  • A055799 (program): T(2n+6,n), array T as in A055794.
  • A055802 (program): a(n) = T(n,n-2), array T as in A055801.
  • A055808 (program): a(n) and floor(a(n)/4) are both squares; i.e., squares that remain squares when written in base 4 and last digit is removed.
  • A055809 (program): a(n) = T(n,n-4), array T as in A055807.
  • A055819 (program): Row sums of array T in A055818; twice the odd-indexed Fibonacci numbers after initial term.
  • A055820 (program): a(n) = T(n,n-3), array T as in A055818.
  • A055831 (program): T(n,n-4), where T is the array in A055830.
  • A055832 (program): T(n,n-5), where T is the array in A055830.
  • A055841 (program): Number of compositions of n into 3*j-1 kinds of j’s for all j >= 1.
  • A055842 (program): Expansion of (1-x)^2/(1-5*x).
  • A055843 (program): Expansion of (1+3*x)/(1-x)^10.
  • A055844 (program): a(n) = (5n + 9)binomial(n+8, 8)/9.
  • A055845 (program): a(n) = 4*a(n-1) - a(n-2) with a(0)=1, a(1)=8.
  • A055846 (program): a(n) = 25*6^(n-2), with a(0)=1 and a(1)=4.
  • A055848 (program): Expansion of (1+5*x)/(1-x)^10.
  • A055849 (program): a(n) = 3*a(n-1) - a(n-2) with a(0)=1, a(1)=9.
  • A055850 (program): a(n) = 3*a(n-1) - a(n-2) with a(0)=1, a(1)=10.
  • A055860 (program): a(n) = A000169(n+1) if n > 0; a(0) = 0.
  • A055861 (program): Essentially A053506 but with leading 0 (instead of 1) and offset 0.
  • A055862 (program): Fourth column of triangle A055858.
  • A055865 (program): Second column of triangle A055864.
  • A055869 (program): a(n) = (n+1)^n - n^n.
  • A055874 (program): a(n) = largest m such that 1, 2, …, m divide n.
  • A055876 (program): a(n) = round( 1 + e^(n-2) ).
  • A055881 (program): a(n) = largest m such that m! divides n.
  • A055897 (program): a(n) = n*(n-1)^(n-1).
  • A055899 (program): Column 3 of triangle A055898.
  • A055908 (program): Column 2 of triangle A055907.
  • A055930 (program): Number of distinct prime factors of totient of (n-th prime)!.
  • A055938 (program): Integers not generated by b(n) = b(floor(n/2)) + n (cf. A005187).
  • A055941 (program): a(n) = Sum_ j=0..k-1 (i(j) - j) where n = Sum_ j=0..k-1 2^i(j).
  • A055944 (program): a(n) = n + (reversal of base-2 digits of n) (written in base 10).
  • A055945 (program): a(n) = n - (reversal of base-2 digits of n) (and then the result is written in base 10).
  • A055946 (program): n + reversal of base 3 digits of n (written in base 10).
  • A055947 (program): n - reversal of base 3 digits of n (written in base 10).
  • A055948 (program): n + reversal of base 4 digits of n (written in base 10).
  • A055949 (program): n - reversal of base 4 digits of n (written in base 10).
  • A055950 (program): n + reversal of base 5 digits of n (written in base 10).
  • A055951 (program): n - reversal of base 5 digits of n (written in base 10).
  • A055952 (program): n + reversal of base 6 digits of n (written in base 10).
  • A055953 (program): n - reversal of base 6 digits of n (written in base 10).
  • A055954 (program): n + reversal of base 7 digits of n (written in base 10).
  • A055955 (program): n - reversal of base 7 digits of n (written in base 10).
  • A055956 (program): n + reversal of base 8 digits of n (written in base 10).
  • A055957 (program): n - reversal of base 8 digits of n (written in base 10).
  • A055958 (program): a(n) = n + reversal of base 9 digits of n (written in base 10).
  • A055959 (program): n - reversal of base 9 digits of n (written in base 10).
  • A055960 (program): n + reversal of base 11 digits of n (written in base 10).
  • A055961 (program): a(n) = n - (reversal of base-11 digits of n) (written in base 10).
  • A055962 (program): n + reversal of base 12 digits of n (written in base 10).
  • A055963 (program): n - reversal of base 12 digits of n (written in base 10).
  • A055964 (program): n + reversal of hexadecimal (base 16) digits of n (written in base 10).
  • A055965 (program): n - reversal of hexadecimal (base 16) digits of n (written in base 10).
  • A055976 (program): Remainder when (n-1)! + 1 is divided by n.
  • A055988 (program): Sequence is its own 4th difference.
  • A055989 (program): a(n) is its own 4th difference.
  • A055990 (program): a(n) is its own 4th difference.
  • A055991 (program): a(n) is its own 4th difference.
  • A055994 (program): Expansion of (1+6x)/(1-x)^10.
  • A055997 (program): Numbers n such that n(n - 1)/2 is a square.
  • A055998 (program): a(n) = n*(n+5)/2.
  • A055999 (program): a(n) = n*(n + 7)/2.
  • A056000 (program): a(n) = n*(n+9)/2.
  • A056001 (program): A second-order recursive sequence.
  • A056003 (program): A second-order recursive sequence.
  • A056020 (program): Numbers that are congruent to +-1 mod 9.
  • A056021 (program): Numbers k such that k^4 == 1 (mod 5^2).
  • A056040 (program): Swinging factorial, a(n) = 2^(n-(n mod 2))*Product_ k=1..n k^((-1)^(k+1)).
  • A056051 (program): a(n) = (n-2)! - 1 (mod n).
  • A056064 (program): The Kubelsky sequence: Jack Benny’s reported age, sampled annually.
  • A056074 (program): Number of 3-element ordered antichain covers of an unlabeled n-element set.
  • A056078 (program): Number of proper T_1-hypergraphs with 3 labeled nodes and n hyperedges.
  • A056081 (program): Numbers that are congruent to 1,26 mod 27.
  • A056084 (program): Numbers k such that k^8 == 1 (mod 9^3).
  • A056105 (program): First spoke of a hexagonal spiral.
  • A056106 (program): Second spoke of a hexagonal spiral.
  • A056107 (program): Third spoke of a hexagonal spiral.
  • A056108 (program): Fourth spoke of a hexagonal spiral.
  • A056109 (program): Fifth spoke of a hexagonal spiral.
  • A056113 (program): Most significant digit of n-th primorial A002110.
  • A056114 (program): Expansion of (1+9*x)/(1-x)^11.
  • A056115 (program): a(n) = n*(n+11)/2.
  • A056117 (program): Expansion of (1+8*x)/(1-x)^9.
  • A056118 (program): a(n) = (11n+5)(n+4)(n+3)(n+2)*(n+1)/120.
  • A056119 (program): a(n) = n*(n+13)/2.
  • A056120 (program): a(n) = (3^3)*4^(n-3) with a(0)=1, a(1)=1 and a(2)=7.
  • A056121 (program): a(n) = n*(n + 15)/2.
  • A056122 (program): a(n) = (8n+9)C(n+8,8)/9.
  • A056123 (program): a(n) = 3*a(n-1) - a(n-2) with a(0)=1, a(1)=11.
  • A056124 (program): a(n) = 3*a(n-1) - a(n-2) + 8 with a(0)=1, a(1)=11.
  • A056125 (program): a(n) = (5n + 4)binomial(n+7,7)/4.
  • A056126 (program): a(n) = n*(n + 17)/2.
  • A056128 (program): a(n) = (9n + 11)binomial(n+10, 10)/11.
  • A056129 (program): Final nonzero digit of n-th primorial.
  • A056134 (program): Smallest positive integer which is the geometric mean of n and an integer other than n.
  • A056136 (program): Largest positive integer whose harmonic mean with another positive integer is n.
  • A056142 (program): Concatenate n, floor[n/10], floor[n/100] … (but do not continue if floor[.]=0).
  • A056143 (program): Concatenate … floor[n/100], floor[n/10], n.
  • A056155 (program): Positive integer k, 1 <= k <= n, which maximizes k^(n+1-k).
  • A056158 (program): Equivalent of the Kurepa hypothesis for left factorial.
  • A056159 (program): a(n)=floor[10^(n-1)/n].
  • A056167 (program): Numbers n such that n! is not divisible by the square of (f+1)!, where f=Floor[n/2].
  • A056169 (program): Number of unitary prime divisors of n.
  • A056170 (program): Number of non-unitary prime divisors of n.
  • A056172 (program): Number of non-unitary prime divisors of n!.
  • A056174 (program): Number of non-monotone maps from 1,…,n to 1,…,n.
  • A056182 (program): First differences of A003063.
  • A056199 (program): a(n) = n * a(n-1) - Sum_ k=1..n-2 a(k) with a(1) = 0 and a(2) = 1.
  • A056220 (program): a(n) = 2*n^2 - 1.
  • A056236 (program): a(n) = (2 + sqrt(2))^n + (2 - sqrt(2))^n.
  • A056237 (program): a(n) = 2n^2 + 9n - 5.
  • A056309 (program): Number of reversible strings with n beads using exactly two different colors.
  • A056311 (program): Number of reversible strings with n beads using exactly four different colors.
  • A056323 (program): Number of reversible string structures with n beads using a maximum of four different colors.
  • A056326 (program): Number of reversible string structures with n beads using exactly two different colors.
  • A056449 (program): a(n) = 3^floor((n+1)/2).
  • A056450 (program): a(n) = (3*2^n - (-2)^n)/2.
  • A056451 (program): Number of palindromes using a maximum of five different symbols.
  • A056452 (program): a(n) = 6^floor((n+1)/2).
  • A056453 (program): Number of palindromes of length n using exactly two different symbols.
  • A056454 (program): Number of palindromes of length n using exactly three different symbols.
  • A056455 (program): Palindromes using exactly four different symbols.
  • A056469 (program): Number of elements in the continued fraction for Sum_ k=0..n 1/2^2^k.
  • A056473 (program): Number of palindromic structures using exactly four different symbols.
  • A056486 (program): a(n) = (9*2^n + (-2)^n)/4 for n>0.
  • A056487 (program): a(n) = 5^(n/2) for n even, a(n) = 3*5^((n-1)/2) for n odd.
  • A056488 (program): Number of periodic palindromes using a maximum of six different symbols.
  • A056489 (program): Number of periodic palindromes using exactly three different symbols.
  • A056520 (program): a(n) = (n + 2)(2n^2 - n + 3)/6.
  • A056524 (program): Palindromes with even number of digits.
  • A056525 (program): Palindromes with odd number of digits.
  • A056526 (program): First differences of Flavius Josephus’s sieve.
  • A056527 (program): Numbers where iterated sum of digits of square settles down to a cyclic pattern (in fact 13, 16, 13, 16, …).
  • A056530 (program): Sequence remaining after third round of Flavius Josephus sieve; remove every fourth term of A047241.
  • A056531 (program): Sequence remaining after a fourth round of Flavius Josephus sieve; remove every fifth term of A056530.
  • A056533 (program): Even sieve: start with natural numbers, remove every 2nd term, remove every 4th term from what remains, remove every 6th term from what remains, etc.
  • A056541 (program): a(n) = 2n*a(n-1) + 1 with a(0)=0.
  • A056542 (program): a(n) = n*a(n-1) + 1, a(1) = 0.
  • A056543 (program): a(n) = n*a(n-1) - 1 with a(1)=1.
  • A056545 (program): a(n) = 4na(n-1) + 1 with a(0)=1.
  • A056546 (program): a(n) = 5na(n-1) + 1 with a(0)=1.
  • A056547 (program): a(n) = 6na(n-1) + 1 with a(0)=1.
  • A056548 (program): a(n) = Sum_ k>=1 round(n/k) where round(1/2) = 0.
  • A056549 (program): a(n) = Sum_ k>=1 round(n/k) where round(1/2)=1.
  • A056551 (program): Smallest cube divisible by n divided by largest cube which divides n.
  • A056552 (program): Powerfree kernel of cubefree part of n.
  • A056553 (program): Smallest 4th-power divisible by n divided by largest 4th-power which divides n.
  • A056554 (program): Powerfree kernel of 4th-powerfree part of n.
  • A056556 (program): First tetrahedral coordinate; repeat m (m+1)*(m+2)/2 times.
  • A056557 (program): Second tetrahedral coordinate.
  • A056558 (program): Third tetrahedral coordinate, i.e., tetrahedron with T(t,n,k)=k; succession of growing finite triangles with increasing values towards bottom right.
  • A056560 (program): Tetrahedron with T(t,n,k)=n-k; succession of growing finite triangles with increasing values towards bottom left.
  • A056570 (program): Third power of Fibonacci numbers (A000045).
  • A056571 (program): Fourth power of Fibonacci numbers A000045.
  • A056572 (program): Fifth power of Fibonacci numbers A000045.
  • A056573 (program): Sixth power of Fibonacci numbers A000045.
  • A056574 (program): Seventh power of Fibonacci numbers A000045.
  • A056576 (program): Highest k with 2^k <= 3^n.
  • A056577 (program): Difference between 3^n and highest power of 2 less than or equal to 3^n.
  • A056578 (program): a(n) = 1 + 2n + 3n^2 + 4n^3.
  • A056579 (program): 1+2n+3n^2+4n^3+5n^4.
  • A056585 (program): Eighth power of Fibonacci numbers A000045.
  • A056586 (program): Ninth power of Fibonacci numbers A000045.
  • A056587 (program): Tenth power of Fibonacci numbers A000045.
  • A056594 (program): Periodic sequence 1,0,-1,0,…; expansion of 1/(1 + x^2).
  • A056608 (program): Least prime factor of the n-th composite number.
  • A056615 (program): Binomial(2*n - 1, n - 1) - 1 (mod n^2).
  • A056616 (program): Numerator of binomial(2n,n)/(2n+1).
  • A056617 (program): Denominator of binomial(2n,n) / (2n+1).
  • A056624 (program): Number of unitary square divisors of n.
  • A056640 (program): At stage 1, start with a unit square. At each successive stage add 4*(n-1) new squares around outside with edge-to-edge contacts. Sequence gives number of squares (regardless of size) at n-th stage.
  • A056653 (program): Composite numbers together with 1 but excluding 4.
  • A056671 (program): 1 + the number of unitary and squarefree divisors of n = number of divisors of reduced squarefree part of n.
  • A056699 (program): First differences are 2,1,-2,3 (repeated).
  • A056737 (program): Minimum nonnegative integer m such that n = k*(k+m) for some positive integer k.
  • A056738 (program): Positions where 2’s occur in A056731.
  • A056771 (program): a(n) = a(-n) = 34*a(n-1) - a(n-2), and a(0)=1, a(1)=17.
  • A056788 (program): a(n) = n^n + (n-1)^(n-1).
  • A056791 (program): Weight of binary expansion of n + length of binary expansion of n.
  • A056792 (program): Minimal number of steps to get from 0 to n by (a) adding 1 or (b) multiplying by 2.
  • A056810 (program): Numbers whose fourth power is a palindrome.
  • A056811 (program): Number of primes not exceeding square root of n: primepi(sqrt(n)).
  • A056822 (program): Nearest integer to n^2/16.
  • A056827 (program): a(n) = floor(n^2/6).
  • A056829 (program): Nearest integer to n^2/6.
  • A056830 (program): Alternate digits 1 and 0.
  • A056832 (program): All a(n) = 1 or 2; a(1) = 1; get next 2^k terms by repeating first 2^k terms and changing last element so sum of first 2^(k+1) terms is odd.
  • A056833 (program): Nearest integer to n^2/7.
  • A056834 (program): a(n) = floor(n^2/7).
  • A056838 (program): a(n) = floor(n^2/9).
  • A056847 (program): Nearest integer to n - sqrt(n).
  • A056849 (program): Final digit of n^n.
  • A056854 (program): a(n) = Lucas(4*n).
  • A056864 (program): Nearest integer to n^2/10.
  • A056865 (program): a(n) = floor(n^2/10).
  • A056892 (program): a(n) = square excess of the n-th prime.
  • A056914 (program): a(n) = Lucas(4*n+1).
  • A056924 (program): Number of divisors of n that are smaller than sqrt(n).
  • A056925 (program): Largest integer power of n which divides product of divisors of n.
  • A056926 (program): a(n) = sqrt(n) if n is a square, otherwise 1.
  • A056927 (program): Difference between n^2 and largest prime less than n^2.
  • A056942 (program): Area of rectangle needed to enclose a non-touching spiral of length n on a square lattice.
  • A056943 (program): Unused area of rectangle needed to enclose a non-touching spiral of length n on a square lattice.
  • A056944 (program): Amount by which used area of rectangle needed to enclose a non-touching spiral of length n on a square lattice exceeds unused area.
  • A056955 (program): Euclid set of class 2 and modulus 3.
  • A056960 (program): Base 11 reversal of n (written in base 10).
  • A056961 (program): Base 12 reversal of n (written in base 10).
  • A056962 (program): Base 16 reversal of n (written in base 10).
  • A056964 (program): a(n) = n + reversal of digits of n.
  • A056965 (program): a(n) = n - (reversal of digits of n).
  • A056968 (program): 10^(n-1) modulo n.
  • A056969 (program): a(n) = 10^n modulo n.
  • A056973 (program): Number of blocks of 0,0 in the binary expansion of n.
  • A056974 (program): Number of blocks of 0, 0, 0 in the binary expansion of n.
  • A056981 (program): a(n) = A002596(n)^2.
  • A056982 (program): a(n) = 4^A005187(n). The denominators of the Landau constants.
  • A056991 (program): Numbers with digital root 1, 4, 7 or 9.
  • A056992 (program): Digital roots of square numbers A000290.
  • A056998 (program): Number of days in months of Islamic calendar.
  • A057003 (program): Write the natural numbers in groups: 1; 2,3; 4,5,6; 7,8,9,10; … and multiply the members of each group.
  • A057023 (program): Largest odd factor of (n-th prime-1); k when n-th prime is written as k*2^m+1 [with k odd].
  • A057024 (program): Largest odd factor of (n-th prime+1); k when n-th prime is written as k*2^m-1 [with k odd].
  • A057025 (program): Smallest prime of form (2n+1)*2^m+1 for some m.
  • A057029 (program): Central column of arrays in A057027 and A057028.
  • A057032 (program): Let P(n) of a sequence s(1), s(2), s(3), … be obtained by leaving s(1), …, s(n-1) fixed and forward-cyclically permuting every n consecutive terms thereafter; apply P(2) to 1, 2, 3, … to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. The limit of PS(n) as n -> oo is this sequence.
  • A057033 (program): Let P(n) of a sequence s(1),s(2),s(3),… be obtained by leaving s(1),…s(n-1) fixed and reverse-cyclically permuting every n consecutive terms thereafter; apply P(2) to 1,2,3,… to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. The limit of PS(n) is A057033.
  • A057036 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057036(n)=i(2n-1).
  • A057037 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057037(n)=j(2n-1).
  • A057038 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057038(n)=i(2n).
  • A057039 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057039(n)=j(2n).
  • A057040 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057040(n)=i(F(n)), where F(n) is the n-th Fibonacci number.
  • A057041 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057041(n)=j(F(n)), where F(n) is the n-th Fibonacci number.
  • A057042 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; the n-th Fibonacci number is in antidiagonal a(n).
  • A057043 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057043(n)=i(L(n)), where L(n) is the n-th Lucas number.
  • A057044 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057044(n)=j(L(n)), where L(n) is the n-th Lucas number.
  • A057046 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057046(n)=i(2^n).
  • A057047 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057047(n)=j(2^n).
  • A057049 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057049(n) = i(n^2).
  • A057050 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057050(n)=j(n^2).
  • A057052 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057052(n) = i(n^3).
  • A057053 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057053(n)=j(n^3).
  • A057054 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; n^3 is in antidiagonal a(n).
  • A057055 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057055(n)=i(C(n,3)).
  • A057057 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; C(n,3) is in antidiagonal a(n).
  • A057060 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057058(n)=i(n-th prime)).
  • A057061 (program): Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; …; each k is an R(i(k),j(k)) and A057058(n)=j(n-th prime)).
  • A057062 (program): Let R(i,j) be the infinite square array with antidiagonals 1; 2,3; 4,5,6; …; the n-th prime is in antidiagonal a(n).
  • A057063 (program): Let P(n) of a sequence s(1),s(2),s(3),… be obtained by leaving s(1),…,s(n) fixed and reverse-cyclically permuting every n consecutive terms thereafter; apply P(2) to 1,2,3,… to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. The limit of PS(n) is A057063.
  • A057064 (program): Let P(n) of a sequence s(1),s(2),s(3),… be obtained by leaving s(1),…,s(n) fixed and forward-cyclically permuting every n consecutive terms thereafter; apply P(2) to 1,2,3,… to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. The limit of PS(n) is A057064.
  • A057065 (program): a(n) = floor(n^n/2).
  • A057066 (program): Floor[4^4/n].
  • A057067 (program): a(n) = floor(5^5/n).
  • A057068 (program): floor[6^6/n].
  • A057069 (program): floor[7^7/n].
  • A057070 (program): floor[8^8/n].
  • A057071 (program): floor[9^9/n].
  • A057072 (program): floor[10^10/n].
  • A057073 (program): floor[11^11/n].
  • A057074 (program): floor[12^12/n].
  • A057076 (program): A Chebyshev or generalized Fibonacci sequence.
  • A057077 (program): Periodic sequence 1,1,-1,-1; expansion of (1+x)/(1+x^2).
  • A057078 (program): Periodic sequence 1,0,-1,…; expansion of (1+x)/(1+x+x^2).
  • A057079 (program): Periodic sequence: repeat [1,2,1,-1,-2,-1]; expansion of (1+x)/(1-x+x^2).
  • A057080 (program): Even-indexed Chebyshev U-polynomials evaluated at sqrt(10)/2.
  • A057083 (program): Scaled Chebyshev U-polynomials evaluated at sqrt(3)/2; expansion of 1/(1 - 3x + 3x^2).
  • A057084 (program): Scaled Chebyshev U-polynomials evaluated at sqrt(2).
  • A057085 (program): a(0)=0, a(1)=1; for n>1, a(n) = 9a(n-1) - 9a(n-2).
  • A057086 (program): Scaled Chebyshev U-polynomials evaluated at sqrt(10)/2.
  • A057087 (program): Scaled Chebyshev U-polynomials evaluated at i. Generalized Fibonacci sequence.
  • A057088 (program): Scaled Chebyshev U-polynomials evaluated at i*sqrt(5)/2. Generalized Fibonacci sequence.
  • A057089 (program): Scaled Chebyshev U-polynomials evaluated at i*sqrt(6)/2. Generalized Fibonacci sequence.
  • A057090 (program): Scaled Chebyshev U-polynomials evaluated at i*sqrt(7)/2. Generalized Fibonacci sequence.
  • A057091 (program): Scaled Chebyshev U-polynomials evaluated at i*sqrt(2). Generalized Fibonacci sequence.
  • A057092 (program): Scaled Chebyshev U-polynomials evaluated at i*3/2. Generalized Fibonacci sequence.
  • A057093 (program): Scaled Chebyshev U-polynomials evaluated at i*sqrt(10)/2. Generalized Fibonacci sequence.
  • A057137 (program): Concatenate next digit at right hand end (where the next digit after 9 is again 0).
  • A057138 (program): Add (n mod 10)*10^(n-1) to the previous term, with a(0) = 0.
  • A057147 (program): a(n) = n times sum of digits of n.
  • A057174 (program): a(n+3)=a(n)+a(n+1)-a(n+2), starting with 1,2,3.
  • A057198 (program): a(n) = (5*3^(n-1)+1)/2.
  • A057211 (program): Alternating runs of ones and zeroes, where the n-th run has length n.
  • A057212 (program): n-th run has length n.
  • A057227 (program): Smallest member of smallest set S(n) of positive integers containing n which satisfies “k is in S, iff 2k-1 is in S, iff 4k is in S”.
  • A057237 (program): Maximum k <= n such that 1, 2, …, k are all relatively prime to n.
  • A057334 (program): In A000120, replace each entry k with the k-th prime and replace 0 with 1.
  • A057347 (program): Leap years in the Islamic calendar starting year 1 AH (Anno Hegirae) = 622 CE (Common Era or AD). There are 11 leap years in a 30 year cycle.
  • A057349 (program): Leap years in the Hebrew Calendar starting in year 1 (3761 BCE). The leap year has an extra-month.
  • A057353 (program): a(n) = floor(3n/4).
  • A057354 (program): a(n) = floor(2*n/5).
  • A057355 (program): a(n) = floor(3*n/5).
  • A057356 (program): a(n) = floor(2*n/7).
  • A057357 (program): a(n) = floor(3*n/7).
  • A057358 (program): a(n) = floor(4*n/7).
  • A057359 (program): a(n) = floor(5*n/7).
  • A057360 (program): a(n) = floor(3*n/8).
  • A057361 (program): a(n) = floor(5*n/8).
  • A057362 (program): a(n) = floor(5*n/13).
  • A057363 (program): a(n) = floor(8*n/13).
  • A057364 (program): a(n) = floor(8*n/21).
  • A057365 (program): a(n) = floor(13*n/21).
  • A057366 (program): a(n) = floor(7*n/19).
  • A057367 (program): a(n) = floor(11*n/30).
  • A057427 (program): a(n) = 1 if n > 0, a(n) = 0 if n = 0; series expansion of x/(1-x).
  • A057428 (program): Sign(-n): a(n) = 1 if -n > 0, = -1 if -n < 0, = 0 if n = 0.
  • A057434 (program): a(n) = Sum_ k=1..n phi(k)^2.
  • A057521 (program): Powerful (1) part of n: if n = Product_i (pi^ei) then a(n) = Product_ i : ei > 1 (pi^ei); if n=bc^2d^3 then a(n)=c^2*d^3 when b is minimized.
  • A057524 (program): Number of 3 x n binary matrices without unit columns up to row and column permutations.
  • A057525 (program): Number of applications of f to reduce n to 1, where f(k) is the integer among k/2,(k+1)/4, (k+3)/4.
  • A057526 (program): Number of applications of f to reduce n to 1, where f(k) is the integer among k/2,(k-1)/4, (k+1)/4.
  • A057538 (program): Birthday set of order 5: numbers congruent to +/-1 modulo 2, 3, 4 and 5.
  • A057543 (program): Maximum cycle length (orbit size) in the rotation permutation of 2n non-crossing handshakes.
  • A057544 (program): Maximum cycle length (orbit size) in the rotation permutation of n+2 side polygon triangularizations.
  • A057552 (program): a(n) = Sum_ k=0..n C(2k+2,k).
  • A057566 (program): Number of collinear triples in a 3 X n rectangular grid.
  • A057569 (program): Numbers of the form k(5k+1)/2 or k(5k-1)/2.
  • A057570 (program): Numbers of the form n*(7n+-1)/2.
  • A057587 (program): Nonnegative numbers of form n*(n^2+-1)/2.
  • A057588 (program): Kummer numbers: -1 + product of first n consecutive primes.
  • A057590 (program): Numbers of the form n*(n^3+-1)/2.
  • A057627 (program): Number of nonsquarefree numbers not exceeding n.
  • A057651 (program): a(n) = (3 * 5^n - 1)/2.
  • A057656 (program): Number of points (x,y) in square lattice with (x-1/2)^2+y^2 <= n.
  • A057658 (program): a(n) = n(n+1)^2(n+2)^3(n+3)^2(n+4).
  • A057660 (program): a(n) = Sum_ k=1..n n/gcd(n,k).
  • A057661 (program): a(n) = Sum_ k=1..n lcm(n,k)/n.
  • A057666 (program): n(n+1)^2(n+2)(n+3)^2(n+4).
  • A057675 (program): 1 - (5/6)n + (5/2)n^2 + (10/3)*n^3 + n^4.
  • A057681 (program): a(n) = Sum_ j=0..floor(n/3) (-1)^jbinomial(n,3j).
  • A057682 (program): a(n) = Sum_ j=0..floor(n/3) (-1)^jbinomial(n,3j+1).
  • A057703 (program): a(n) = n(94 + 5n + 25n^2 - 5n^3 + n^4)/120.
  • A057711 (program): a(0)=0, a(1)=1, a(n) = n*2^(n-2) for n >= 2.
  • A057716 (program): The nonpowers of 2.
  • A057717 (program): The non-powers of 10.
  • A057721 (program): a(n) = n^4 + 3*n^2 + 1.
  • A057722 (program): a(n) = n^4 - 3*n^2 + 1.
  • A057728 (program): A triangular table of decreasing powers of two (with first column all ones).
  • A057744 (program): Expansion of (1-2x^3)/(1-2x-x^3+2*x^4).
  • A057769 (program): a(n) = 4n^4 + 8n^3 - 4n - 1 = (2n^2 - 1)(2n^2 + 4*n + 1).
  • A057773 (program): Sum_ i=1..n nu_2 ( prime(i) - 1), where prime(i) is the i-th prime and nu_2(m) = exponent of highest power of 2 dividing m.
  • A057780 (program): Multiples of 3 that are one less than a perfect square.
  • A057781 (program): a(n) = n^4+4 = (n^2-2n+2)(n^2+2n+2) = ((n-1)^2+1)((n+1)^2+1).
  • A057788 (program): Expansion of (1+x)/(1-x)^12.
  • A057813 (program): a(n) = (2n+1)(4n^2+4n+3)/3.
  • A057819 (program): a(0)=4, a(1)=9, a(n) = 4a(n-1) - a(n-2).
  • A057843 (program): a(n) = floor(n*tau^2) - 3, where tau = (1+sqrt(5))/2.
  • A057859 (program): Number of residue classes modulo n which contain a prime.
  • A057860 (program): Number of residue classes modulo n which contain only composite numbers.
  • A057862 (program): a(n) = 2^n mod Fibonacci(n).
  • A057863 (program): a(n) = Product_ k=1..n (2k-1)!!.
  • A057889 (program): Bit-reverse of n, including as many leading as trailing zeros.
  • A057901 (program): a(n) = 3^prime(n).
  • A057902 (program): a(n) = 5^prime(n).
  • A057918 (program): Number of pairs of numbers (a,b) each less than n where (a,b,n) is in geometric progression.
  • A057932 (program): a(n) = floor(10^(n+1)/81).
  • A057933 (program): Floor[(80/81)*10^n].
  • A057944 (program): Largest triangular number less than or equal to n; write m-th triangular number m+1 times.
  • A057945 (program): Number of triangular numbers needed to represent n with greedy algorithm.
  • A057947 (program): n has ambiguous representations in “bad hexadecimal”: numbers with the digit 1 followed by a digit less than 6.
  • A057960 (program): Number of base 5 (n+1)-digit numbers starting with a zero and with adjacent digits differing by one or less.
  • A057977 (program): GCD of consecutive central binomial coefficients: a(n) = gcd(A001405(n+1), A001405(n)).
  • A057979 (program): a(n) = 1 for even n and (n-1)/2 for odd n.
  • A058005 (program): a(n) = gcd(2n, binomial(2n, n)).
  • A058006 (program): Alternating factorials: 0! - 1! + 2! - … + (-1)^n n!
  • A058031 (program): a(n) = n^4 - 2n^3 + 3n^2 - 2*n + 1, the Alexander polynomial for reef and granny knots.
  • A058034 (program): Number of numbers whose cube root rounds to n.
  • A058038 (program): a(n) = Fibonacci(2n)Fibonacci(2*n+2).
  • A058060 (program): Number of distinct prime factors of d(n), the number of divisors of n.
  • A058061 (program): Number of prime factors (counted with multiplicity) of d(n), the number of divisors of n.
  • A058062 (program): Number of distinct prime factors of sigma(n), the sum of the divisors of n.
  • A058063 (program): Number of prime factors (when counted with multiplicity) of sigma(n), the sum of divisors of n.
  • A058065 (program): Complement of A057843.
  • A058066 (program): Floor(n*t), t = 1 + sqrt(5)/2.
  • A058126 (program): a(n) = n^n - n^2 with 0^0=1.
  • A058128 (program): a(1) = 1, a(n) = (n^n-n)/(n-1)^2 for n >= 2.
  • A058161 (program): Number of labeled cyclic groups with a fixed identity.
  • A058183 (program): Number of digits in concatenation of first n positive integers.
  • A058187 (program): Expansion of (1+x)/(1-x^2)^4: duplicated tetrahedral numbers.
  • A058195 (program): Areas of a sequence of right-angled figures described below.
  • A058200 (program): Coefficients of the highest power of r in a sequence of parametric solutions for the Diophantine equation x^3+y^3+z^3=1.
  • A058207 (program): Three steps forward, two steps back.
  • A058212 (program): a(n) = 1 + floor(n*(n-3)/6).
  • A058224 (program): Largest d such that the linear programming bound for quantum codes of length n is feasible for some real K>1.
  • A058261 (program): a(n) = n times the Collatz number of n (as given in A006577).
  • A058278 (program): Expansion of (1 - x^2)/(1 - x - x^3).
  • A058281 (program): Continued fraction for square root of e.
  • A058296 (program): Average of consecutive primes.
  • A058310 (program): (1/2)(n^2+n+2)(n^2+3*n+1).
  • A058319 (program): Coefficients (multiplied by 48) in Alternative Extended Simpson’s rule for numerical integration.
  • A058321 (program): Number of x such that phi(x) = 2^n.
  • A058331 (program): a(n) = 2*n^2 + 1.
  • A058333 (program): Number of 3 X 3 matrices with elements from [0,…,(n-1)] satisfying the condition that the middle element of each row or column is the difference of the two end elements (in absolute value).
  • A058344 (program): Difference between the sum of the odd aliquot divisors of n and the sum of the even aliquot divisors of n.
  • A058372 (program): a(n) = -(n + 1)(2n^2 + n - 12)/6.
  • A058373 (program): a(n) = (1/6)(2n - 3)(n + 2)(n + 1).
  • A058384 (program): Largest power of 2 which is a divisor of p(n)-1, where p(n) = n-th prime.
  • A058396 (program): Expansion of ((1-x)/(1-2*x))^3.
  • A058481 (program): a(n) = 3^n - 2.
  • A058482 (program): Number of 3 X n binary matrices with no zero rows or columns.
  • A058581 (program): (4n^2+2n-3)(2n-1)*n/3.
  • A058582 (program): Expansion of (1+3x+4x^2)/(1-4x^2+4x^4).
  • A058633 (program): Partial sums of the Collatz sequence.
  • A058642 (program): Number of unlabeled graphs with n edges, no nodes of degree 1 or 2, no multiple edges and no cut nodes, under “series-equivalence”.
  • A058645 (program): a(n) = 2^(n-3)n^2(n+3).
  • A058656 (program): a(n) = gcd(n+1, phi(n)).
  • A058665 (program): a(n) = gcd(n+1, n-Phi(n)).
  • A058667 (program): 2^(n-2)n(n+2)!/3.
  • A058738 (program): a(n) = floor(n*exp(n)).
  • A058748 (program): a(n) = round(n*exp(n)).
  • A058749 (program): a(n) = ceiling(n*exp(n)).
  • A058764 (program): Smallest number x such that cototient(x) = 2^n.
  • A058794 (program): Row 3 of A007754.
  • A058795 (program): Row 4 of A007754.
  • A058798 (program): a(n) = n*a(n-1) - a(n-2) with a(0) = 0, a(1) = 1.
  • A058799 (program): Column 2 of A007754.
  • A058809 (program): The sequence lambda(3,n), where lambda is defined in A055203. Number of ways of placing n identifiable positive intervals with a total of exactly three starting and/or finishing points.
  • A058842 (program): From Renyi’s “beta expansion of 1 in base 3/2”: sequence gives a(1), a(2), … where x(n) = a(n)/2^n, with 0 < a(n) < 2^n, a(1) = 1, a(n) = 3*a(n-1) modulo 2^n.
  • A058877 (program): Number of labeled acyclic digraphs with n nodes containing exactly n-1 points of in-degree zero.
  • A058888 (program): Number of terms in the set invphi(2*p(n)), where p(n) is the n-th prime.
  • A058895 (program): a(n) = n^4 - n.
  • A058896 (program): a(n) = 4^n - 4.
  • A058919 (program): a(n) = n^4/2 - n^3 + 3n^2/2 - n + 1.
  • A058920 (program): a(n) = 2n^4 + 2n^3 + 3n^2 + 2n + 1.
  • A058922 (program): a(n) = n*2^n - 2^n.
  • A058923 (program): a(n) = binomial(n,0) - binomial(n,2) + binomial(n,4).
  • A058932 (program): Number of unlabeled claw-free cubic graphs with 2n nodes and connectivity 1.
  • A058937 (program): Maximal exponent of x in all terms of Somos polynomial of order n.
  • A058962 (program): a(n) = 2^(2n)(2*n+1).
  • A058966 (program): a(3) = 1, otherwise a(n) = n*2^(n-3) - 2^(n-2) - 2.
  • A058968 (program): a(n) = 2^n + 2^(n - 1) - n - 8.
  • A058974 (program): a(n) = 0 if n = 1 or a prime, otherwise a(n) = s + a(s) iterated until no change occurs, where s (A008472) is sum of distinct primes dividing n.
  • A058986 (program): Sorting by prefix reversal (or “flipping pancakes”). You can only reverse segments that include the initial term of the current permutation; a(n) is the number of reversals that are needed to transform an arbitrary permutation of n letters to the identity permutation.
  • A058992 (program): Gossip Problem: there are n people and each of them knows some item of gossip not known to the others. They communicate by telephone and whenever one person calls another, they tell each other all that they know at that time. How many calls are required before each gossip knows everything?
  • A059009 (program): Numbers having an odd number of zeros in their binary expansion.
  • A059010 (program): Natural numbers having an even number of nonleading zeros in their binary expansion.
  • A059011 (program): Odd number of 0’s and 1’s in binary expansion.
  • A059013 (program): Odd number of 0’s and even number of 1’s in binary expansion.
  • A059015 (program): Total number of 0’s in binary expansions of 0, …, n.
  • A059016 (program): Number of 0’s in binary expansion of Fibonacci(n).
  • A059018 (program): Write 10*n in base 4; a(n) = sum of digits mod 4.
  • A059020 (program): Number of 2 X n checkerboards (with at least one red square) in which the set of red squares is edge connected.
  • A059029 (program): a(n) = n if n is even, 2*n + 1 if n is odd.
  • A059030 (program): Fourth main diagonal of A059026: a(n) = B(n+3,n) = lcm(n+3,n)/(n+3) + lcm(n+3,n)/n - 1 for all n >= 1.
  • A059031 (program): Fifth main diagonal of A059026: a(n) = B(n+4,n) = lcm(n+4,n)/(n+4) + lcm(n+4,n)/n - 1 for all n >= 1.
  • A059036 (program): In a triangle of numbers (such as that in A059032, A059033, A059034) how many entries lie above position (n,k)? Answer: T(n,k) = (n+1)*(k+1)-1 (n >= 0, k >= 0).
  • A059100 (program): a(n) = n^2 + 2.
  • A059116 (program): The sequence lambda(4,n), where lambda is defined in A055203. Number of ways of placing n identifiable positive intervals with a total of exactly four starting and/or finishing points.
  • A059125 (program): A self-generated dragon-like folding sequence.
  • A059132 (program): A hierarchical sequence (W2 2 c - see A059126).
  • A059133 (program): A hierarchical sequence (S(W2 2 c) - see A059126).
  • A059134 (program): A hierarchical sequence (W2 3 c - see A059126).
  • A059137 (program): A hierarchical sequence (W3 2,2 cc - see A059126).
  • A059138 (program): A hierarchical sequence (S(W3 2,2 cc) - see A059126).
  • A059139 (program): A hierarchical sequence (W2 2 *c - see A059126).
  • A059140 (program): A hierarchical sequence (S(W2 2 *c) - see A059126).
  • A059141 (program): A hierarchical sequence (W2 3 *c - see A059126).
  • A059142 (program): A hierarchical sequence (S(W2 3 *) - see A059126).
  • A059144 (program): A hierarchical sequence (W3 2,2 *cc - see A059126).
  • A059145 (program): A hierarchical sequence (S(W3 2,2 *cc) - see A059126).
  • A059152 (program): A hierarchical sequence (W’2 2 c - see A059126).
  • A059153 (program): a(n) = 2^(n+2)*(2^(n+1)-1).
  • A059154 (program): A hierarchical sequence (W’2 3 c - see A059126).
  • A059155 (program): A hierarchical sequence (S(W’2 3 c) - see A059126).
  • A059157 (program): A hierarchical sequence (W’3 2,2 cc - see A059126).
  • A059158 (program): A hierarchical sequence (S(W’3 2,2 cc) - see A059126).
  • A059159 (program): A hierarchical sequence (W’2 2 *c) - see A059126).
  • A059161 (program): A hierarchical sequence (W’2 3 *c - see A059126).
  • A059162 (program): A hierarchical sequence (S(W’2 3 *c) - see A059126).
  • A059164 (program): A hierarchical sequence (W’3 2,2 *cc - see A059126).
  • A059165 (program): a(n) = (n+1)*2^(n+4).
  • A059169 (program): Number of partitions of n into 3 parts which form the sides of a nondegenerate isosceles triangle.
  • A059171 (program): Size of largest conjugacy class in S_n, the symmetric group on n symbols.
  • A059173 (program): Maximal number of regions into which 4-space can be divided by n hyper-spheres.
  • A059174 (program): Maximal number of regions into which 5-space can be divided by n hyper-spheres.
  • A059193 (program): Engel expansion of 1/e = 0.367879… .
  • A059204 (program): Number of non-unimodal permutations of n items (i.e., those which do not simply go up for the first part and then down for the rest, but at some point go down then up).
  • A059222 (program): Minimal number of disjoint edge-paths into which the graph of the n-ary cube can be partitioned.
  • A059224 (program): a(n) = 2^(n-3)(n + 3)(2*n - 3).
  • A059249 (program): Tersum n + (n-1); write n and n-1 in base 3 and add mod 3 with no carries.
  • A059255 (program): Both sum of n+1 consecutive squares and sum of the immediately following n consecutive squares.
  • A059268 (program): Concatenate subsequences [2^0, 2^1, …, 2^n] for n = 0, 1, 2, …
  • A059270 (program): Numbers which are both the sum of n+1 consecutive integers and the sum of the n immediately higher consecutive integers.
  • A059288 (program): a(n) = binomial(2*n,n) mod n.
  • A059289 (program): a(n) = 1 + (binomial(2n,n) mod n).
  • A059292 (program): a(n) = n + 2 - (number of divisors of n).
  • A059293 (program): a(n) = round(n(5n - 14)/12) + 1.
  • A059302 (program): A diagonal of A008296.
  • A059304 (program): a(n) = 2^n * (2*n)! / (n!)^2.
  • A059325 (program): Numbers n such that 6n + 5 is prime.
  • A059328 (program): Table T(n,k) = T(n - 1,k) + T(n,k - 1) + T(n - 1,k)*T(n,k - 1) starting with T(0,0)=1, read by antidiagonals.
  • A059329 (program): Number of 3 X 3 matrices, with elements from 0,…,n , having the property that the middle element of each of the eight 3-element horizontal, vertical and diagonal lines equals the average of the two end elements.
  • A059332 (program): Determinant of n X n matrix A defined by A[i,j] = (i+j-1)! for 1 <= i,j <= n.
  • A059387 (program): Jordan function J_n(6) (see A059379).
  • A059396 (program): Number of primes less than square root of n-th prime; i.e., number of trial divisions by smaller primes to show that n-th prime is indeed prime.
  • A059403 (program): Quarter-squared applied twice.
  • A059409 (program): a(n) = 4^n * (2^n - 1).
  • A059410 (program): J_n(9) (see A059379).
  • A059421 (program): A diagonal of A059419.
  • A059426 (program): First differences of A026273.
  • A059428 (program): Number of points of rotation in a prime block spiral.
  • A059448 (program): The parity of the number of zero digits when n is written in binary.
  • A059480 (program): a(0) = a(1) = 1; a(n) = a(n-1) + (n+1)*a(n-2).
  • A059481 (program): Triangle T(n,k) = binomial(n+k-1,k), 0 <= k <= n, read by rows.
  • A059482 (program): a(0)=1, a(n) = a(n-1) + 8*10^(n-1).
  • A059502 (program): a(n) = (3nF(2n-1) + (3-n)*F(2n))/5 where F() = Fibonacci numbers A000045.
  • A059517 (program): The sequence A059515(3,n). Number of ways of placing n identifiable nonnegative intervals with a total of exactly three starting and/or finishing points.
  • A059532 (program): Beatty sequence for 1 + Pi.
  • A059542 (program): Beatty sequence for 1 + 1/log(2).
  • A059549 (program): Beatty sequence for 1 + 1/log(10).
  • A059557 (program): Beatty sequence for 1 + gamma^2, (gamma is the Euler-Mascheroni constant A001620).
  • A059558 (program): Beatty sequence for 1 + 1/gamma^2.
  • A059570 (program): Number of fixed points in all 231-avoiding involutions in S_n.
  • A059582 (program): First differences give digits of Pi = 3.1415926…
  • A059591 (program): Squarefree part of n^2+1.
  • A059592 (program): Square-full part of n^2+1.
  • A059599 (program): Expansion of (3+x)/(1-x)^6.
  • A059600 (program): Expansion of (1+6*x+x^2)/(1-x)^8.
  • A059601 (program): Expansion of (1+10x+5x^2)/(1-x)^10.
  • A059602 (program): Expansion of (5+10*x+x^2)/(1-x)^10.
  • A059605 (program): a(n) = (1/3!)(n^3 + 24n^2 + 107*n + 90), compare A059604.
  • A059620 (program): Colors of the 88 keys of the standard piano: white keys = 0, black keys = 1, start with A0 = the 0th key.
  • A059648 (program): a(n) = [[(k^2)n]-(k[k*n])], where k = sqrt(2) and [] is the floor function.
  • A059672 (program): Sum of binary numbers with n 1’s and one (possibly leading) 0.
  • A059673 (program): Sum of binary numbers with n 1’s and one (non-leading) 0.
  • A059721 (program): Mean of first six positive powers of n, i.e., (n + n^2 + n^3 + n^4 + n^5 + n^6)/6.
  • A059722 (program): a(n) = n(2n^2 - 2*n + 1).
  • A059727 (program): a(n) = Fibonacci(n)*(Fibonacci(n) + 1).
  • A059734 (program): Carryless 11^n base 10; a(n) is carryless sum of 10*a(n-1) and a(n-1).
  • A059772 (program): Smallest prime p such that n is a solution mod p of x^2 = 2, or 0 if no such prime exists.
  • A059786 (program): Smallest prime after 2*(n-th prime).
  • A059787 (program): Distance between 2*(n-th prime) and next prime.
  • A059788 (program): a(n) = largest prime < 2*prime(n).
  • A059789 (program): Distance of 2*Prime[n] from previous prime.
  • A059793 (program): Stationary value of quotient in the continued fraction expansion of sqrt(prime) when the quotient-cycle-length = 1.
  • A059811 (program): Let g_n be the ball packing n-width for the manifold torus X interval; sequence gives numerator of (g_n/Pi)^2.
  • A059826 (program): a(n) = (n^2 - n + 1)*(n^2 + n + 1).
  • A059827 (program): Cubes of triangular numbers: (n*(n+1)/2)^3.
  • A059830 (program): a(n) = n^6 + n^4 + n^2 + 1.
  • A059833 (program): “Madonna’s Sequence”: add 1 (mod 10) to each digit of Pi.
  • A059834 (program): Sum of squares of entries of Wilkinson’s eigenvalue test matrix of order 2n+1.
  • A059837 (program): Diagonal T(s,s) of triangle A059836.
  • A059839 (program): a(n) = n^8 + n^6 + n^4 + n^2 + 1.
  • A059840 (program): a(n) = F(n)F(n-1) if n odd otherwise F(n)F(n-1)-1, where F = Fibonacci numbers A000045.
  • A059841 (program): Period 2: Repeat [1,0]. a(n) = 1 - (n mod 2).
  • A059845 (program): a(n) = n(3n + 11)/2.
  • A059851 (program): a(n) = n - floor(n/2) + floor(n/3) - floor(n/4) + … (this is a finite sum).
  • A059855 (program): Period of continued fraction for sqrt(n^2+4), n >= 1.
  • A059859 (program): Sum of squares of first n quarter-squares (A002620).
  • A059860 (program): a(n) = binomial(n+1, 2)^5.
  • A059867 (program): Number of irreducible representations of the symmetric group S_n that have odd degree.
  • A059893 (program): Reverse the order of all but the most significant bit in binary expansion of n: if n = 1ab..yz then a(n) = 1zy..ba.
  • A059894 (program): Complement and reverse the order of all but the most significant bit in binary expansion of n. n = 1ab..yz -> 1ZY..BA = a(n), where A = 1-a, B = 1-b, … .
  • A059924 (program): Write the numbers from 1 to n^2 in a spiraling square; a(n) is the total of the sums of the two diagonals.
  • A059929 (program): a(n) = Fibonacci(n)*Fibonacci(n+2).
  • A059937 (program): Sum of binary numbers with n 1’s and two (possibly leading) 0’s.
  • A059938 (program): Sum of binary numbers with n 1’s and two (non-leading) 0’s.
  • A059939 (program): a(n) = floor(log_2(n+1) - 1).
  • A059944 (program): Denominators of Maclaurin series coefficients for 2cos(x/sqrt(3) + arctan(-sqrt(3))) = cos(x/sqrt(3)) + sqrt(3)sin(x/sqrt(3)).
  • A059952 (program): Ordering of a deck of 52 cards after an in-shuffle.
  • A059953 (program): Ordering of a deck of 52 cards after an out-shuffle.
  • A059957 (program): Sum of distinct prime factors of n and n+1, or number of prime factors of n(n+1) or of lcm(n,n+1).
  • A059967 (program): Number of 9-ary trees.
  • A059968 (program): 10-ary trees.
  • A059974 (program): a(n)=a(p)+a(q) where p and q are the two primes less than n and closest to n; with a(1)=1, a(2)=1.
  • A059975 (program): a(n) is the least number of prime factors (counted with multiplicity) of any integer with n divisors.
  • A059977 (program): a(n) = binomial(n+2, 2)^4.
  • A059978 (program): a(n) = binomial(n+2,n)^6.
  • A059979 (program): Number of 7-dimensional cage assemblies.
  • A059980 (program): Number of 8-dimensional cage assemblies.
  • A059986 (program): Number of rods required to make a 3-D cube of side length n.
  • A059988 (program): a(n) = (10^n - 1)^2.
  • A059989 (program): Numbers n such that 3n+1 and 4n+1 are both squares.
  • A059990 (program): Number of points of period n under the dual of the map x->2x on Z[1/6].
  • A059991 (program): a(n) = 2^(n-2^ord_2(n)) (or 2^(n-A006519(n))).
  • A059993 (program): Pinwheel numbers: a(n) = 2n^2 + 6n + 1.
  • A059995 (program): Drop the final digit of n.
  • A059997 (program): a(n) = (n/2)(n + 1)(3*n + 11).
  • A060008 (program): a(n) = 9binomial(n,4) = 3n(n-1)(n-2)(n-3)/8.
  • A060011 (program): Schizophrenic sequence: these are the repeating digits in the decimal expansion of sqrt(f(2n+1)), where f(m) = A014824(m).
  • A060013 (program): New record highs reached in A060000.
  • A060018 (program): a(n) = floor(2*sqrt(n-2)).
  • A060019 (program): a(n) = floor(2*sqrt(prime(n)-2)) where prime(n) = n-th prime.
  • A060068 (program): Divide n! by largest power of n which will leave the result an integer.
  • A060072 (program): a(n) = (n^(n-1) - 1)/(n-1) for n>1, a(1) = 0.
  • A060073 (program): a(n) = (n^(n-1)-1)/(n-1)^2.
  • A060091 (program): Number of 4-block ordered bicoverings of an unlabeled n-set.
  • A060099 (program): G.f.: 1/((1-x^2)^3*(1-x)^4).
  • A060104 (program): Fifth column (m=4) of triangle A060102.
  • A060106 (program): Numbers that are congruent to 1, 4, 6, 9, 11 mod 12. The Ebony keys on a piano, start with A0 = the 0th key.
  • A060107 (program): Numbers that are congruent to 0, 2, 3, 5, 7, 8, 10 mod 12. The ivory keys on a piano, start with A0 = the 0th key.
  • A060108 (program): Sequence of sums based on primes = 7 mod 8.
  • A060130 (program): Number of nonzero digits in factorial base representation (A007623) of n; minimum number of transpositions needed to compose each permutation in the lists A060117 & A060118.
  • A060143 (program): a(n) = floor(n/tau), where tau = (1 + sqrt(5))/2.
  • A060144 (program): a(n) = floor(n/(1+tau)), or equivalently floor(n/(tau)^2), where tau is the golden ratio (A001622).
  • A060145 (program): a(n) = floor(n/tau) - floor(n/(1 + tau)).
  • A060150 (program): a(0) = 1; for n > 0, binomial(2n-1, n-1)^2.
  • A060156 (program): a(n) = floor(10^n/n).
  • A060157 (program): Number of permutations of [n] with 3 sequences.
  • A060161 (program): a(n) = 2^n - 1 + 2*Fibonacci(n-1).
  • A060163 (program): a(n) = (n^3 + 5*n + 18)/6.
  • A060182 (program): a(0) = 1, a(1) = 5, a(2) = 13; a(n) = 2*a(n-1) + 2, n > 2.
  • A060188 (program): A column and diagonal of A060187.
  • A060191 (program): Union_i p(4i), p(4i+1), where p(k) = k-th prime.
  • A060192 (program): Union_i p(4i+2), p(4i+3), where p(k) = k-th prime.
  • A060195 (program): a(n) = 8^(n-1)*(2^n-1).
  • A060196 (program): Decimal expansion of 1 + 1/(13) + 1/(135) + 1/(1357) + …
  • A060197 (program): Start at n, repeatedly apply pi(x) until reach 0; a(n) = number of steps to reach 0.
  • A060226 (program): a(n) = n^n - n*(n-1)^(n-1).
  • A060236 (program): If n mod 3 = 0 then a(n) = a(n/3), otherwise a(n) = n mod 3.
  • A060242 (program): a(n) = (2^n - 1)*(4^n - 1).
  • A060264 (program): First prime after 2n.
  • A060265 (program): Largest prime less than 2n.
  • A060266 (program): Difference between 2n and the following prime.
  • A060275 (program): At least two unordered triples of positive numbers have sum n and equal products.
  • A060286 (program): 2^(p-1)*(2^p-1) where p is a prime.
  • A060296 (program): Number of regular convex polytopes in n-dimensional space, or -1 if the number is infinite.
  • A060300 (program): a(n) = (2n(n+1))^2.
  • A060308 (program): Largest prime <= 2n.
  • A060343 (program): Smallest prime which is the sum of n composite numbers.
  • A060348 (program): a(n) = n^n * (n^2 - 1)/24.
  • A060352 (program): a(n) = n*3^n - 1.
  • A060354 (program): The n-th n-gonal number: a(n) = n(n^2-3n+4)/2.
  • A060365 (program): Multiples of one thousand which are described by single words in American English.
  • A060366 (program): Powers of one thousand which are described by single words in dated British English usage, extended by using “-ard” beyond 10^9.
  • A060371 (program): a(n) = (prime(n) - 1)! + 1.
  • A060378 (program): Even-odd sieve.
  • A060389 (program): a(1)=p_1, a(2)=p_1 + p_1p_2, a(3)=p_1 + p_1p_2 + p_1p_2p_3, … where p_i is the i-th prime.
  • A060416 (program): a(n) = n*4^n - 1.
  • A060418 (program): Largest decimal digit in n-th prime.
  • A060420 (program): Least decimal digit in n-th prime.
  • A060422 (program): Number of acute triangles made from vertices of a regular n-gon.
  • A060423 (program): Number of obtuse triangles made from vertices of a regular n-gon.
  • A060429 (program): a(n) = 4*prime(n)^2+1.
  • A060431 (program): Number of cubefree numbers <= n.
  • A060432 (program): Partial sums of A002024.
  • A060446 (program): Number of ways to color vertices of a pentagon using <= n colors, allowing rotations and reflections.
  • A060453 (program): Dot product of the squares and the quarter-squares: a(n) = sum(i=1..n, i^2 * floor(i^2/4)).
  • A060458 (program): Maximal value seen in the final n decimal digits of 2^j for all values of j.
  • A060459 (program): a(n) = (n*(n+1))^3.
  • A060460 (program): Consider the final n decimal digits of 2^j for all values of j. They are periodic. Sequence gives position (or phase) of the maximal value seen in these n digits.
  • A060462 (program): Integers k such that k! is divisible by k*(k+1)/2.
  • A060464 (program): Numbers that are not congruent to 4 or 5 mod 9.
  • A060469 (program): Smallest positive a(n) such that number of solutions to a(n) = a(j)+a(k) j<k<n is one or less.
  • A060470 (program): Smallest positive a(n) such that number of solutions to a(n)=a(j)+a(k) j<k<n is two or less.
  • A060471 (program): Smallest positive a(n) such that number of solutions to a(n)=a(j)+a(k) j<k<n is three or less.
  • A060482 (program): New record highs reached in A060030.
  • A060488 (program): Number of 4-block ordered tricoverings of an unlabeled n-set.
  • A060493 (program): A diagonal of A036969.
  • A060494 (program): a(n) = floor(n^4/64).
  • A060505 (program): a(n) = floor(2^n/(n^2)).
  • A060509 (program): Largest power of n not exceeding 2^n.
  • A060510 (program): Alternating with hexagonal stutters: if n is hexagonal (2k^2 - k, i.e., A000384) then a(n)=a(n-1), otherwise a(n) = 1 - a(n-1).
  • A060511 (program): Hexagonal excess: smallest amount by which n exceeds a hexagonal number (2k^2-k, A000384).
  • A060531 (program): 9th binomial transform of (1,0,1,0,1,…), A059841.
  • A060532 (program): Number of ways to color vertices of a heptagon using <= n colors, allowing rotations and reflections.
  • A060541 (program): C(4n,4).
  • A060542 (program): a(n) = (1/6)multinomial(3n;n,n,n).
  • A060544 (program): Centered 9-gonal (also known as nonagonal or enneagonal) numbers. Every third triangular number, starting with a(1)=1.
  • A060545 (program): a(n) = C(n^2,n)/n.
  • A060546 (program): a(n) = 2^ceiling(n/2).
  • A060547 (program): a(n) is the number of patterns, invariant under 120 degree rotations, that may appear in a top-down equilateral triangular arrangement of closely packed black and white cells satisfying the local matching rule of Pascal’s triangle modulo 2, where n is the number of cells in each edge of the arrangement.
  • A060548 (program): a(n) is the number of D3-symmetric patterns that may be formed with a top-down equilateral triangular arrangement of closely packed black and white cells satisfying the local matching rule of Pascal’s triangle modulo 2, where n is the number of cells in each edge of the arrangement. The matching rule is such that any elementary top-down triangle of three neighboring cells in the arrangement contains either one or three white cells.
  • A060557 (program): Row sums of triangle A060556.
  • A060561 (program): Number of ways to color vertices of a 9-gon using <= n colors, allowing rotations and reflections.
  • A060566 (program): a(n) = n^2 - 79*n + 1601.
  • A060571 (program): Tower of Hanoi: the optimal way to move an even number of disks from peg 0 to peg 2 or an odd number from peg 0 to peg 1 is on move n to move disk A001511 from peg A060571 (here) to peg A060572.
  • A060572 (program): Tower of Hanoi: the optimal way to move an even number of disks from peg 0 to peg 2 or an odd number from peg 0 to peg 1 is on move n to move disk A001511 from peg A060571 to peg A060572 (here).
  • A060573 (program): Tower of Hanoi: using the optimal way to move an even number of disks from peg 0 to peg 2 or an odd number from peg 0 to peg 1, a(n) is the smallest disk on peg 0 after n moves.
  • A060576 (program): Number of homeomorphically irreducible general graphs on 1 labeled node and with n edges.
  • A060577 (program): Number of homeomorphically irreducible general graphs on 2 labeled nodes and with n edges.
  • A060582 (program): If the final digit of n in base 3 is the same as a([n/3]) then this digit, otherwise a(n)= mod 3-sum of these two digits, with a(0)=0.
  • A060584 (program): Compare ultimate and penultimate digits of n base 3, i.e., 0 if n mod 3 = floor(n/3) mod 3, 1 otherwise; also 0 if (n mod 9) is a multiple of 4, 1 otherwise.
  • A060588 (program): If the final two digits of n written in base 3 are the same then this digit, otherwise mod 3-sum of these two digits.
  • A060589 (program): a(n) = 2(2^n-1)3^(n-1).
  • A060590 (program): Numerator of the expected time to finish a random Tower of Hanoi problem with n disks using optimal moves.
  • A060593 (program): a(n) is the number of ways that a cycle of length 2n+1 in the symmetric group S_(2n+1) can be decomposed as the product of two cycles of length 2n+1.
  • A060602 (program): Number of d-dimensional tilings of unary zonotopes. The zonotope Z(D,d) is the projection of the D-dimensional hypercube onto the d-dimensional space and the tiles are the projections of the d-dimensional faces of the hypercube. Here the codimension, i.e., D-d, is constant = 3 and d varies from 0 to …
  • A060603 (program): Number of ways of expressing an n-cycle in the symmetric group S_n as a product of n+1 transpositions.
  • A060604 (program): a(n) = binomial(prime(n), n) where prime(n) = n-th prime.
  • A060605 (program): a(n) = sum of lengths of the iteration sequences of Euler totient function from 1 to n.
  • A060606 (program): The n-th term is the sum of lengths of iteration chains to get fixed points(=1) for the Euler totient function from 1 to n.
  • A060607 (program): Number of iterations of phi(x) at prime(n) needed to reach 1.
  • A060620 (program): Average of the first n primes rounded down.
  • A060621 (program): Number of flips between the d-dimensional tilings of the unary zonotope Z(D,d). Here the codimension D-d is equal to 3 and d varies.
  • A060626 (program): Number of right triangles of a given area required to form successively larger squares.
  • A060632 (program): a(n) = 2^wt(floor(n/2)) (i.e., 2^A000120(floor(n/2)), or A001316(floor(n/2))).
  • A060633 (program): Surround numbers of an n X 1 rectangle.
  • A060635 (program): a(n) is the number of 2 X 1 domino tilings of the set S in the plane R^2 consisting of the union of the following two rectangles: rectangle1: x <= n, y <= 1, rectangle2: x <= 1, y <= n.
  • A060641 (program): Surround numbers of a length 2n zig-zag.
  • A060644 (program): a(n) = floor((n+1)^(n+1)/n^n).
  • A060645 (program): a(0) = 0, a(1) = 4, then a(n) = 18*a(n-1) - a(n-2).
  • A060646 (program): Bonse sequence: a(n) = minimal j such that n-j+1 < prime(j).
  • A060647 (program): Number of alpha-beta evaluations in a tree of depth n and branching factor b=3.
  • A060655 (program): Pack n integer-sided rectangles into the smallest possible square so that no sides of the rectangle are the same. Sequence gives the side of the smallest square.
  • A060656 (program): a(n) = 2a(n-1)a(n-2)/a(n-3), with a(0)=a(1)=1.
  • A060659 (program): a(n)= smallest number of squares on a checkerboard that has exactly n domino tilings.
  • A060677 (program): Number of linear n-celled polyominoes, those with the property that a line can be drawn that intersects the interior of every cell.
  • A060681 (program): Largest difference between consecutive divisors of n (ordered by size).
  • A060685 (program): Largest difference between consecutive divisors (ordered by size) of 2n+1.
  • A060690 (program): a(n) = binomial(2^n + n - 1, n).
  • A060706 (program): For n >= 1 a(n) is the size of the conjugacy class in the symmetric group S_(4n) consisting of permutations whose cycle decomposition is a product of n disjoint 4-cycles.
  • A060715 (program): Number of primes between n and 2n exclusive.
  • A060747 (program): a(n) = 2*n - 1.
  • A060762 (program): Number of conjugacy classes (the same as the number of irreducible representations) in the dihedral group with 2n elements.
  • A060775 (program): The greatest divisor d n such that d < n/d, with a(1) = 1.
  • A060783 (program): Number of conics which pass through 3 points and are bitangent to a general curve of order n.
  • A060784 (program): Number of double tangents of order n.
  • A060785 (program): a(n) = 3(n-2)(5*n -11).
  • A060787 (program): a(n) = 18(n-2)(2*n-5).
  • A060788 (program): a(n) = 9(n-2)^2 * (n^2 - 2n - 1).
  • A060789 (program): a(n) = n / (gcd(n,2) * gcd(n,3)).
  • A060791 (program): a(n) = n / gcd(n,5).
  • A060798 (program): Numbers k such that difference between the upper and lower central divisors of k is 1.
  • A060800 (program): a(n) = p^2 + p + 1 where p runs through the primes.
  • A060801 (program): Invert transform of odd numbers: a(n) = Sum_ k=1..n (2k+1)a(n-k), a(0)=1.
  • A060805 (program): Numerators of special continued fraction for 2*zeta(3).
  • A060806 (program): Denominators of special continued fraction for 2*zeta(3).
  • A060816 (program): a(0) = 1; a(n) = (5*3^(n-1) - 1)/2 for n > 0.
  • A060818 (program): a(n) = 2^(floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + …).
  • A060819 (program): a(n) = n / gcd(n,4).
  • A060820 (program): (2n-1)^2 + (2n)^2.
  • A060823 (program): 4-wave sequence beginning with 2’s with middles dropped.
  • A060828 (program): Size of the Sylow 3-subgroup of the symmetric group S_n.
  • A060831 (program): a(n) = Sum_ k=1..n (number of odd divisors of k) (cf. A001227).
  • A060832 (program): a(n) = Sum_ k>0 floor(n/k!).
  • A060834 (program): a(n) = 6n^2 + 6n + 31.
  • A060836 (program): Number of permutations of n letters where exactly 5 change position.
  • A060851 (program): a(n) = (2n-1) * 3^(2n-1).
  • A060862 (program): a(n) = 0 if n is deficient, 1 if n is abundant, 2 if n is perfect.
  • A060865 (program): a(n) is the exact power of 2 that divides the n-th Fibonacci number (A000045).
  • A060867 (program): a(n) = (2^n - 1)^2.
  • A060868 (program): Number of n X n matrices over GF(3) with rank 1.
  • A060869 (program): Number of n X n matrices over GF(4) with rank 1.
  • A060870 (program): Number of n X n matrices over GF(5) with rank 1.
  • A060871 (program): Number of n X n matrices over GF(7) with rank 1.
  • A060872 (program): Sum of dd’ over all unordered pairs (d,d’) with dd’ = n.
  • A060880 (program): Compositorial numbers (A036691) - 1.
  • A060882 (program): a(n) = n-th primorial (A002110) minus next prime.
  • A060883 (program): a(n) = n^6 + n^3 + 1.
  • A060884 (program): a(n) = n^4 - n^3 + n^2 - n + 1.
  • A060885 (program): a(n) = Sum_ j=0..10 n^j.
  • A060886 (program): a(n) = n^4 - n^2 + 1.
  • A060887 (program): a(n) = Sum_ j=0..12 n^j.
  • A060888 (program): a(n) = n^6 - n^5 + n^4 - n^3 + n^2 - n + 1.
  • A060890 (program): n^8 + 1.
  • A060891 (program): a(n) = n^6 - n^3 + 1.
  • A060892 (program): n^8-n^6+n^4-n^2+1.
  • A060893 (program): n^8 - n^4 + 1.
  • A060895 (program): n^16 + 1.
  • A060896 (program): n^12 - n^6 + 1.
  • A060899 (program): Number of walks of length n on square lattice, starting at origin, staying on points with x+y >= 0.
  • A060901 (program): Exact power of 3 that divides the n-th Fibonacci number (sequence A000045).
  • A060904 (program): Largest power of 5 that divides n.
  • A060919 (program): Number of corners in a 4-sided fractal.
  • A060925 (program): a(n) = 2a(n-1) + 3a(n-2), a(0) = 1, a(1) = 4.
  • A060934 (program): Second column of Lucas bisection triangle (even part).
  • A060937 (program): Number of iterations of d(n) (A000005) needed to reach 2 starting at n (n is counted).
  • A060939 (program): a(n) = (Sum of the first n primes) + n.
  • A060945 (program): Number of compositions (ordered partitions) of n into 1’s, 2’s and 4’s.
  • A060946 (program): Trace of Vandermonde matrix of numbers 1,2,…,n, i.e., the matrix A with A[i,j] = i^(j-1), 1 <= i <= n, 1 <= j <= n.
  • A060954 (program): Largest prime factor of 10*n + 1.
  • A060956 (program): Leading digit of 3^n.
  • A060973 (program): a(2n+1) = a(n+1)+a(n), a(2n) = 2*a(n), with a(1)=0 and a(2)=1.
  • A060992 (program): a(n) = Sum_ gcd(i,j) 0 < i <= j < n and i+j = n .
  • A060995 (program): Number of routes of length 2n on the sides of an octagon from a point to opposite point.
  • A060998 (program): Squares of 1 and primes, written backwards.
  • A060999 (program): Nearest integer to (n+1)^3/9.
  • A061001 (program): x.x, x = first n terms of A060999.
  • A061003 (program): Nearest integer to n^5/25.
  • A061004 (program): Nearest integer to n^6/36.
  • A061005 (program): (Nearest integer to n^6/36) / 2.
  • A061006 (program): a(n) = (n-1)! mod n.
  • A061007 (program): a(n) = -(n-1)! mod n.
  • A061008 (program): a(n) = Sum_ j=1..n (-(n-1)! mod n).
  • A061009 (program): a(n) = -2 + Sum_ j=1..n (-(n-1)!) mod n.
  • A061019 (program): Negate primes in factorization of n.
  • A061037 (program): Numerator of 1/4 - 1/n^2.
  • A061038 (program): Denominator of 1/4 - 1/n^2.
  • A061041 (program): Numerator of 1/16 - 1/n^2.
  • A061047 (program): Numerator of 1/49 - 1/n^2.
  • A061054 (program): Floor(n+n^(3/4)).
  • A061062 (program): Sum of squared factorials: (0!)^2 + (1!)^2 + (2!)^2 + (3!)^2 +…+ (n!)^2.
  • A061066 (program): a(n) = (prime(n)^2 - 1)/8.
  • A061076 (program): a(n) is the sum of the products of the digits of all the numbers from 1 to n.
  • A061077 (program): a(n) = sum of the products of the digits of the first n odd numbers.
  • A061078 (program): Sum of the products of the digits of the first n even numbers.
  • A061079 (program): Denominators in the series for sin integral Si(x).
  • A061082 (program): a(n) = A053061(n)/n.
  • A061084 (program): Fibonacci-type sequence based on subtraction: a(0) = 1, a(1) = 2 and a(n) = a(n-2)-a(n-1).
  • A061085 (program): a(n) = A019550(n) / 3.
  • A061086 (program): a(n) is the concatenation of n with n^3.
  • A061087 (program): a(n) = A061086(n) / n.
  • A061091 (program): Number of k with 1 <= k <= n relatively prime to phi(k).
  • A061094 (program): The alternating group A_n contains an element x which is not conjugate to its inverse (equivalently not all the entries in the character table of A_n are real numbers).
  • A061099 (program): Squares with digital root 1.
  • A061100 (program): Squares with digital root 4.
  • A061101 (program): Squares with digital root 7.
  • A061104 (program): Smallest number whose digit sum is n^2.
  • A061142 (program): Replace each prime factor of n with 2: a(n) = 2^bigomega(n), where bigomega = A001222, number of prime factors counted with multiplicity.
  • A061146 (program): Decimal expansion of 11*Pi/10.
  • A061165 (program): Polynomial extrapolation of 2, 3, 5, 7, 11.
  • A061167 (program): a(n) = n^5 - n.
  • A061168 (program): Partial sums of floor(log_2(k)) (= A000523(k)).
  • A061171 (program): One half of second column of Lucas bisection triangle (odd part).
  • A061190 (program): a(n) = n^n - n.
  • A061205 (program): a(n) = n times R(n) where R(n) (A004086) is the digit reversal of n.
  • A061206 (program): a(n) = total number of occurrences of the consecutive pattern 1324 in all permutations of [n+3].
  • A061213 (program): a(n) = product of first n triangular numbers (A000217) + 1.
  • A061219 (program): a(n) is the largest number which can be formed with no zeros, using least number of digits and having digit sum = n.
  • A061222 (program): a(n) = n^2 + (n + 1)^3 + (n + 2)^4.
  • A061223 (program): a(n) = n^3 + (n + 1)^4 + (n + 2)^5.
  • A061224 (program): a(n) = n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5.
  • A061226 (program): a(n) = n^2 + (n^2 with digits reversed).
  • A061227 (program): a(n) = p + R p where R p is the digit reversal of n-th prime p.
  • A061228 (program): a(1) = 2, a(n) = smallest number greater than n which is not coprime to n.
  • A061234 (program): Smallest number with prime(n)^2 divisors where prime(n) is the n-th prime.
  • A061237 (program): Prime numbers == 1 (mod 9).
  • A061238 (program): Prime numbers == 2 (mod 9).
  • A061239 (program): Prime numbers == 4 (mod 9).
  • A061240 (program): Prime numbers == 5 (mod 9).
  • A061241 (program): Prime numbers == 7 (mod 9).
  • A061242 (program): Primes of the form 9*k - 1.
  • A061249 (program): Smallest number with digit sum = Fibonacci(n).
  • A061250 (program): (n-2)*(n-1)^n.
  • A061252 (program): a(n) = 16^n - 15^n.
  • A061253 (program): Let G_n be the elementary Abelian group G_n = (C_3)^n; a(n) is the number of times the number 1 appears in the character table of G_n.
  • A061263 (program): a(n) = floor(n^3/9).
  • A061265 (program): Number of squares between n-th prime and (n+1)st prime.
  • A061278 (program): a(n) = 5a(n-1) - 5a(n-2) + a(n-3) with a(1) = 1 and a(k) = 0 if k <= 0.
  • A061282 (program): Minimal number of steps to get from 0 to n by (a) adding 1 or (b) multiplying by 3. A stopping problem: begin with n and at each stage if a multiple of 3 divide by 3, otherwise subtract 1.
  • A061285 (program): a(n) = 2^((prime(n) - 1)/2).
  • A061286 (program): Smallest integer for which the number of divisors is the n-th prime.
  • A061288 (program): Integer part of square root of n-th triangular number.
  • A061302 (program): n*(n-1)^(n-2).
  • A061313 (program): Minimal number of steps to get from 1 to n by (a) subtracting 1 or (b) multiplying by 2.
  • A061316 (program): a(n) = n(n+1)(n^2 + n + 4)/4.
  • A061317 (program): Split positive integers into extending even groups and sum: 1+2, 3+4+5+6, 7+8+9+10+11+12, 13+14+15+16+17+18+19+20, …
  • A061318 (program): Column 3 of A061314.
  • A061319 (program): Column 4 of A061315.
  • A061347 (program): Period 3: repeat [1, 1, -2].
  • A061349 (program): Sum of antidiagonals of A060736.
  • A061352 (program): First row of array shown below.
  • A061353 (program): First column of array shown in A061352.
  • A061370 (program): a(n) = floor(ratio of product and sum of first n numbers).
  • A061378 (program): Product of all numbers formed by permuting the digits of n.
  • A061392 (program): a(n) = a(floor(n/3)) + a(ceiling(n/3)) with a(0) = 0 and a(1) = 1.
  • A061393 (program): Number of appearances of n in sequence defined by b(k) = b(floor(k/3)) + b(ceiling(k/3)) with b(0)=0 and b(1)=1, i.e., in A061392.
  • A061395 (program): Let p be the largest prime factor of n; if p is the k-th prime then set a(n) = k; a(1) = 0 by convention.
  • A061397 (program): Characteristic function sequence of primes multiplied componentwise by N, the natural numbers.
  • A061402 (program): a(n) = floor(n*sqrt(e)).
  • A061418 (program): a(n) = floor(a(n-1)*3/2) with a(1) = 2.
  • A061419 (program): a(n) = ceiling(a(n-1)*3/2) with a(1) = 1.
  • A061420 (program): a(n) = a(ceiling((n-1)*2/3)) + 1 with a(0) = 0.
  • A061462 (program): The exact power of 2 that divides the n-th Bell number (A000110). Has period 12.
  • A061468 (program): a(n) = d(n) + phi(n), where d(n) is the number of divisors (A000005) and phi(n) is Euler’s totient function (A000010).
  • A061479 (program): Smallest number m such that first digit - second digit + third digit - fourth digit … (of m) = n.
  • A061480 (program): n-th digit in decimal expansion of 1/n.
  • A061486 (program): Let the number of digits in n be k; a(n) = sum of the products of the digits of n taken r at a time where r ranges from 1 to k.
  • A061495 (program): a(n) = lcm(3n+1, 3n+2, 3n+3).
  • A061501 (program): a(1) = 1, a(n+1) = (a(n) + n) mod 10.
  • A061502 (program): a(n) = Sum_ k<=n tau(k)^2, where tau = number of divisors function A000005.
  • A061503 (program): a(n) = Sum_ k=1..n tau(k^2), where tau is the number of divisors function A000005.
  • A061504 (program): a(n+1) = le nombre des lettres dans a(n).
  • A061505 (program): Leading digit of n^n.
  • A061506 (program): a(n) = lcm(6n+2, 6n+4, 6n+6).
  • A061524 (program): Surround numbers of an n X 2 rectangle when n is even.
  • A061525 (program): Surround numbers of an n X 2 rectangle when n is odd.
  • A061534 (program): Expansion of (1-x^2)/(1-3*x-x^2+x^3).
  • A061536 (program): a(1) = 1 and a(n) = a(n-1) + (the number of primes <= n) for n > 1.
  • A061537 (program): Product of unitary divisors of n.
  • A061547 (program): Number of 132 and 213-avoiding derangements of 1,2,…,n .
  • A061548 (program): Numerator of probability that there is no error when average of n numbers is computed, assuming errors of +1, -1 are possible and they each occur with p = 1/4.
  • A061549 (program): Denominator of probability that there is no error when average of n numbers is computed, assuming errors of +1, -1 are possible and they each occur with p=1/4.
  • A061550 (program): a(n) = (2n+1)(2n+3)(2n+5).
  • A061557 (program): a(n) = (7n+2)C(n)/(n+2), where C(n) is the n-th Catalan number.
  • A061570 (program): a(1)=0, a(2)=1, a(n)=3*n-1 for n >= 3.
  • A061573 (program): a(n) = (n!)^2*Sum_ k=1..n 1/k!.
  • A061579 (program): Reverse one number (0), then two numbers (2,1), then three (5,4,3), then four (9,8,7,6), etc.
  • A061600 (program): a(n) = n^3 - n + 1.
  • A061640 (program): a(n) = !n*n!.
  • A061646 (program): a(n) = 2a(n-1) + 2a(n-2) - a(n-3) with a(-1) = 1, a(0) = 1, a(1) = 1.
  • A061647 (program): Beginning at the well for the topograph of a positive definite quadratic form with values 1, 1, 1 at a superbase (i.e., 1, 1 and 1 are the vonorms of the superbase), these numbers indicate the labels of the edges of the topograph on a path of greatest ascent.
  • A061650 (program): a(n) = n*20^(n-1).
  • A061654 (program): a(n) = (3*16^n + 2)/5.
  • A061667 (program): a(n) = Fibonacci(2*n+1) - 2^(n-1).
  • A061669 (program): a(n) = n*(mu(n) + 1), where mu(n) is the Moebius function A008683.
  • A061679 (program): Concatenation of n^3 and 7.
  • A061693 (program): Generalized Bell numbers.
  • A061705 (program): Number of matchings in the wheel graph with n spokes.
  • A061711 (program): a(n) = n!*n^n.
  • A061716 (program): Binary order of n-th prime.
  • A061717 (program): Binary order of n^n.
  • A061718 (program): a(n) = (n*(n+1)/2)^n.
  • A061722 (program): a(n) = 10 * n^2 + 7.
  • A061723 (program): Floor of arithmetic-geometric mean of n and 2*n - 1.
  • A061725 (program): p^2 + 2 where p is a prime.
  • A061726 (program): If n-th triangular number (A000217(n)) is odd, multiply it by 4; if even, multiply it by 5.
  • A061728 (program): Start with (a, b) = (2, 4). The next pair (a’, b’) is ((b + 1) mod 10, (a + 1) mod 10) where (a, b) is the previous pair.
  • A061742 (program): a(n) is the square of the product of first n primes.
  • A061761 (program): a(n) = 2^n + 2*n - 1.
  • A061776 (program): Start with a single triangle; at n-th generation add a triangle at each vertex, allowing triangles to overlap; sequence gives number of triangles in n-th generation.
  • A061777 (program): Start with a single triangle; at n-th generation add a triangle at each vertex, allowing triangles to overlap; sequence gives total population of triangles at n-th generation.
  • A061787 (program): a(n) = Sum_ k=1..n (2k-1)^(2k-1).
  • A061788 (program): a(n) = Sum_ k=1..n (2k)^(2k).
  • A061792 (program): 49(n(n+1)/2)+6.
  • A061793 (program): a(n) = 25n(n + 1)/2 + 3.
  • A061800 (program): a(n) = n + (-1)^(n mod 3).
  • A061801 (program): (7*6^n - 2)/5.
  • A061803 (program): Sum of n-th row of triangle of 4th powers: 1; 1 16 1; 1 16 81 16 1; 1 16 81 256 81 16 1; …
  • A061804 (program): a(n) = 2n(2*n^2 + 1).
  • A061818 (program): Multiples of 2 containing only digits 0,1,2.
  • A061819 (program): Multiples of 3 containing only digits 0,1,2,3.
  • A061821 (program): Multiples of 5 containing only digits 0,…,5.
  • A061824 (program): Multiples of 8 containing only the digits 0, …, 8.
  • A061834 (program): a(n) = binomial(n,2) * !n.
  • A061866 (program): a(n) is the number of solutions to x+y+z = 0 mod 3, where 1 <= x < y < z <= n.
  • A061874 (program): First digit - second digit + third digit - fourth digit … = 5.
  • A061885 (program): n + largest triangular number less than or equal to n.
  • A061887 (program): n + largest square less than or equal to n; numbers in the range [2k^2,2k^2+2k] for some k.
  • A061891 (program): a(0) = 1; for n>0, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 3 otherwise.
  • A061924 (program): Number of combinations in card games with 4 suits and 4 players.
  • A061925 (program): a(n) = ceiling(n^2/2) + 1.
  • A061927 (program): a(n) = n(n+1)(2n+1)(n^2+n+3)/30.
  • A061981 (program): a(n) = 3^n - 2n - 1.
  • A061982 (program): 3^n - (n + 1)(n + 2)/2.
  • A061983 (program): 3^n - (3n^2 + n + 2)/2.
  • A061989 (program): Number of ways to place 3 nonattacking queens on a 3 X n board.
  • A061995 (program): Number of ways to place 2 nonattacking kings on an n X n board.
  • A062004 (program): a(n) = mu(n)*(2n).
  • A062005 (program): Floor of arithmetic-geometric mean of n and 2n.
  • A062006 (program): a(n) = prime(n)^n + 1.
  • A062011 (program): a(n) = 2tau(n) = 2A000005(n).
  • A062018 (program): a(n) = n^n written backwards.
  • A062020 (program): Let P(n) = 2,3,5,7,…,p(n) where p(n) is n-th prime; then a(1) =0 and a(n) = Sum [mod p(i) - p(j) ], for all i and j from 1 to n.
  • A062023 (program): a(n) = n^(n+1)+n^(n-1) /2.
  • A062024 (program): a(n) = ((n+1)^n + (n-1)^n)/2.
  • A062025 (program): a(n) = n(13n^2 - 7)/6.
  • A062026 (program): a(n) = n(n+1)(n^2 -3n +6)/4
  • A062028 (program): a(n) = n + sum of the digits of n.
  • A062033 (program): Binary expansion of n does not contain 1-bits at even positions. Integers whose base 4 representation consists of only 0’s and 2s.
  • A062046 (program): Sum of even numbers between consecutive primes.
  • A062048 (program): a(n) = Sum k=1…n floor(sqrt(prime(k))).
  • A062050 (program): n-th chunk consists of the numbers 1, …, 2^n.
  • A062068 (program): a(n) = d(sigma(n)), where d(k) is the number of divisors function (A000005) and sigma(k) is the sum of divisor function (A000203).
  • A062069 (program): a(n) = sigma(d(n)), where d(k) is the number of divisors function (A000005) and sigma(k) is the sum of divisors function (A000203).
  • A062074 (program): a(n) = n^3 * 3^n.
  • A062075 (program): a(n) = n^4 * 4^n.
  • A062076 (program): a(n) = (2n-1)^n * n^(2n-1).
  • A062077 (program): a(n) = (2n)^n * n^(2n).
  • A062092 (program): a(n) = 2*a(n-1)-(-1)^n for n>0, a(0)=2.
  • A062096 (program): a(1) = 2; for n > 1, a(n) is smallest number, greater than a(n-1), which is relatively prime to the sum of all previous terms.
  • A062098 (program): a(n) = 7 * n!.
  • A062107 (program): Diagonal of table A062104.
  • A062108 (program): a(n) = floor(n^(3/4)).
  • A062114 (program): a(n) = 2*Fibonacci(n) - (1 - (-1)^n)/2.
  • A062116 (program): a(n) = 2^n mod 17.
  • A062119 (program): a(n) = n! * (n-1).
  • A062123 (program): a(n) = 2 + 9n(1 + n)/2.
  • A062124 (program): Fourth column of A046741.
  • A062141 (program): Third column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).
  • A062148 (program): Second (unsigned) column sequence of triangle A062138 (generalized a=5 Laguerre).
  • A062149 (program): Third column sequence of triangle A062138 (generalized a=5 Laguerre).
  • A062153 (program): a(n) = floor(log_3(n)).
  • A062157 (program): a(n) = 0^n-(-1)^n.
  • A062158 (program): a(n) = n^3 - n^2 + n - 1.
  • A062159 (program): a(n) = n^5 - n^4 + n^3 - n^2 + n - 1.
  • A062173 (program): a(n) = 2^(n-1) mod n.
  • A062174 (program): a(n) = 3^(n-1) mod n.
  • A062175 (program): a(n) = 4^(n-1) mod n.
  • A062176 (program): a(n) = 5^(n-1) mod n.
  • A062189 (program): a(n) = 2 * 3^(n-2)n(1+2*n).
  • A062199 (program): Second (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).
  • A062206 (program): a(n) = n^(2n).
  • A062207 (program): 2*n^n-1.
  • A062234 (program): a(n) = 2*prime(n) - prime(n+1).
  • A062249 (program): a(n) = n + d(n), where d(n) = number of divisors of n, cf. A000005.
  • A062260 (program): Third (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).
  • A062267 (program): Row sums of (signed) triangle A060821 (Hermite polynomials).
  • A062276 (program): a(n) = floor(n^(n+1) / (n+1)^n).
  • A062278 (program): a(n) = floor(3^n / n^3).
  • A062289 (program): Numbers n such that n-th row in Pascal triangle contains an even number, i.e., A048967(n) > 0.
  • A062296 (program): a(n) = number of entries in n-th row of Pascal’s triangle divisible by 3.
  • A062298 (program): Number of nonprimes <= n.
  • A062301 (program): Number of ways writing n-th prime as a sum of two primes.
  • A062302 (program): Number of ways writing n-th prime as a sum of a prime and a nonprime.
  • A062312 (program): Nonprime numbers squared.
  • A062313 (program): Factorials of nonprime numbers.
  • A062317 (program): Numbers k such that 5*k-1 is a perfect square.
  • A062318 (program): Numbers of the form 3^m - 1 or 2*3^m - 1; i.e., the union of sequences A048473 and A024023.
  • A062344 (program): Triangle of binomial(2*n, k) with n >= k.
  • A062346 (program): Consider 2n tennis players; a(n) is the number of matches needed to let every possible pair play each other.
  • A062355 (program): a(n) = d(n) * phi(n), where d(n) is the number of divisors function.
  • A062356 (program): a(n) = floor(n/phi(n)).
  • A062359 (program): a(n) = floor(n!/sigma(n)).
  • A062362 (program): a(n) = floor of Sum_ d divides n phi(d)/d.
  • A062363 (program): a(n) = Sum_ d n d!.
  • A062378 (program): n divided by largest cubefree factor of n.
  • A062383 (program): a(0) = 1: for n>0, a(n) = 2^floor(log_2(n)+1) or a(n) = 2*a(floor(n/2)).
  • A062389 (program): a(n) = floor( (2n-1)*Pi/2 ).
  • A062392 (program): a(n) = n^4 - (n-1)^4 + (n-2)^4 - … 0^4.
  • A062393 (program): a(n) = n^5 - (n-1)^5 + (n-2)^5 - … +(-1)^n*0^5.
  • A062394 (program): a(n) = 6^n + 1.
  • A062395 (program): a(n) = 8^n + 1.
  • A062396 (program): a(n) = 9^n + 1.
  • A062397 (program): a(n) = 10^n + 1.
  • A062401 (program): a(n) = phi(sigma(n)).
  • A062402 (program): a(n) = sigma(phi(n)).
  • A062411 (program): a(n) = (-1)^(p-1)*(p-1)! + 1 where p = prime(n).
  • A062457 (program): a(n) = prime(n)^n.
  • A062458 (program): Nearest integer to (n+1)^(n+1)/n^n.
  • A062481 (program): a(n) = n^prime(n).
  • A062501 (program): Number of distinct prime divisors of the nonprimes (including 1).
  • A062502 (program): Number of prime divisors (with repetition) of the nonprimes (including 1).
  • A062503 (program): Squarefree numbers squared.
  • A062508 (program): a(n) = 3^(2n)+7.
  • A062509 (program): a(n) = n^omega(n).
  • A062510 (program): a(n) = 2^n + (-1)^(n+1).
  • A062539 (program): Decimal expansion of the Lemniscate constant or Gauss’s constant.
  • A062544 (program): a(n) = n plus sum of previous three terms.
  • A062545 (program): Continued fraction for the 2nd Du Bois-Reymond constant.
  • A062546 (program): Decimal expansion of the 2nd Du Bois-Reymond constant.
  • A062547 (program): a(n) is least odd integer not a partial sum of 1, 3, …, a(n-1).
  • A062548 (program): Even integers that are not partial sums of A062547.
  • A062550 (program): a(n) = Sum_ k = 1..2n floor(2n/k).
  • A062557 (program): 2n-1 1’s followed by a 2.
  • A062558 (program): Number of nonisomorphic cyclic subgroups of dihedral group with 2n elements.
  • A062561 (program): a(n) = 3binomial(2n, n-1).
  • A062562 (program): a(n) = Sum_ k=1..n mu(k)*sigma(k).
  • A062563 (program): a(n) = Sum_ k=1..n d(k)* mu(k), where d(k) is the number of divisors function.
  • A062570 (program): a(n) = phi(2*n).
  • A062708 (program): Write 0,1,2,3,4,… in a triangular spiral; then a(n) is the sequence found by reading the terms along the line from 0 in the direction 0,2,…
  • A062709 (program): a(n) = 2^n + 3.
  • A062717 (program): Numbers m such that 6*m+1 is a perfect square.
  • A062720 (program): If n is odd then 2*n else prime(n).
  • A062722 (program): a(n) = ceiling(n/3)*round(n/4).
  • A062724 (program): a(n) = floor(tau^n) + 1, where tau = (1 + sqrt(5))/2.
  • A062725 (program): Write 0,1,2,3,4,… in a triangular spiral, then a(n) is the sequence found by reading the terms along the line from 0 in the direction 0,7,…
  • A062728 (program): Second 11-gonal (or hendecagonal) numbers: a(n) = n(9n+7)/2.
  • A062730 (program): Rows of Pascal’s triangle which contain 3 terms in arithmetic progression.
  • A062731 (program): Sum of divisors of 2*n.
  • A062741 (program): 3 times pentagonal numbers: 3n(3*n-1)/2.
  • A062748 (program): Fourth column (r=3) of FS(3) staircase array A062745.
  • A062749 (program): Sixth column (r=5) of FS(3) staircase array A062745.
  • A062754 (program): a(n) = gcd(n, sigma(n+1)).
  • A062756 (program): Number of 1’s in ternary (base-3) expansion of n.
  • A062758 (program): Product of squares of divisors of n.
  • A062765 (program): n(n-1)(n-3)*(n-5).
  • A062777 (program): 2^n - mu(n).
  • A062779 (program): a(n) = 2n(2*n)!.
  • A062781 (program): Number of arithmetic progressions of four terms and any mean which can be extracted from the set of the first n positive integers.
  • A062783 (program): a(n) = 3n(4*n-1).
  • A062785 (program): Chowla’s function * sigma(n).
  • A062786 (program): Centered 10-gonal numbers.
  • A062796 (program): Inverse Moebius transform of f(n) = n^n (A000312).
  • A062805 (program): a(n) = Sum_ i=1..n i*n^(n-i).
  • A062806 (program): a(n) = Sum_ i=1..n i*n^i.
  • A062808 (program): a(n) = Sum_ i=1..n n^i * (n - i).
  • A062809 (program): a(n) = Sum_ i = 1..n (n - i)^(1 + i).
  • A062810 (program): a(n) = Sum_ i=1..n i^(n - i) + (n - i)^i.
  • A062811 (program): a(n) = Sum_ i=1..n i^(n - i) + (i - n)^i.
  • A062812 (program): a(n) = Sum_ i=1..n i^(n - i) + (-1)^(n - i)*(n - i)^i.
  • A062813 (program): a(n) = Sum_ i=0..n-1 i*n^i.
  • A062814 (program): a(n) = Sum_ i=0..n-1 i * (n - i)^(n - i).
  • A062815 (program): a(n) = Sum_ i=1..n i^(i+1).
  • A062821 (program): Number of divisors of totient of n.
  • A062828 (program): a(n) = gcd(2n, n(n+1)/2).
  • A062830 (program): a(n) = n - phi(n) + 1.
  • A062835 (program): a(1) = 0; for n > 1 a(n) = sum of divisors of n^2-1; or sigma(A005563(n-1)).
  • A062838 (program): Cubes of squarefree numbers.
  • A062875 (program): Records in A046112 (or A006339).
  • A062876 (program): Numbers of lattice points corresponding to incrementally largest circle radii in A062875.
  • A062880 (program): Zero together with numbers which can be written as a sum of distinct odd powers of 2.
  • A062918 (program): Sum of the digit reversals of the first n natural numbers.
  • A062938 (program): a(n) = n(n+1)(n+2)(n+3)+1, which equals (n^2 +3n + 1)^2.
  • A062947 (program): C(n,[n/7]).
  • A062948 (program): H(A002808(n)) where H(n) is the half-totient function, H(n) = phi(n)/2: (A023022) and A002808(n) are the composites.
  • A062953 (program): Multiplicative with a(p^e) = -p.
  • A062955 (program): a(n) = phi(n^2) - phi(n) = (n-1) * phi(n).
  • A062956 (program): a(n) = h(n^2) - h(n), where h(n) is the half-totient function (A023022).
  • A062963 (program): Mu(n) * H(n) where H(n) is A023022.
  • A062966 (program): a(n) = C(3+n, n) + C(4+n, n) + C(5+n, n) + C(6+n, n).
  • A062967 (program): a(n) = 2*(sigma(n)-n-1)+1, where sigma = A000203, sum of divisors of n.
  • A062968 (program): n + 1 - d(n), where d(n) is the number of divisors function.
  • A062970 (program): a(n) = 1 + Sum_ j=1..n j^j.
  • A062971 (program): a(n) = (2*n)^n.
  • A062981 (program): a(n) = n^phi(n).
  • A062988 (program): a(n) = binomial(n+6,5) - 1.
  • A062989 (program): a(n) = C(n+6, 6) - n - 1.
  • A062990 (program): Eighth column (r=7) of FS(5) staircase array A062985.
  • A062994 (program): Eighth column of triangle A062993 (without leading zeros). A Pfaff-Fuss or 9-Raney sequence.
  • A063003 (program): Difference between 3^n and the next larger power of 2.
  • A063009 (program): Write n in binary then square as if written in base 10.
  • A063010 (program): Carryless binary square of n; also Moser-de Bruijn sequence written in binary.
  • A063070 (program): a(n) = phi(n) - d(n), where d(n) is the number of divisors function (A000005).
  • A063077 (program): a(n) = phi(n^2 + 1) - 2n.
  • A063079 (program): Bisection of A001790.
  • A063081 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 13 ).
  • A063087 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 19 ).
  • A063088 (program): a(n) = Sum_ k=1..n phi(k) - Sum k=1..n d(k), where d() is the number of divisors function.
  • A063089 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 21 ).
  • A063092 (program): a(0)=1, a(1)=2 and, for n>1, a(n) = a(n-1) + 11*a(n-2).
  • A063093 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 25 ).
  • A063094 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 26 ).
  • A063097 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 29 ).
  • A063098 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 30 ).
  • A063099 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 31 ).
  • A063102 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 34 ).
  • A063105 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 37 ).
  • A063107 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 39 ).
  • A063109 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 41 ).
  • A063110 (program): Dimension of the space of weight 2n cusp forms for Gamma_0(42).
  • A063111 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 43 ).
  • A063116 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 48 ).
  • A063117 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 49 ).
  • A063118 (program): Dimension of the space of weight 2n cusp forms for Gamma_0(50).
  • A063120 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 52 ).
  • A063121 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 53 ).
  • A063122 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 54 ).
  • A063123 (program): Number of solutions (r,s), 0< r< s, to the equation 1/n = 1/r + 1/s + 1/(r*s).
  • A063124 (program): a(n) = # i prime prime(n) <= i < prime(n)*2 (prime(n) = A000040, the prime enumeration).
  • A063125 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 57 ).
  • A063126 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 58 ).
  • A063128 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 60 ).
  • A063129 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 61 ).
  • A063130 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 62 ).
  • A063133 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 65 ).
  • A063134 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 66 ).
  • A063135 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 67 ).
  • A063136 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 68 ).
  • A063139 (program): Composite numbers which in base 3 contain their largest proper factor as a substring.
  • A063140 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 72 ).
  • A063141 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 73 ).
  • A063142 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 74 ).
  • A063143 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 75 ).
  • A063144 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 76 ).
  • A063146 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 78 ).
  • A063147 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 79 ).
  • A063148 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 80 ).
  • A063149 (program): Composite numbers which in base 5 contain their largest proper factor as a substring.
  • A063150 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 82 ).
  • A063151 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 83 ).
  • A063152 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 84 ).
  • A063153 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 85 ).
  • A063154 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 86 ).
  • A063155 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 87 ).
  • A063157 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 89 ).
  • A063158 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 90 ).
  • A063159 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 91 ).
  • A063160 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 92 ).
  • A063161 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 93 ).
  • A063162 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 94 ).
  • A063164 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 96 ).
  • A063165 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 97 ).
  • A063166 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 98 ).
  • A063168 (program): Dimension of the space of weight 2n cusp forms for Gamma_0( 100 ).
  • A063169 (program): a(n) = n*A001865(n).
  • A063170 (program): Schenker sums with n-th term.
  • A063195 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 6 ).
  • A063196 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 7 ).
  • A063197 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 9 ).
  • A063198 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 10 ).
  • A063199 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 11 ).
  • A063200 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 15 ).
  • A063201 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 18 ).
  • A063202 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 22 ).
  • A063203 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 23 ).
  • A063204 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 25 ).
  • A063205 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 29 ).
  • A063206 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 31 ).
  • A063207 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 33 ).
  • A063208 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 36 ).
  • A063209 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 41 ).
  • A063210 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 42 ).
  • A063211 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 43 ).
  • A063212 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 44 ).
  • A063213 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0(45).
  • A063214 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 46 ).
  • A063215 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 47 ).
  • A063216 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 49 ).
  • A063217 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 50 ).
  • A063218 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 51 ).
  • A063219 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 53 ).
  • A063220 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 55 ).
  • A063221 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 57 ).
  • A063222 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 58 ).
  • A063223 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 59 ).
  • A063224 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 60 ).
  • A063225 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 62 ).
  • A063226 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0(63).
  • A063227 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 66 ).
  • A063228 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 67 ).
  • A063229 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 69 ).
  • A063230 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 71 ).
  • A063231 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 75 ).
  • A063232 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 77 ).
  • A063233 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 79 ).
  • A063234 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 82 ).
  • A063235 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 83 ).
  • A063236 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 85 ).
  • A063237 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 86 ).
  • A063238 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 87 ).
  • A063240 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 89 ).
  • A063241 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0(90).
  • A063242 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 92 ).
  • A063244 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 94 ).
  • A063245 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 98 ).
  • A063246 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 99 ).
  • A063247 (program): Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 100 ).
  • A063249 (program): Doubly hexagonal numbers.
  • A063250 (program): Number of binary right-rotations (iterations of A038572) to reach fixed point.
  • A063258 (program): a(n) = binomial(n+5,4) - 1.
  • A063262 (program): Eighth column (k=7) of sextinomial array A063260.
  • A063267 (program): Eighth column (k=7) of septinomial array A063265.
  • A063270 (program): a(n) = 9^(2n) + 1.
  • A063281 (program): Dimension of the space of weight n cuspidal newforms for Gamma_1( 8 ).
  • A063289 (program): Dimension of the space of weight n cuspidal newforms for Gamma_1( 16 ).
  • A063300 (program): Dimension of the space of weight n cuspidal newforms for Gamma_1( 27 ).
  • A063305 (program): Dimension of the space S_n^ new (Gamma_1(32)) of weight n cuspidal newforms for Gamma_1( 32 ).
  • A063321 (program): Dimension of the space of weight n cuspidal newforms for Gamma_1( 48 ).
  • A063327 (program): Dimension of the space of weight n cuspidal newforms for Gamma_1( 54 ).
  • A063337 (program): Dimension of the space of weight n cuspidal newforms for Gamma_1( 64 ).
  • A063354 (program): Dimension of the space of weight n cuspidal newforms for Gamma_1( 81 ).
  • A063369 (program): Dimension of the space of weight n cuspidal newforms for Gamma_1( 96 ).
  • A063376 (program): a(-1) = 1; for n >= 0, a(n) = 2^n + 4^n = 2^n*(1 + 2^n).
  • A063377 (program): Sophie Germain degree of n: number of iterations of n under f(k) = 2k+1 before we reach a number that is not a prime.
  • A063396 (program): T(3,n) with T(n,m) as in A063394.
  • A063417 (program): Ninth column (k=8) of septinomial array A063265.
  • A063428 (program): a(n) is the smallest positive integer of the form n*k/(n+k).
  • A063436 (program): Write 1,2,3,4,… counterclockwise in a hexagonal spiral around 0 starting left down, then a(n) is the sequence found by reading from 0 in the vertical upward direction.
  • A063439 (program): a(n) = phi(n)^phi(n).
  • A063440 (program): Number of divisors of n-th triangular number.
  • A063441 (program): a(n) = sigma(n) * mu(n).
  • A063459 (program): A Beatty sequence: a(n) = floor(n*(Pi - 1)).
  • A063462 (program): n * last digit of n.
  • A063473 (program): M(2*n-1), where M(n) is Mertens’s function (A002321): Sum_ k=1..n mu(k), where mu = Moebius function (A008683).
  • A063481 (program): a(n) = 4^n + 8^n.
  • A063482 (program): p(n) * last digit of p(n) where p(n) is n-th prime.
  • A063488 (program): a(n) = (2n-1)(n^2 -n +2)/2.
  • A063489 (program): a(n) = (2n-1)(5n^2-5n+6)/6.
  • A063490 (program): a(n) = (2n - 1)(7n^2 - 7n + 6)/6.
  • A063491 (program): a(n) = (2n - 1)(3n^2 - 3n + 2)/2.
  • A063492 (program): a(n) = (2n - 1)(11n^2 - 11n + 6)/6.
  • A063493 (program): a(n) = (2n-1)(13n^2-13n+6)/6.
  • A063494 (program): a(n) = (2n - 1)(7n^2 - 7n + 3)/3.
  • A063495 (program): a(n) = (2n-1)(5n^2-5n+2)/2.
  • A063496 (program): a(n) = (2n-1)(8n^2-8n+3)/3.
  • A063497 (program): Number of atoms in first n shells of type I hyperfullerene.
  • A063498 (program): Atoms in cluster of n layers around C_60.
  • A063510 (program): a(1) = 1, a(n) = a(floor(square root(n))) + 1 for n > 1.
  • A063511 (program): a(n) = a(floor(square root(n))) * 2.
  • A063518 (program): Values of 17^n mod 23.
  • A063521 (program): a(n) = n(7n^2-4)/3.
  • A063522 (program): a(n) = n(5n^2 - 3)/2.
  • A063523 (program): a(n) = n(8n^2 - 5)/3.
  • A063524 (program): Characteristic function of 1.
  • A063534 (program): C(n) = H(n) + d(n), where C(n) is Chowla’s function A048050, H(n) is the half-totient function A023022 and d(n) is the number of divisors function A000005.
  • A063541 (program): Least number of empty triangles determined by n points in the plane.
  • A063542 (program): Least number of empty convex quadrilaterals (4-gons) determined by n points in the plane.
  • A063549 (program): Smallest number of crossing-free matchings on n points in the plane.
  • A063647 (program): Number of ways to write 1/n as a difference of exactly 2 unit fractions.
  • A063655 (program): Smallest semiperimeter of integral rectangle with area n.
  • A063656 (program): Numbers k such that the truncated square root of k is equal to the rounded square root of k.
  • A063657 (program): Numbers with property that truncated square root is unequal to rounded square root.
  • A063712 (program): Table of bits required for product of n- and k-bit positive numbers read by antidiagonals.
  • A063717 (program): a(n) is the greatest divisor of n^2 that is less than n.
  • A063724 (program): Consider problem of placing N queens on an n X n board so that each queen attacks precisely 4 others. Sequence gives maximal number of queens.
  • A063727 (program): a(n) = 2a(n-1) + 4a(n-2), a(0)=1, a(1)=2.
  • A063732 (program): Numbers n such that Lucas representation of n excludes L_0 = 2.
  • A063757 (program): G.f.: (1+3x+2x^2)/((1-x)(1-2x^2)).
  • A063758 (program): a(0)=1, a(n) = 2*Fibonacci(n+4) - 6.
  • A063759 (program): Spherical growth series for modular group.
  • A063772 (program): a(k^2 + i) = k + a(i) for k >= 0 and 0 <= i <= k * 2; a(0) = 0.
  • A063782 (program): a(0) = 1, a(1) = 3; for n > 1, a(n) = 2a(n-1) + 4a(n-2).
  • A063787 (program): a(2^k) = k + 1 and a(2^k + i) = 1 + a(i) for k >= 0 and 0 < i < 2^k.
  • A063808 (program): Spherical growth series for Z as generated by 2, 3 .
  • A063822 (program): Growth series for fundamental group of orientable closed surface of genus 12.
  • A063823 (program): G.f.: (1-2x^2-3x^3)/((1-x^3)(1-2x))
  • A063826 (program): Let 1, 2, 3, 4 represent moves to the right, down, left and up; this sequence describes the movements in the clockwise square spiral (a.k.a. Ulam Spiral).
  • A063842 (program): Number of colorings of K_4 using at most n colors.
  • A063886 (program): Number of n-step walks on a line starting from the origin but not returning to it.
  • A063896 (program): a(n) = 2^Fibonacci(n) - 1.
  • A063905 (program): Each prime p appears p times.
  • A063914 (program): Odd numbers interlaced with numbers 3m+2.
  • A063915 (program): G.f.: (1 + Sum_ i >= 0 2^i*x^(2^(i+1)-1)) / (1-x)^2.
  • A063916 (program): G.f.: (1 + Sum_ i >= 0 2^i*x^(2^(i+1)-1)) / (1-x)^3.
  • A063918 (program): a(1) = 1 and - applying the sieve of Eratosthenes - for n > 1: a(n) = if n is prime then 0 else the first prime p which marks n as composite.
  • A063920 (program): Numbers n such that n = 2*phi(n) + phi(phi(n)).
  • A063929 (program): Radius of A-excircle of Pythagorean triangle with a = (n+1)^2 - m^2, b = 2(n+1)m and c = (n+1)^2 + m^2.
  • A063941 (program): a(n) = 17*39^n.
  • A063942 (program): Follow k with k-1 and k-2.
  • A063945 (program): Number of nonnegative integers with n digits.
  • A063957 (program): Numbers not of the form round(m*sqrt(2)) for any integer m, i.e., complement of A022846.
  • A063958 (program): Sum of the non-unitary prime factors of n: sum of those prime factors for which the exponent exceeds 1.
  • A063960 (program): Sum of non-unitary prime divisors of n!: sum of those prime factors for which the exponent exceeds 1.
  • A063978 (program): Sum_ i for which n - i(i-1)/2 >= 0 binomial (n - i(i-1)/2, i).
  • A063985 (program): Partial sums of cototient sequence A051953.
  • A064017 (program): Number of ternary trees (A001764) with n nodes and maximal diameter.
  • A064038 (program): Numerator of average number of swaps needed to bubble sort a string of n distinct letters.
  • A064043 (program): Number of length 3 walks on an n-dimensional hypercubic lattice starting at the origin and staying in the nonnegative part.
  • A064046 (program): Number of length 6 walks on an n-dimensional hypercubic lattice starting and finishing at the origin and staying in the nonnegative part.
  • A064056 (program): Seventh column of quintinomial coefficients.
  • A064059 (program): Seventh column of Catalan triangle A009766.
  • A064061 (program): Eighth column of Catalan triangle A009766.
  • A064096 (program): Fifth diagonal of triangle A064094.
  • A064097 (program): A quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1.
  • A064099 (program): a(n) = ceiling(log(3 + 2*n)/log(3)).
  • A064100 (program): a(n) = (100^n - 1)/99*n.
  • A064108 (program): a(n) = (20^n-1)/19.
  • A064161 (program): Least abundant number divisible by the n-th prime number.
  • A064170 (program): a(1) = 1; a(n+1) = product of numerator and denominator in Sum_ k=1..n 1/a(k).
  • A064194 (program): a(2n) = 3a(n), a(2n+1) = 2a(n+1)+a(n), with a(1) = 1.
  • A064197 (program): a(n) = 27(n-1)(n-2)(n-3)(3*n-8)/2.
  • A064198 (program): a(n) = 3(n-2)(n-3)(3n^2-3*n-8)/2.
  • A064199 (program): a(n) = 9(n-2)^2(n^2-2*n-1)/2.
  • A064200 (program): a(n) = 12n(n-1).
  • A064201 (program): 9 times octagonal numbers: a(n) = 9n(3n-2).
  • A064216 (program): Replace each p^e with prevprime(p)^e in the prime factorization of odd numbers; inverse of sequence A048673 considered as a permutation of the natural numbers.
  • A064223 (program): a(1) = 1; a(n+1) = a(n) + number of decimal digits of a(n) for n > 0.
  • A064225 (program): (9n^2+5n+2)/2.
  • A064226 (program): a(n) = (9n^2 + 13n + 6) / 2.
  • A064232 (program): a(n) = n^(n+2) mod (n+1)^(n+1).
  • A064235 (program): The smallest power of 3 that is greater than or equal to n.
  • A064263 (program): a(n) = 11*n mod 30.
  • A064264 (program): a(n) = 19*n mod 30.
  • A064266 (program): Lune of Jan 01 in Julian calendar for a year with Golden Number n.
  • A064267 (program): Clavis terminorum in Julian calendar for a year with Golden Number n.
  • A064276 (program): Number of 2 X 2 singular integer matrices with elements from 0,…,n up to row and column permutation.
  • A064302 (program): Sixth diagonal of triangle A064094.
  • A064303 (program): Seventh diagonal of triangle A064094.
  • A064304 (program): Eighth diagonal of triangle A064094.
  • A064318 (program): a(n) satisfies a(n)! <= n^n < (a(n)+1)!.
  • A064321 (program): n(n-1)^3(n-2)^3*(n-3).
  • A064322 (program): Triply triangular numbers.
  • A064323 (program): a(n) = a(n-1)+ceiling(a(n-2)/2) with a(0)=0, a(1)=1.
  • A064324 (program): a(n) = a(n-1) + floor(a(n-2)/2) with a(0)=1, a(1)=2.
  • A064350 (program): a(n) = (3*n)!/n!.
  • A064352 (program): a(n) = (3n)!/(2n)!.
  • A064359 (program): Inverse of sequence A052331 considered as a permutation of the natural numbers.
  • A064378 (program): a(0) = 2, a(n) = 2^(n+1)*(n-1)! (n >= 1).
  • A064385 (program): a(n) = 2*5^n - 3.
  • A064400 (program): Number of ordered pairs a,b of elements in the dihedral group D_2n such that the subgroup generated by the pair a,b is the entire group D_2n.
  • A064405 (program): Number of even entries (A048967) minus the number of odd entries (A001316) in row n of Pascal’s triangle (A007318).
  • A064412 (program): At stage 1, start with a unit equilateral equiangular triangle. At each successive stage add 3*(n-1) new triangles around outside with edge-to-edge contacts. Sequence gives number of triangles (regardless of size) at n-th stage.
  • A064415 (program): a(1) = 0, a(n) = iter(n) if n is even, a(n) = iter(n)-1 if n is odd, where iter(n) = A003434(n) = smallest number of iterations of Euler totient function phi needed to reach 1.
  • A064427 (program): (Number of primes <= n - 1) + n.
  • A064429 (program): a(n) = floor(n / 3) * 3 + sign(n mod 3) * (3 - n mod 3).
  • A064433 (program): Number of iterations of A064455 to reach 2 (or 1 in the case of 1).
  • A064434 (program): a(n) = (2*a(n-1) + 1) mod n.
  • A064437 (program): a(1)=1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.
  • A064455 (program): a(2n) = 3n, a(2n-1) = n.
  • A064458 (program): Highest power of 11 dividing n!.
  • A064459 (program): a(n) = Sum_ k>=1 floor(n/12^k).
  • A064485 (program): Number of ordered pairs a,b of elements in the dihedral group D_2n such that the subgroup generated by the pair a,b is a proper subgroup of D_2n.
  • A064488 (program): A Beatty sequence: Floor[n*c], where c = A064648 is the sum of the reciprocals of primorials.
  • A064506 (program): a(n) = Max k k(k+1)/2 <= n(n+1)/2 - k*(k+1)/2 .
  • A064524 (program): Number of noncubes <= n.
  • A064549 (program): a(n) = n * Product_ primes p n p.
  • A064551 (program): Ado [Simone Caramel]’s Fibonacci function: define the Fibonacci sequence by f(0) = 1, f(1) = 1, f(n) = f(n-1)+f(n-2); then a(0) = 1, a(n) = a(n-1) + 2*(f(n)-n), n > 0.
  • A064557 (program): a(n) = # p A064553(k) = p prime and k <= n .
  • A064583 (program): a(n) = n^4(n^4+1)(n^2-1).
  • A064601 (program): a(n) = # p A064558(k) = p prime and k <= n .
  • A064602 (program): Partial sums of A001157: Sum_ j=1..n sigma_2(j).
  • A064603 (program): Partial sums of A001158: Sum_ j=1..n sigma_3(j).
  • A064604 (program): Partial sums of A001159: Sum_ j=1..n sigma_4(j).
  • A064608 (program): Partial sums of A034444: sum of number of unitary divisors from 1 to n.
  • A064616 (program): (10^n-1)(91/81)-n10^n/9.
  • A064617 (program): a(n) = (10^n-1)*(80/81)+n/9.
  • A064628 (program): Floor(4^n / 3^n).
  • A064629 (program): a(n) = 4^n mod 3^n.
  • A064633 (program): a(n) = 3^nn!(n+2)!/2!.
  • A064650 (program): a(n) = floor(a(n-1)/2) + a(n-2) with a(0)=1, a(1)=2.
  • A064651 (program): a(n) = ceiling(a(n-1)/2) + a(n-2) with a(0)=0 and a(1)=1.
  • A064671 (program): Number of n-digit base 4 biquanimous numbers (with leading 0’s allowed, but not all-0 string).
  • A064680 (program): Halve every even number, double every odd number.
  • A064685 (program): Length of orbit of 2n+1 in the 3x+1 problem.
  • A064686 (program): a(n) = number of n-digit base-3 biquams.
  • A064706 (program): Square of permutation defined by A003188.
  • A064707 (program): Inverse square of permutation defined by A003188.
  • A064717 (program): A Beatty sequence for 2^i + 2^(-i) where i = sqrt(-1).
  • A064718 (program): A Beatty sequence for 2^i + 2^-i where i = sqrt(-1).
  • A064722 (program): a(1) = 0; for n >= 2, a(n) = n - (largest prime <= n).
  • A064724 (program): A Beatty sequence for 2^sqrt(2).
  • A064727 (program): Number of pairs x,y such that 0 < x <= y < n and x+y = n and x*y = kn for some k.
  • A064746 (program): a(n) = n*8^n + 1.
  • A064747 (program): a(n) = n*9^n + 1.
  • A064748 (program): a(n) = n*10^n + 1.
  • A064749 (program): a(n) = n*11^n + 1.
  • A064750 (program): a(n) = n*12^n + 1.
  • A064751 (program): a(n) = n*5^n - 1.
  • A064752 (program): a(n) = n*6^n - 1.
  • A064753 (program): a(n) = n*7^n - 1.
  • A064754 (program): a(n) = n*8^n - 1.
  • A064755 (program): a(n) = n*9^n - 1.
  • A064756 (program): a(n) = n*10^n - 1.
  • A064757 (program): a(n) = n*11^n - 1.
  • A064758 (program): a(n) = n*12^n - 1.
  • A064761 (program): a(n) = 15*n^2.
  • A064762 (program): a(n) = 21*n^2.
  • A064763 (program): a(n) = 28*n^2.
  • A064766 (program): Fill a triangular array by rows by writing numbers 1, then 1 up to 23/2, then 1 up to 34/2, then 1 up to 4*5/2 and so on from 1 up to the n-th triangular number. The final elements of the rows form the sequence.
  • A064775 (program): Card k<=n, k such that all prime divisors of k are <= sqrt(k) .
  • A064778 (program): Largest m such that 1..m all divide n!.
  • A064784 (program): Difference between n-th triangular number t(n) and the largest square <= t(n).
  • A064796 (program): Largest integer m such that every permutation (p_1, …, p_n) of (1, …, n) satisfies p_i * p_ i+1 >= m for some i, 1 <= i <= n, where p_ n+1 = p_1.
  • A064800 (program): n plus the number of its prime factors: a(n) = n + A001222(n).
  • A064801 (program): Take 1, skip 2, take 2, skip 3, take 3, etc.
  • A064806 (program): a(n) = n + digital root of n.
  • A064808 (program): a(n) is the (n+1)st (n+2)-gonal number.
  • A064813 (program): a(n) = binomial(composite(n), n), where composite = A002808, composite numbers.
  • A064831 (program): Partial sums of A001654, or sum of the areas of the first n Fibonacci rectangles.
  • A064840 (program): a(n) = tau(n)*sigma(n).
  • A064842 (program): Maximal value of Sum_ i=1..n (p(i) - p(i+1))^2, where p(n+1) = p(1), as p ranges over all permutations of 1, 2, …, n .
  • A064843 (program): A064842/2.
  • A064847 (program): Sequence a(n) such that there is a sequence b(n) with a(1) = b(1) = 1, a(n+1) = a(n) * b(n) and b(n+1) = a(n) + b(n) for n >= 1.
  • A064853 (program): Lemniscate constant.
  • A064865 (program): Fill a triangular array by rows by writing numbers 1, then 1 up to 2^2, then 1 up to 3^2, then 1 up to 4^2 and so on. The final elements of the rows form the sequence.
  • A064866 (program): Write numbers 1, then 1 up to 2^2, then 1 up to 3^2, then 1 up to 4^2 and so on.
  • A064873 (program): First of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = a(n)^2 + A064874(n)^2 + A064875(n)^2 + A064876(n)^2.
  • A064911 (program): If n is semiprime (or 2-almost prime) then 1 else 0.
  • A064916 (program): a(n) = n/lpf(n) + lpf(n) - 1, where lpf = A020639 = least prime factor.
  • A064917 (program): a(n) is the result of beginning with n and iterating k -> A064916(k) until a prime is reached.
  • A064918 (program): a(n) is the number of iterations of k -> A064916(k) to reach a prime, starting at n.
  • A064919 (program): a(n) = Min k A064916(k) = n .
  • A064920 (program): a(n) = n/gpf(n) + gpf(n) - 1, where gpf = A006530 = greatest prime factor.
  • A064946 (program): a(n) = Sum_ i n, j n, j>i j.
  • A064947 (program): a(n) = Sum_ i n, j n, j>i i.
  • A064987 (program): a(n) = n*sigma(n).
  • A064989 (program): Multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.
  • A064990 (program): If A_k denotes the first 3^k terms, then A_0 = 0, A_ k+1 = A_k A_k B_k, where B_k is obtained from A_k by interchanging 0’s and 1’s.
  • A064994 (program): A Beatty sequence from Khintchine’s constant (A002210).
  • A064995 (program): A Beatty sequence from Khintchine’s constant (A002210).
  • A064996 (program): A Beatty sequence: [Pi^2 -8].
  • A064997 (program): A Beatty sequence: [Pi^2 -8].
  • A064999 (program): Partial sums of sequence (essentially A002378): 1, 2, 6, 12, 20, 30, 42, 56, 72, 90, …
  • A065033 (program): 1 appears three times, other numbers twice.
  • A065034 (program): a(n) = Lucas(2*n) + 1.
  • A065039 (program): If n in base 10 is d_1 d_2 … d_k then a(n) = d_1 + d_1d_2 + d_1d_2d_3 + … + d_1…d_k.
  • A065040 (program): Triangle read by rows: T(m,k) = exponent of the highest power of 2 dividing the binomial coefficient binomial(m,k).
  • A065043 (program): Characteristic function of the numbers with an even number of prime factors (counted with multiplicity): a(n) = 1 if n = A028260(k) for some k then 1 else 0.
  • A065073 (program): n-th prime + sum of digits of n-th prime.
  • A065081 (program): Alternating bit sum (A065359) for n-th prime p: replace 2^k with (-1)^k in binary expansion of p.
  • A065087 (program): a(n) = A000166(n)*binomial(n+1,2).
  • A065088 (program): a(n) = A000166(n)*binomial(n,2).
  • A065090 (program): Natural numbers which are not odd primes: composites plus 1 and 2.
  • A065091 (program): Odd primes.
  • A065097 (program): a(n) = ((2n+1) + (2n-1) - 1)!/((2n+1)!*(2n-1)!).
  • A065100 (program): a(n+2) = 9*a(n+1) - a(n), a(0) = 3, a(1) = 27.
  • A065101 (program): a(0) = c, a(1) = pc^3; a(n+2) = pc^2*a(n+1) - a(n), for p = 3, c = 2.
  • A065102 (program): a(0) = c, a(1) = pc^3; a(n+2) = pc^2*a(n+1) - a(n), for p = 2, c = 3.
  • A065113 (program): Sum of the squares of the n-th and the (n+1)st triangular numbers (A000217) is a perfect square.
  • A065120 (program): Highest power of 2 dividing A057335(n).
  • A065130 (program): a(n) = A005228(n) - A000217(n).
  • A065134 (program): Remainder when n is divided by the number of primes not exceeding n.
  • A065140 (program): a(n) = 2^n(2n)!.
  • A065141 (program): a(n) = (n+1)2^n(2*n)!.
  • A065151 (program): a(n) = prime(1 + A064722(n)).
  • A065164 (program): Permutation t->t+1 of Z, folded to N.
  • A065165 (program): Permutation t->t+2 of Z, folded to N.
  • A065168 (program): Permutation t->t-1 of Z, folded to N.
  • A065169 (program): Permutation t->t-2 of Z, folded to N.
  • A065170 (program): Permutation t->t-3 of Z, folded to N.
  • A065171 (program): Permutation of Z, folded to N, corresponding to the site swap pattern …26120123456… which ascends infinitely after t=0.
  • A065172 (program): Inverse permutation to A065171.
  • A065173 (program): Site swap sequence that rises infinitely after t=0. The associated delta sequence p(t)-t for the permutation of Z: A065171.
  • A065176 (program): Site swap sequence associated with the permutation A065174 of Z.
  • A065186 (program): a(1)=1, a(2)=3, a(3)=5, a(4)=2, a(5)=4; for n > 5, a(n) = a(n-5) + 5.
  • A065187 (program): “Greedy Dragons” permutation of the natural numbers, inverse of A065186.
  • A065190 (program): Self-inverse permutation of the positive integers: 1 is fixed, followed by an infinite number of adjacent transpositions (n n+1).
  • A065202 (program): Characteristic function of A065201: a(n) = if A065201(k) = n for some k then 1 else 0.
  • A065220 (program): a(n) = Fibonacci(n) - n.
  • A065223 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the heptagonal numbers (A000566). The final elements of the rows form a(n).
  • A065226 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the decagonal numbers. The final elements of the rows form a(n).
  • A065227 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the triangular numbers. The first elements of the rows form a(n).
  • A065228 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the square numbers. The first elements of the rows form a(n).
  • A065229 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the pentagonal numbers. The first elements of the rows form a(n).
  • A065230 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the hexagonal numbers. The first elements of the rows form a(n).
  • A065231 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the heptagonal numbers (A000566). The first elements of the rows form a(n).
  • A065232 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the octagonal numbers. The first elements of the rows form a(n).
  • A065233 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where the b(n) are the nonzero 9-gonal (nonagonal) numbers 1, 9, 24, 46, … (A001106). The initial elements of the rows form a(n).
  • A065234 (program): Fill a triangular array by rows by writing numbers 1 up to b(0), 1 up to b(1), etc., where b(n) are the decagonal numbers. The first elements of the rows form a(n).
  • A065251 (program): Simple quasi-periodic sequence consisting of the terms 1, 0 and -1.
  • A065252 (program): The sequence A065251 reduced modulo 3 (i.e., replace every -1 with 2).
  • A065259 (program): A057114 conjugated with A059893, inverse of A065260.
  • A065260 (program): A057115 conjugated with A059893, inverse of A065259.
  • A065261 (program): The siteswap sequence (the deltas p[i]-i, i in ]-inf,+inf[, folded from Z to N, mapping 0->1, 1->2, -1->3, 2->4, -2->5, etc.) for A065260.
  • A065262 (program): The nonpositive side (-1, -2, -3, …) of the site swap sequence A065261. The bisection of odd terms of A065261.
  • A065308 (program): Prime(n - PrimePi(n)).
  • A065310 (program): Number of occurrences of n-th prime in A065308, where A065308(j) = prime(j - pi(j)).
  • A065311 (program): Primes which occur exactly twice in the sequence of a(n) = prime(n) - prime(n - pi(n)) = A065308(n).
  • A065328 (program): a(n) is the number of primes less than or equal to prime(n) - n.
  • A065330 (program): a(n) = max k gcd(n, k) = k and gcd(k, 6) = 1 .
  • A065331 (program): Largest 3-smooth divisor of n.
  • A065332 (program): 3-smooth numbers in their natural position, gaps filled with 0.
  • A065333 (program): Characteristic function of 3-smooth numbers, i.e., numbers of the form 2^i*3^j (i, j >= 0).
  • A065334 (program): 2-exponents to represent 3-smooth numbers (A065332).
  • A065335 (program): 3-exponents to represent 3-smooth numbers (A065332).
  • A065339 (program): Number of primes congruent to 3 modulo 4 dividing n (with multiplicity).
  • A065344 (program): a(n) = Mod( binomial(2n,n), (n+1)(n+2) ).
  • A065355 (program): a(n) = n! - Sum_ k=0..n-1 k!.
  • A065357 (program): a(n) = (-1)^pi(n) where pi(n) is the number of primes <= n.
  • A065358 (program): The Jacob’s Ladder sequence: a(n) = Sum_ k=1..n (-1)^pi(k), where pi = A000720.
  • A065359 (program): Alternating bit sum for n: replace 2^k with (-1)^k in binary expansion of n.
  • A065361 (program): Rebase n from 3 to 2. Replace 3^k with 2^k in ternary expansion of n.
  • A065363 (program): Sum of balanced ternary digits in n. Replace 3^k with 1 in balanced ternary expansion of n.
  • A065364 (program): Alternating sum of balanced ternary digits in n. Replace 3^k with (-1)^k in balanced ternary expansion of n.
  • A065383 (program): a(n) = smallest prime >= n*(n + 1)/2.
  • A065384 (program): Largest prime <= n * (n + 1) / 2.
  • A065423 (program): Number of ordered length 2 compositions of n with at least one even summand.
  • A065424 (program): Catalan-like formula: a(n) = binomial(6m, 3m+1)/(9m+6).
  • A065438 (program): Complement of A065039.
  • A065440 (program): a(n) = (n-1)^n.
  • A065475 (program): Natural numbers excluding 2.
  • A065482 (program): a(n) = round( 2^n/n ).
  • A065502 (program): Positive numbers divisible by 2 or 5; 1/n not purely periodic after decimal point.
  • A065504 (program): a(n+1) = a(n) + n + the number of a(k)’s <= n, 1 <= k <= n and a(1) = 1.
  • A065513 (program): Number of endofunctions of [n] with a cycle a->b->c->a and for all x in [n], some iterate f^k(x)=a.
  • A065515 (program): Number of prime powers <= n.
  • A065530 (program): If n is odd then a(n) = n, else a(n) = n*(n+2).
  • A065532 (program): a(n) = 48*n^2 - 1.
  • A065535 (program): Number of strongly perfect lattices in dimension n.
  • A065565 (program): a(n) = floor((5/4)^n).
  • A065599 (program): If n odd, a(n) = n^2 else a(n) = n.
  • A065603 (program): Transposition diameter: maximal number of moves in an optimal sorting of n objects by moving blocks.
  • A065608 (program): Sum of divisors of n minus the number of divisors of n.
  • A065621 (program): Reversing binary representation of n. Converting sum of powers of 2 in binary representation of a(n) to alternating sum gives n.
  • A065651 (program): Sum_ k=1..n (-1)^tau(k)=n-2*floor(sqrt(n)).
  • A065653 (program): a(0) = 0, a(1) = 1, a(n) = a(n-2)*a(n-2) + 2 for n > 1.
  • A065679 (program): If n is even, a(n) = n^2 else a(n) = n.
  • A065705 (program): a(n) = Lucas(10*n).
  • A065713 (program): Sum of digits of 4^n.
  • A065730 (program): Largest square <= n-th prime.
  • A065733 (program): Largest square <= n^3.
  • A065734 (program): Largest square <= sigma(n).
  • A065737 (program): Largest square <= binomial(n,2).
  • A065739 (program): Largest square <= sum of first n squares.
  • A065741 (program): Largest square <= sum of squares of divisors of n.
  • A065764 (program): Sum of divisors of square numbers.
  • A065765 (program): Sum of divisors of twice square numbers.
  • A065766 (program): Sum of divisors of twice a square number, divided by three.
  • A065803 (program): a(n) = (sigma_2(n) mod 2) * (sigma_2(n) mod 5). Residue-product modulo 2 and 5 of sum of square of divisors.
  • A065827 (program): Sum of squares of divisors of square numbers.
  • A065855 (program): Number of composites <= n.
  • A065858 (program): m-th composite number c(m) = A002808(m), where m is the n-th prime number: a(n) = A002808(A000040(n)).
  • A065860 (program): Remainder when the n-th composite number is divided by n.
  • A065866 (program): a(n) = n! * Catalan(n+1).
  • A065881 (program): Ultimate modulo 10: right-hand nonzero digit of n.
  • A065882 (program): Ultimate modulo 4: right-hand nonzero digit of n when written in base 4.
  • A065883 (program): Remove factors of 4 from n (i.e., write n in base 4, drop final zeros, then rewrite in decimal).
  • A065890 (program): Number of composites less than the n-th prime.
  • A065896 (program): Number of composites <= 2*n.
  • A065897 (program): The a(n)-th composite number is twice the n-th prime.
  • A065915 (program): Numerator of sigma(8n^2)/sigma(4n^2).
  • A065916 (program): Denominator of sigma(8n^2)/sigma(4n^2).
  • A065928 (program): (x,y) = (a(n),a(n+1)) are the solutions of (t(x)+t(y))/(1+xy)) = t(2) = 3, where t(n) denotes the n-th triangular number t(n) = n(n+1)/2.
  • A065942 (program): Central column of triangle A065941.
  • A065949 (program): Bessel polynomial y_n ‘’‘(0).
  • A065961 (program): a(n) = (3n - 1)!n/2.
  • A065994 (program): a(n) = prime(prime(n) - n).
  • A065995 (program): a(n) = prime(prime(n) + n).
  • A065999 (program): Sum of digits of 9^n.
  • A066001 (program): Sum of digits of 5^n.
  • A066002 (program): Sum of digits of 6^n.
  • A066003 (program): Sum of digits of 7^n.
  • A066004 (program): Sum of digits of 8^n.
  • A066005 (program): Sum of digits of 11^n.
  • A066006 (program): Sum of digits of 12^n.
  • A066014 (program): Highest minimal Euclidean norm of any Type 4^Z self-dual code of length n over Z/4Z which does not have all Euclidean norms divisible by 8, that is, is strictly Type I. Compare A105682.
  • A066022 (program): Number of digits in n^n.
  • A066023 (program): (a(n)^7+1)/(n^7+1) is the smallest integer > 1.
  • A066043 (program): a(1) = 1; for m > 0, a(2m) = 2m, a(2m+1) = 4m+2.
  • A066068 (program): a(n) = n^n + n.
  • A066070 (program): a(1) = 1; for m > 0, a(2m) = 2(2m+1), a(2m+1) = 2m+1.
  • A066084 (program): a(n) = (n!)^2 + n! + n.
  • A066090 (program): a(n) = binomial(sigma(n), n).
  • A066096 (program): Duplicate values in A060143.
  • A066104 (program): a(2n) = 2n, a(2n+1) = 4(n+1).
  • A066106 (program): a(2n) = (2n)(2n+2); a(2n+1) = 4n + 4.
  • A066107 (program): a(0) = 0; for n > 0, a(2n+1) = (2n+1)*(2n+3); a(2n) = 2n + 2.
  • A066108 (program): Sum n^d over all divisors of n.
  • A066114 (program): a(0) = 1; for n > 0, a(n) = (n!(3n+1))/2.
  • A066118 (program): a(n) = n!(3n-1)/2.
  • A066138 (program): a(n) = 10^(2n) + 10^n + 1.
  • A066141 (program): a(n) = n^(n-1) + n + 1.
  • A066142 (program): a(n) = (n!)^2 + n! + 1.
  • A066143 (program): a(n) = n! + n^2 + n.
  • A066164 (program): Sum of interior angles in an n-sided polygon in degrees.
  • A066168 (program): a(n) = least k such that phi(k) > sigma(n).
  • A066169 (program): Least k such that phi(k) >= n.
  • A066181 (program): Permutation of the integers with cycle form 1 , 2, 3 , 4, 5, 6 , 7, 8, 9, 10 , …
  • A066182 (program): Permutation of the integers with cycle form 1 , 3, 2 , 6, 5, 4 , 10, 9, 8, 7 , …
  • A066194 (program): A permutation of the integers (a fractal sequence): a(n) = A006068(n-1) + 1.
  • A066209 (program): A053041(n)-10^(n-1).
  • A066210 (program): a(n) = ((2n)^(2n+2) - 1)/(4*n^2 - 1).
  • A066211 (program): a(n) = Sum_ j=0..n (2n)!/(2n-j)!.
  • A066221 (program): Bisection of A001189.
  • A066222 (program): Bisection of A001189.
  • A066223 (program): Bisection of A000085.
  • A066224 (program): Bisection of A000085.
  • A066237 (program): First differences give A052849.
  • A066246 (program): 0 unless n is a composite number A002808(k) when a(n) = k.
  • A066247 (program): Characteristic function of composite numbers: 1 if n is composite else 0.
  • A066274 (program): Number of endofunctions of [n] such that 1 is not a fixed point.
  • A066279 (program): a(n) = n^n + n + 1.
  • A066280 (program): a(n) = 1^n + 2^(n+1) + 3^(n+2).
  • A066288 (program): Number of 3-dimensional polyominoes (or polycubes) with n cells and symmetry group of order exactly 24.
  • A066293 (program): a(n) = A000203(n)^2 - A001157(n) = sigma(n)^2 - sigma_2(n).
  • A066298 (program): a(n) = googol (mod n).
  • A066300 (program): Number of n X n matrices with exactly 2 1’s in each row, other entries 0.
  • A066301 (program): a(n) = 0 if n is squarefree, otherwise 1 + a(n/rad(n)) where rad = A007947 (squarefree kernel).
  • A066318 (program): Number of necklaces with n labeled beads of 2 colors.
  • A066319 (program): A labeled structure simultaneously a tree and a cycle.
  • A066339 (program): Number of primes p of the form 4m+1 with p <= n.
  • A066343 (program): Beatty sequence for log_2(10).
  • A066344 (program): Beatty sequence for log_5(10).
  • A066353 (program): 1 + partial sums of A032378.
  • A066368 (program): a(n) = (n+2)2^(n-1) - 2n.
  • A066370 (program): Quadruply triangular numbers.
  • A066373 (program): a(n) = (3n-2)2^(n-3).
  • A066374 (program): (3n+4)2^(n-3)-(2*n-1).
  • A066375 (program): a(n) = 6binomial(n,4) + 3binomial(n,3) + 4*binomial(n,2) - n + 2.
  • A066377 (program): Number of numbers m <= n such that floor(sqrt(m)) divides m.
  • A066382 (program): a(n) = Sum_ k=0..n binomial(n^2,k).
  • A066393 (program): Coordination sequence for (9^3, 3.9^2) net with respect to a vertex of type 9^3.
  • A066394 (program): Coordination sequence for ReO_3 net with respect to oxygen atom O_1.
  • A066406 (program): a(n) = 2^n*(3^n-3).
  • A066429 (program): a(n) = 7^n mod n^7.
  • A066430 (program): a(n) = 8^n mod n^8.
  • A066431 (program): a(n) = 9^n mod n^9.
  • A066432 (program): a(n) = 10^n mod n^10.
  • A066438 (program): a(n) = 7^n mod n.
  • A066439 (program): a(n) = 8^n mod n.
  • A066440 (program): a(n) = 9^n mod n.
  • A066441 (program): a(n) = 11^n mod n.
  • A066442 (program): a(n) = 12^n mod n.
  • A066443 (program): Number of distinct paths of length 2n+1 along edges of a unit cube between two fixed adjacent vertices.
  • A066444 (program): a(n) = 11^n mod n^11.
  • A066445 (program): a(n) = 12^n mod n^12.
  • A066446 (program): Number of unordered divisor pairs of n.
  • A066449 (program): Binomial(n, phi(n)), where phi(n) is the Euler totient function.
  • A066455 (program): 6binomial(n,4)+5binomial(n,2)-4*n+5.
  • A066456 (program): Upper bound on number of regular triangulations of cyclic polytope C(n, n-4).
  • A066459 (program): Product of factorials of the digits of n.
  • A066481 (program): Largest anti-divisor of n.
  • A066490 (program): Number of primes of the form 4m+3 <= n.
  • A066492 (program): a(n) = A056524(n)/11.
  • A066503 (program): a(n) = n - squarefree kernel of n, A007947.
  • A066520 (program): Number of primes of the form 4m+3 <= n minus number of primes of the form 4m+1 <= n.
  • A066524 (program): a(n) = n*(2^n - 1).
  • A066526 (program): a(n) = binomial(Fibonacci(n), Fibonacci(n-1)).
  • A066530 (program): Expansion of (1+x+x^3)/((1-x)*(1-x^4)).
  • A066532 (program): If n is odd a(n) = 1, if n is even a(n) = 2^(n-1).
  • A066534 (program): Total number of walks with length > 0 in the Hasse diagram of a Boolean algebra of order n.
  • A066558 (program): a(n) = A066557(n)/n.
  • A066559 (program): a(n) = ceiling(10^(n-1)/n).
  • A066560 (program): Smallest composite number divisible by n.
  • A066568 (program): a(n) = n - sum of digits of n.
  • A066577 (program): a(n) = floor(n/(product of nonzero digits of n)).
  • A066578 (program): a(n) = floor(n/(sum of digits of n)).
  • A066586 (program): Number of normal subgroups of the group of n X n signed permutations matrices (described in sequence A066051).
  • A066588 (program): The sum of the digits of n^n.
  • A066601 (program): a(n) = 3^n mod n.
  • A066602 (program): a(n) = 4^n mod n.
  • A066603 (program): a(n) = 5^n mod n.
  • A066604 (program): a(n) = 6^n mod n.
  • A066606 (program): a(n) = 2^n mod n^2.
  • A066607 (program): a(n) = 3^n mod n^3.
  • A066608 (program): a(n) = 4^n mod n^4.
  • A066609 (program): a(n) = remainder when 5^n is divided by n^5.
  • A066610 (program): a(n) = remainder when 6^n is divided by n^6.
  • A066616 (program): a(1) = 1; a(n) = n*a(n-1) if n does not divide a(n-1), otherwise a(n) = a(n-1).
  • A066628 (program): a(n) = n - the largest Fibonacci number <= n.
  • A066629 (program): a(n) = 2*Fibonacci(n+2) + ((-1)^n - 3)/2.
  • A066643 (program): a(n) = floor(Pi*n^2).
  • A066660 (program): Number of divisors of 2n excluding 1.
  • A066665 (program): a(n) = # (x,y) 0<=y<=x<=n and x+y is prime .
  • A066674 (program): Least number m such that phi(m) = A000010(m) is divisible by the n-th prime.
  • A066675 (program): a(n) = A066674(n)-1 divided by the n-th prime.
  • A066714 (program): Coordination sequence for ReO_3 net with respect to Re atom.
  • A066715 (program): a(n) = gcd(2n+1, sigma(2n+1)).
  • A066728 (program): a(n) is the number of integers of the form (n+k+n*k)/(n-k) for k = 1,2,…,n-1.
  • A066729 (program): a(n) = Product_ d n, d<n d if n is composite, n otherwise.
  • A066746 (program): Conjectured values of a(n) defined by a(n) = least number of applications of f(k) = k^2 + 1 to n to yield a prime, if this number exists; = -1 otherwise.
  • A066750 (program): Greatest common divisor of n and its digit sum.
  • A066752 (program): a(n) = gcd(prime(n)+1, n+1).
  • A066760 (program): Sum_ 1<=k<=n, k is not a divisor of n and k is not coprime to n k.
  • A066761 (program): Number of positive integers of the form (n^2+k^2)/(n-k) for k=1,2,3,4,….,n-1.
  • A066770 (program): a(n) = 5^nsin(2narctan(1/2)) or numerator of tan(2n*arctan(1/2)).
  • A066778 (program): a(n) = Sum_ i=1..n floor((3/2)^i).
  • A066781 (program): a(n) = 2^phi(n).
  • A066791 (program): a(n) = phi(n^2 + n + 1).
  • A066796 (program): a(n) = Sum_ i=1..n binomial(2*i,i).
  • A066797 (program): a(n) = Sum_ i=1..n binomial(4i,2i).
  • A066798 (program): a(n) = Sum_ i=1..n binomial(6i,3i).
  • A066802 (program): a(n) = binomial(6n,3n).
  • A066804 (program): Sum of diagonal elements and those below it for a square matrix of integers, starting with 1.
  • A066810 (program): Expansion of x^2/((1-3x)(1-2*x)^2).
  • A066827 (program): a(n) = gcd(2^((n*(n+1)/2)) + 1, 2^n + 1).
  • A066829 (program): 1 if product of odd number of primes; 0 if product of even number of primes.
  • A066830 (program): a(n) = lcm(n+1, n-1).
  • A066839 (program): a(n) = sum of positive divisors k of n with k <= sqrt(n).
  • A066859 (program): Product of sums of divisors and non-divisors.
  • A066872 (program): p^2 + 1 as p runs through the primes.
  • A066880 (program): Biased numbers: n such that all terms of the sequence f(n), f(f(n)), f(f(f(n))), …, 1, where f(k) = Floor(k/2), are odd.
  • A066885 (program): a(n) = (prime(n)^2 + 1)/2.
  • A066886 (program): Sum of the elements in any transversal of a prime(n) X prime(n) array containing the numbers from 1 to prime(n)^2 in standard order.
  • A066908 (program): n^n minus largest factorial less than or equal to n^n.
  • A066915 (program): a(n) = n^phi(n) + 1.
  • A066916 (program): a(n) = n^phi(n) - 1.
  • A066927 (program): Least k such that between p and 2p, for all primes > 3, there is always a number that is twice a square, i.e.; a k such that p < 2k^2 < 2p.
  • A066959 (program): Bigomega(n^n) where bigomega(x) is the number of prime factors in x (counted with multiplicity).
  • A066971 (program): a(n) = sigma(sigma(sigma(n))).
  • A066979 (program): a(n) = floor(n!/2^n).
  • A066982 (program): a(n) = Lucas(n+1) - (n+1).
  • A066983 (program): a(n+2) = a(n+1) + a(n) + (-1)^n, with a(1) = a(2) = 1.
  • A066997 (program): Survivor number for 2nd-order Josephus problem.
  • A066998 (program): a(0)=0; a(n) = n^2*a(n-1) + 1.
  • A067018 (program): Start with a(0)=1, a(1)=4, a(2)=3, a(3)=2; for n>=3, a(n+1) = mex_i (nim-sum a(i)+a(n-i)), where mex means smallest nonnegative missing number.
  • A067029 (program): Exponent of least prime factor in prime factorization of n, a(1)=0.
  • A067040 (program): a(n) = n^(sum of digits of n).
  • A067041 (program): a(n) = n^(product of digits of n).
  • A067046 (program): a(n) = lcm(n, n+1, n+2)/6.
  • A067047 (program): a(n) = lcm(n, n+1, n+2, n+3)/12.
  • A067053 (program): Floor[ Sum_ 1..n 1/i ]^n.
  • A067056 (program): a(n) = (1)(2 + 3 + 4 + … + n) + (1 + 2)(3 + 4 + 5 + … + n) + (1 + 2 + 3)(4 + 5 + 6 + … + n) + … + (1 + 2 + 3 + … + n-1)n.
  • A067060 (program): A permutation of the positive integers in groups of four such that any two consecutive numbers differ by at least 2.
  • A067067 (program): Product of nonzero digits of n! (A000142).
  • A067076 (program): Numbers k such that 2*k + 3 is a prime.
  • A067078 (program): a(1) = 1, a(2) = 2, a(n) = (n-1)a(n-1) - (n-2)a(n-2).
  • A067080 (program): If n = ab…def in decimal notation then the left digitorial function Ld(n) = ab…defab…deab…dab*a.
  • A067082 (program): If n = abc…def in decimal notation then the right digit sum function = abc…def + bc…def + c…def + … + def + ef + f.
  • A067126 (program): Numbers for which phi(n) >= phi(k) for all k = 1 to n-1.
  • A067132 (program): Number of elements in the largest set of divisors of n which are in geometric progression.
  • A067161 (program): a(n) = prime(sigma(n)).
  • A067175 (program): Number of digits in the n-th primorial (A002110).
  • A067187 (program): Numbers that can be expressed as the sum of two primes in exactly one way.
  • A067239 (program): a(0)=1, a(n) = 8n*(2n-1).
  • A067251 (program): Numbers with no trailing zeros in decimal representation.
  • A067272 (program): 2*10^(n-1)-1.
  • A067273 (program): a(n) = n(a(n-1)2+1), a(0) = 0.
  • A067274 (program): Number of ordered integer pairs (b,c), with -n<=b<=n, -n<=c<=n, such that both roots of x^2+bx+c=0 are integers.
  • A067275 (program): Number of Fibonacci numbers A000045(k), k <= 10^n, which end in 4.
  • A067318 (program): Total number of transpositions in all permutations of n letters.
  • A067342 (program): Sum of decimal digits of sum of divisors of n.
  • A067353 (program): Divide the natural numbers in sets of consecutive numbers starting with 1,2 as the first set. The number of elements of the n-th set is equal to the sum of the n-1 final numbers in the (n-1)st set. The final number of the n-th set gives a(n).
  • A067389 (program): a(n) = 3n^3 + 2n^2 + n.
  • A067392 (program): Sum of numbers <= n which have common prime factors with n.
  • A067397 (program): Maximal power of 3 that divides n-th Catalan number.
  • A067403 (program): Third column of triangle A067402.
  • A067404 (program): Fourth column of triangle A067402.
  • A067405 (program): Fifth column of triangle A067402.
  • A067406 (program): Sixth column of triangle A067402.
  • A067407 (program): Seventh column of triangle A067402.
  • A067408 (program): Eighth column of triangle A067402.
  • A067409 (program): Ninth column of triangle A067402.
  • A067411 (program): Third column of triangle A067410 and second column of A067417.
  • A067412 (program): Fourth column of triangle A067410.
  • A067413 (program): Sixth column of triangle A067410.
  • A067414 (program): Seventh column of triangle A067410.
  • A067415 (program): Eighth column of triangle A067410.
  • A067416 (program): Ninth column of triangle A067410.
  • A067419 (program): Fourth column of triangle A067417.
  • A067421 (program): Sixth column of triangle A067417.
  • A067422 (program): Seventh column of triangle A067417.
  • A067423 (program): Eighth column of triangle A067417.
  • A067424 (program): Ninth column of triangle A067417.
  • A067426 (program): Sixth column of triangle A067425.
  • A067427 (program): Seventh column of triangle A067425.
  • A067428 (program): Eighth column of triangle A067425.
  • A067429 (program): Ninth column of triangle A067425.
  • A067435 (program): a(n) is the sum of all the remainders when n-th odd number is divided by odd numbers < 2n-1.
  • A067436 (program): a(n) = sum of all the remainders when n-th even number is divided by even numbers < 2n.
  • A067440 (program): Sum(i(n)), where i(n) is the smallest integer with i(n)^m=n for some m.
  • A067460 (program): mu(prime(n)-1)+1.
  • A067461 (program): mu(prime(n)+1)+1.
  • A067462 (program): a(n) = (1! + 2! + … + (n-1)!) mod n.
  • A067471 (program): n-th root of A067470(n).
  • A067482 (program): Powers of 4 with initial digit 4.
  • A067488 (program): Powers of 2 with initial digit 1.
  • A067491 (program): Powers of 5 with initial digit 1.
  • A067492 (program): Powers of 6 with initial digit 1.
  • A067497 (program): Smallest power of 2 with n+1 digits (n>=0). Also numbers k such that 1 is the first digit of 2^k.
  • A067535 (program): Smallest squarefree number >= n.
  • A067550 (program): a(n) = (n-1)!(n+2)!/(3*2^n).
  • A067558 (program): Sum of squares of proper divisors of n.
  • A067589 (program): Numbers k such that A067588(k) is an odd number.
  • A067602 (program): 5^n reduced modulo 3^n.
  • A067623 (program): Consider the power series (x+1)^(1/3)=1+x/3-x^2/9+5x^3/81+…; sequence gives denominators of coefficients.
  • A067624 (program): a(n) = 2^(2n)(2*n)!.
  • A067626 (program): a(n) = 2^(2n+1)*(2n+1)!.
  • A067628 (program): Minimal perimeter of polyiamond with n triangles.
  • A067630 (program): Denominators in power series for cos(x)*cosh(x).
  • A067692 (program): a(n) = Sum_ 0<d<=t<=n, d n, t n d*t.
  • A067699 (program): Number of comparisons made in a version of the sorting algorithm QuickSort for an array of size n with n identical elements.
  • A067705 (program): a(n) = 11n^2 + 22n.
  • A067707 (program): a(n) = 3n^2 + 12n.
  • A067724 (program): a(n) = 5n^2 + 10n.
  • A067725 (program): a(n) = 3n^2 + 6n.
  • A067726 (program): a(n) = 6n^2 + 12n.
  • A067727 (program): a(n) = 7n^2 + 14n.
  • A067728 (program): a(n) = 2n^2 + 8n.
  • A067731 (program): Maximum number of distinct parts in a self-conjugate partition of n, or 0 if n=2.
  • A067745 (program): Numerator of ((3n - 2)/(n^(2n - 1)(2n - 1)*4^(n - 1))).
  • A067749 (program): Numbers k such that k and 3^k end with the same two digits.
  • A067761 (program): Positive integers divisible by 5 but not by 7.
  • A067771 (program): Number of vertices in Sierpiński triangle of order n.
  • A067782 (program): Minimal delay time for an n-element sorting network.
  • A067792 (program): a(n) is the least prime >= sigma(n).
  • A067815 (program): a(n) = gcd(n, floor(sqrt(n))).
  • A067844 (program): Numbers k such that k and 2^k end with the same digit.
  • A067850 (program): Highest power of 2 not exceeding n!.
  • A067865 (program): Numbers n such that n and 2^n end with the same two digits.
  • A067866 (program): Numbers n such that n and 2^n end with the same three digits.
  • A067867 (program): Numbers n such that n and 2^n end with the same 4 digits.
  • A067869 (program): Numbers n such that n and 2^n end with the same 5 digits.
  • A067870 (program): Numbers k such that k and 3^k end with the same digit.
  • A067894 (program): Write 0, 1, …, n in binary and add as if they were decimal numbers.
  • A067900 (program): a(n) = 14*a(n-1) - a(n-2); a(0) = 0, a(1) = 8.
  • A067902 (program): a(n) = 14*a(n-1) - a(n-2); a(0) = 2, a(1) = 14.
  • A067911 (program): Product of gcd(k,n) for 1 <= k <= n.
  • A067980 (program): Convolution of L(n+1) := A000204(n+1) (Lucas), n>=0, with L(n+2), n>=0.
  • A067988 (program): Row sums of triangle A067330; also of triangle A067418.
  • A067989 (program): Row sums of triangle A067979; also of triangle A067990.
  • A067994 (program): Hermite numbers.
  • A067998 (program): a(n) = n^2 - 2*n.
  • A068018 (program): Number of fixed points in all 132- and 213-avoiding permutations of 1,2,…,n (these are permutations with runs consisting of consecutive integers).
  • A068028 (program): Decimal expansion of 22/7.
  • A068037 (program): Number of subsets of 1,2,3,…,n that sum to 0 mod 16.
  • A068061 (program): Palindromic numbers j that are not of the form k + reverse(k) for any k.
  • A068068 (program): Number of odd unitary divisors of n. d is a unitary divisor of n if d divides n and gcd(d,n/d)=1.
  • A068073 (program): Period 4 sequence [ 1, 2, 3, 2, …].
  • A068087 (program): a(n) = n^(2*n-2).
  • A068096 (program): a(n) = F(L(n)) where F(n) = n-th Fibonacci number and L(n) = n-th Lucas number.
  • A068098 (program): a(n) = Lucas(Fibonacci(n)).
  • A068156 (program): G.f.: (x+2)(x+1)/((x-1)(x-2)) = Sum_ n>=0 a(n)*(x/2)^n.
  • A068159 (program): a(n) = floor[ n/R(n) ], where R(n) (A004086) = Digit reversal of n.
  • A068181 (program): a(n)=-1/b(2n) where 1/(e^y-e^(y/3))= sum(i=-1,inf,b(i)*y^i).
  • A068204 (program): Let (x_n, y_n) be n-th solution to the Pell equation x^2 = 14*y^2 + 1. Sequence gives y_n .
  • A068211 (program): Largest prime factor of Euler totient function phi(n).
  • A068212 (program): a(n) = phi(n) divided by its largest prime factor.
  • A068217 (program): Denominators of coefficients in log(1+x)*sqrt(1+x) power series.
  • A068219 (program): Denominators of coefficients in log(1+x)*(1+x)^(1/3) power series.
  • A068227 (program): The “genity” sequence of the primes, i.e., a(n) = g(p) = ((p mod 4) + (p mod 6))/2, where p is the n-th prime.
  • A068228 (program): Primes congruent to 1 (mod 12).
  • A068229 (program): Primes congruent to 7 (mod 12).
  • A068231 (program): Primes congruent to 11 mod 12.
  • A068236 (program): First differences of (n+1)^5-n^5.
  • A068293 (program): a(1) = 1; thereafter a(n) = 6*(2^(n-1) - 1).
  • A068310 (program): n^2 - 1 divided by its largest square divisor.
  • A068311 (program): Arithmetic derivative of n!.
  • A068312 (program): Arithmetic derivative of triangular numbers.
  • A068327 (program): Arithmetic derivative of n^n.
  • A068344 (program): Square array read by antidiagonals of T(n,k) = sign(n-k).
  • A068346 (program): a(n) = n’’ = second arithmetic derivative of n.
  • A068377 (program): Engel expansion of sinh(1).
  • A068379 (program): Engel expansion of sinh(1/2).
  • A068380 (program): Engel expansion of sinh(1/3).
  • A068395 (program): a(n) = n-th prime minus its sum of digits.
  • A068396 (program): n-th prime minus its reversal.
  • A068397 (program): a(n) = Lucas(n) + (-1)^n + 1.
  • A068398 (program): Number of digits in (2^n)*(n!).
  • A068409 (program): a(n) = binomial(binomial(2*n,n),n).
  • A068425 (program): a(n) = floor(2^n*Pi).
  • A068426 (program): Expansion of log(2) in base 2.
  • A068444 (program): a(0) = 10; for n>0, a(n) = n*a(n-1)-n-2.
  • A068475 (program): a(n) = Sum_ m=0..n m*n^(m-1).
  • A068494 (program): a(n) = n mod phi(n).
  • A068499 (program): Numbers m such that m! reduced modulo (m+1) is not zero.
  • A068503 (program): Highest power of 3 dividing prime(n)-1.
  • A068504 (program): Highest power of 2 dividing prime(n)+1.
  • A068527 (program): Difference between smallest square >= n and n.
  • A068548 (program): Coefficients of (-x^(2n-6)) in Chebyshev polynomial of degree 2n.
  • A068551 (program): a(n) = 4^n - binomial(2*n,n).
  • A068562 (program): Denominators of coefficients in (1+x)^(1/3)-(1-x)^(1/3) power series.
  • A068601 (program): a(n) = n^3 - 1.
  • A068605 (program): Number of functions from [1,2,…,n] to [1,2,…,n] such that the image contains exactly two elements.
  • A068626 (program): a(3n) = a(3n-1) = 3n^2, a(3n-2) = 3n^2 - 3*n + 1.
  • A068628 (program): Numbers occurring twice in A068627.
  • A068636 (program): a(n) = Min(n, R(n)), where R(n) (A004086) = digit reversal of n.
  • A068637 (program): a(n) = Max(n, R(n)), where R(n) (A004086) = digit reversal of n.
  • A068639 (program): a(0) = 0, a(n) = a(n-1) + (-1)^p(n) for n >= 1, where p(n) = highest power of 2 dividing n.
  • A068719 (program): Arithmetic derivative of even numbers: a(n) = n+2*A003415(n).
  • A068720 (program): Arithmetic derivative of squares: a(n) = 2nA003415(n).
  • A068721 (program): Arithmetic derivative of cubes: a(n) = 3n^2A003415(n).
  • A068722 (program): Number of solenoidal flows (flow in = flow out) in a 3 X 3 square array with integer velocities -n .. n.
  • A068762 (program): Alternating sum sigma(1)-sigma(2)+sigma(3)-sigma(4)+…+((-1)^(n+1))*sigma(n).
  • A068792 (program): (n-1)n^(n-2)+sum (n-i)(n^(n-i-1)+n^(n+i-3)) 1<i<n .
  • A068794 (program): In prime factorization of n replace all primes with the least prime factor of n; a(1)=1.
  • A068875 (program): Expansion of (1 + xC)C, where C = (1 - (1 - 4x)^(1/2))/(2x) is the g.f. for Catalan numbers, A000108.
  • A068901 (program): Least number that when added to the n-th prime gives a multiple of n.
  • A068902 (program): Least multiple of n not less than the n-th prime.
  • A068904 (program): a(n) = binomial(sigma(n),tau(n)), where sigma(n) is the sum and tau(n) the number of divisors of n (A000203, A000005).
  • A068911 (program): Number of n step walks (each step +/-1 starting from 0) which are never more than 2 or less than -2.
  • A068921 (program): Number of ways to tile a 2 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.
  • A068922 (program): Number of ways to tile a 3 X 2n room with 1 X 2 Tatami mats. At most 3 Tatami mats may meet at a point.
  • A068952 (program): Squares in A068949.
  • A068985 (program): Decimal expansion of 1/e.
  • A068996 (program): Decimal expansion of 1 - 1/e.
  • A069010 (program): Number of runs of 1’s in the binary representation of n.
  • A069011 (program): Triangle with T(n,k) = n^2 + k^2.
  • A069017 (program): Triangular numbers of the form k^2 + k + 1.
  • A069038 (program): Expansion of x*(1+x)^4/(1-x)^6.
  • A069039 (program): Expansion of x(1+x)^5/(1-x)^7.
  • A069071 (program): (2n+1)*((2n+1)^4+4).
  • A069072 (program): a(n) = (2n+1)(2n+2)(2n+3).
  • A069073 (program): a(n) = n*(4n^2 - 1)^2.
  • A069074 (program): a(n) = (2n+2)(2n+3)(2n+4) = 24A000330(n+1).
  • A069075 (program): a(n) = (4*n^2 - 1)^2.
  • A069076 (program): a(n) = (4*n^2 - 1)^3.
  • A069078 (program): a(n) = n(4*n^4 + 1).
  • A069079 (program): a(n) = (2n+1)(2n+2)(2n+4)(2n+5).
  • A069080 (program): a(n) = (2n+1)(2n+2)(2n+6)(2n+7).
  • A069097 (program): Moebius transform of A064987, n*sigma(n).
  • A069099 (program): Centered heptagonal numbers.
  • A069102 (program): a(1) = 1; a(2) = 1; a(n) = Prime[n-1] + Prime[n-2] if n > 2.
  • A069114 (program): Squarefree part of prime(n)-1 : the smallest number such that a(n)*(prime(n)-1) is a square.
  • A069115 (program): Squarefree part of prime(n)+1 : the smallest number such that a(n)*(prime(n)+1) is a square.
  • A069121 (program): a(n) = n^4*binomial(2n,n).
  • A069125 (program): a(n) = (11n^2 - 11n + 2)/2.
  • A069126 (program): Centered 13-gonal numbers.
  • A069127 (program): Centered 14-gonal numbers.
  • A069128 (program): Centered 15-gonal numbers: a(n) = (15n^2 - 15n + 2)/2.
  • A069129 (program): Centered 16-gonal numbers.
  • A069130 (program): Centered 17-gonal numbers: (17n^2 - 17n + 2)/2.
  • A069131 (program): Centered 18-gonal numbers.
  • A069132 (program): Centered 19-gonal numbers.
  • A069133 (program): Centered 20-gonal (or icosagonal) numbers.
  • A069134 (program): (n!(3n))^2.
  • A069135 (program): (n!*(n+1)!)^2.
  • A069140 (program): a(n) = (4n-1)4n(4n+1).
  • A069153 (program): a(n) = Sum_ d n d*(d-1)/2.
  • A069173 (program): Centered 22-gonal numbers.
  • A069174 (program): Centered 23-gonal numbers.
  • A069177 (program): Maximal power of 2 that divides Phi(n), or the size of the Sylow 2-subgroup of the group of units mod n.
  • A069178 (program): Centered 21-gonal numbers.
  • A069181 (program): Decimal expansion of 1/1024.
  • A069183 (program): Expansion of 1/((1-x)(1-x^2)^2(1-x^3)(1-x^6)).
  • A069190 (program): Centered 24-gonal numbers.
  • A069201 (program): a(n) = Sum_ k=1..n mu(k)^2 * 2^omega(k) where omega(k) is the number of distinct primes in the factorization of k.
  • A069205 (program): a(n) = Sum_ k=1..n 2^bigomega(k).
  • A069210 (program): a(1)=a(2)=1, a(n+2) = a(n+1)+1 if sign(sin(a(n+1)) = sign(sin(a(n)), a(n+2) = a(n)+1 otherwise.
  • A069212 (program): a(n) = Sum_ k=1..n 3^omega(k).
  • A069226 (program): a(n) = gcd(n, 2^n + 1).
  • A069229 (program): a(n) = n*(2^n + 1).
  • A069241 (program): Number of Hamiltonian paths in the graph on n vertices 1,…,n , with i adjacent to j iff i-j <= 2.
  • A069262 (program): a(n) = 4*prime(n)^2.
  • A069268 (program): Greatest common divisor of n! and n*(n+1)/2.
  • A069271 (program): a(n) = binomial(4n+1,n)2/(3*n+2).
  • A069283 (program): a(n) = -1 + number of odd divisors of n.
  • A069290 (program): Sum of square roots of square divisors of n.
  • A069306 (program): Number of 2 X n binary arrays with a path of adjacent 1’s from upper left corner to anywhere in right hand column.
  • A069345 (program): n minus the number of its prime-factors: a(n) = n - A001222(n).
  • A069403 (program): a(n) = 2Fibonacci(2n+1) - 1.
  • A069429 (program): Half the number of 3 X n binary arrays with no path of adjacent 1’s or adjacent 0’s from top row to bottom row.
  • A069459 (program): a(n) = prime(n)^n - 1.
  • A069470 (program): a(n) = Sum_ k>=1 floor(n/(k*(k+1)/2)).
  • A069473 (program): First differences of (n+1)^6-n^6 (A022522).
  • A069474 (program): First differences of A069473.
  • A069475 (program): First differences of A069474, successive differences of (n+1)^6-n^6.
  • A069476 (program): First differences of A069475, successive differences of (n+1)^6-n^6.
  • A069477 (program): a(n) = 60n^2 + 180n + 150.
  • A069478 (program): First differences of A069477, successive differences of (n+1)^5 - n^5.
  • A069482 (program): a(n) = prime(n+1)^2 - prime(n)^2.
  • A069486 (program): 2prime(n)prime(n+1).
  • A069497 (program): Triangular numbers of the form 6*k.
  • A069506 (program): a(1) = 2; a(n) = smallest palindromic number of the form k*a(n-1) + 1 with k > 1.
  • A069513 (program): Characteristic function of the prime powers p^k, k >= 1.
  • A069515 (program): Number of transpositions (interchanges of adjacent digits, sometimes called inversions) needed to change all n-digit base 3 numbers into nondecreasing order.
  • A069517 (program): a(n) = (-1)sum( d divides n, moebius(d)(-1)^d).
  • A069547 (program): n^2 mod n-th prime.
  • A069549 (program): Smallest composite k such that phi(k) > k*(1-1/n).
  • A069553 (program): Define S(k) to be the sequence of divisors and multiples of k, e.g. S(1) = 1,2,3,4,5… S(2) = 1,2,4,6,8,10,… S(10) = 1,2,5,10,20,30,40,50,…; a(n) = n-th term of the n-th sequence S(n).
  • A069584 (program): a(n) = n - largest perfect power <= n.
  • A069623 (program): Number of perfect powers <= n.
  • A069627 (program): Sum_ k=1..n floor(n(n-1)/(2k)).
  • A069637 (program): Number of prime powers <= n with exponents > 1.
  • A069639 (program): Smallest composite k such that phi(k)>k*(1-1/n^2).
  • A069705 (program): a(n) = 2^n mod 7.
  • A069720 (program): a(n) = 2^(n-1)*binomial(2n-1, n).
  • A069721 (program): Number of rooted unicursal planar maps with n edges and no vertices of valency 1 (unicursal means that exactly two vertices are of odd valency; there is an Eulerian path).
  • A069722 (program): Number of rooted unicursal planar maps with n edges and exactly one vertex of valency 1 (unicursal means that exactly two vertices are of odd valency; there is an Eulerian path).
  • A069723 (program): a(n) = 2^(n-1)binomial(2n-3, n-1).
  • A069731 (program): Number of unicursal planar maps with n edges rooted at a vertex of odd valency (unicursal means that exactly two vertices are of odd valency; there is an Eulerian path).
  • A069733 (program): Number of divisors d of n such that d or n/d is odd. Number of non-orientable coverings of the Klein bottle with n lists.
  • A069734 (program): Number of pairs (p,q), 0<=p<=q, such that p+q divides n.
  • A069735 (program): Number of regular orientable coverings of the Klein bottle with 2n lists.
  • A069755 (program): Frobenius number of the numerical semigroup generated by 3 consecutive triangular numbers.
  • A069756 (program): Frobenius number of the numerical semigroup generated by consecutive squares.
  • A069759 (program): Frobenius number of the numerical semigroup generated by consecutive hex numbers.
  • A069760 (program): Frobenius number of the numerical semigroup generated by consecutive centered square numbers.
  • A069778 (program): q-factorial numbers 3!_q.
  • A069779 (program): q-factorial numbers 4!_q.
  • A069782 (program): Numbers k such that gcd(d(k^3), d(k)) = 2^w for some w.
  • A069811 (program): a(n) = Sum_ k=1..n omega(k)^2.
  • A069812 (program): a(n) = Sum_ k=1..n (bigomega(k)-omega(k)).
  • A069813 (program): Maximum number of triangles in polyiamond with perimeter n.
  • A069816 (program): a(n) = (sum of digits of n)^2 - (sum of digits^2 of n).
  • A069829 (program): a(n) = PS(n)(2n), where PS is described in A057032.
  • A069834 (program): a(n) = n-th reduced triangular number: n(n+1)/ 2^k where 2^k is the largest power of 2 that divides product n(n+1).
  • A069879 (program): Number of pairs i,j with i different from j; 1<=i<=n; 1<= j <=n such that i+j is a prime number.
  • A069891 (program): a(n) = Sum_ k=1..n A007913(k), the squarefree part of k.
  • A069894 (program): Centered square numbers: a(n) = 4n^2 + 4n + 2.
  • A069895 (program): 2^a(n) divides (2n)^(2n): exponent of 2 in (2n)^(2n).
  • A069897 (program): Integer quotient of the largest and the smallest prime factors of n, with a(1) = 1.
  • A069901 (program): Smallest prime factor of n-th triangular number.
  • A069902 (program): Largest prime factor of n-th triangular number n(n+1)/2.
  • A069903 (program): Number of distinct prime factors of n-th triangular number.
  • A069904 (program): Number of prime factors of n-th triangular number (with multiplicity).
  • A069905 (program): Number of partitions of n into 3 positive parts.
  • A069908 (program): Numbers congruent to +-2, +-3, +-4 or +-5 mod 16.
  • A069909 (program): Numbers congruent to +-1, +-4, +-6, +-7 mod 16.
  • A069921 (program): Define C(n) by the recursion C(0) = 1 + I where I^2 = -1, C(n+1) = 1/(1+C(n)); then a(n) = (-1)^n/Im(C(n)) where Im(z) is the imaginary part of the complex number z.
  • A069924 (program): Number of k, 1<=k<=n, such that phi(k) divides k.
  • A069928 (program): Number of k, 1<=k<=n, such that tau(k) divides sigma(k) where tau(x) is the number of divisors of x and sigma(x) the sum of divisors of x.
  • A069930 (program): Number of integers of the form (n+k)/(n-k) with 1 <= k <= n-1.
  • A069940 (program): (1/2)*((Sum of digits of n)^2 + (Sum of digits^2 of n)).
  • A069958 (program): (Sum of digits of n)^3 - (sum of digits^3 of n).
  • A069975 (program): a(n) = n*(16n^2-1).
  • A069981 (program): Hermite’s problem: number of positive integral solutions to x + y + z = n subject to x <= y + z, y <= z + x and z <= x + y.
  • A069982 (program): Number of 4-gonal compositions of n into positive parts.
  • A069984 (program): 1123+21460n.
  • A069986 (program): Denominator of b(n)=binomial(2n,n)^3*(42n+5)/2^(12n+4).
  • A069993 (program): a(n) = 2^(2n+1)Sum_ k=1..2n binomial(2n+1,k)*Bernoulli(k)/2^k.
  • A069996 (program): Number of spanning trees on the bipartite graph K_ 3,n .
  • A070004 (program): Numbers of the form 52^n or 532^n; a(n) = 5A029744(n).
  • A070038 (program): a(n) = sum of divisors of n that are at least sqrt(n).
  • A070039 (program): Sum of divisors of n that are smaller than sqrt(n).
  • A070046 (program): Number of primes between prime(n) and 2*prime(n) exclusive.
  • A070050 (program): Number of Bottleneck-Monge matrices with 2 rows. In the formula below, P = 2.
  • A070098 (program): Number of integer triangles with perimeter n which are acute and isosceles.
  • A070169 (program): Rounded total surface area of a regular tetrahedron with edge length n.
  • A070178 (program): Coefficients of Lehmer’s polynomial.
  • A070189 (program): 12345679n.
  • A070196 (program): a(n)=n plus the sorted version of the base-10 digits of n.
  • A070199 (program): Number of palindromes of length <= n.
  • A070229 (program): Next m>n such that m is divisible by lpf(n), lpf=A006530 largest prime factor.
  • A070252 (program): Number of n-digit palindromes.
  • A070260 (program): Third diagonal of triangle defined in A051537.
  • A070261 (program): 4th diagonal of triangle defined in A051537.
  • A070262 (program): 5th diagonal of triangle defined in A051537.
  • A070271 (program): n^reverse(n) (ignore leading 0’s).
  • A070280 (program): a(1) = 1; a(n) = a(n-1) + product of the digits of n-1.
  • A070285 (program): a(n) = n^(n-2) * (n-1)^(n-1).
  • A070290 (program): a(n) = lcm(8,n)/gcd(8,n).
  • A070302 (program): Number of 3 X 3 X 3 magic cubes with sum 3n.
  • A070307 (program): Number of n X n matrices with nonnegative integer entries such that every row sum equals 3.
  • A070313 (program): a(n) = 2^n - (2*n+1).
  • A070320 (program): Max( phi(k) : k=1,2,3,…,n ).
  • A070321 (program): Greatest squarefree number <= n.
  • A070333 (program): Expansion of (1+x)(1-x+x^2)/( (1-x)^4(1+x+x^2) ).
  • A070335 (program): a(n) = 2^n mod 23.
  • A070336 (program): a(n) = 2^n mod 25.
  • A070337 (program): a(n) = 2^n mod 27.
  • A070338 (program): a(n) = 2^n mod 33.
  • A070339 (program): a(n) = 2^n mod 35.
  • A070340 (program): a(n) = 2^n mod 39.
  • A070341 (program): a(n) = 3^n mod 11: Repeat (1, 3, 9, 5, 4), period 5.
  • A070342 (program): a(n) = 3^n mod 19.
  • A070343 (program): a(n) = 3^n mod 25.
  • A070344 (program): a(n) = 3^n mod 29.
  • A070345 (program): a(n) = 3^n mod 35.
  • A070346 (program): a(n) = 3^n mod 37.
  • A070347 (program): a(n) = 2^n mod 21.
  • A070348 (program): a(n) = 2^n mod 41.
  • A070349 (program): a(n) = 2^n mod 43.
  • A070350 (program): a(n) = 2^n mod 45.
  • A070351 (program): a(n) = 2^n mod 47.
  • A070352 (program): a(n) = 3^n mod 5; or period 4, repeat [1, 3, 4, 2].
  • A070353 (program): a(n) = 3^n mod 14.
  • A070354 (program): a(n) = 3^n mod 16.
  • A070355 (program): a(n) = 3^n mod 22.
  • A070356 (program): a(n) = 3^n mod 23.
  • A070357 (program): a(n) = 3^n mod 28.
  • A070358 (program): a(n) = 3^n mod 32.
  • A070359 (program): a(n) = 3^n mod 34.
  • A070360 (program): a(n) = 3^n mod 38.
  • A070361 (program): a(n) = 3^n mod 41.
  • A070362 (program): a(n) = 3^n mod 44.
  • A070363 (program): a(n) = 3^n mod 46.
  • A070364 (program): a(n) = 3^n mod 47.
  • A070365 (program): a(n) = 5^n mod 7.
  • A070366 (program): a(n) = 5^n mod 9.
  • A070367 (program): a(n) = 5^n mod 11.
  • A070368 (program): a(n) = 5^n mod 13.
  • A070369 (program): a(n) = 5^n mod 14.
  • A070370 (program): a(n) = 5^n mod 16.
  • A070371 (program): a(n) = 5^n mod 17.
  • A070372 (program): a(n) = 5^n mod 18.
  • A070373 (program): a(n) = 5^n mod 19.
  • A070374 (program): a(n) = 5^n mod 21.
  • A070375 (program): a(n) = 5^n mod 22.
  • A070376 (program): a(n) = 5^n mod 26.
  • A070377 (program): a(n) = 5^n mod 27.
  • A070378 (program): a(n) = 5^n mod 28.
  • A070379 (program): a(n) = 5^n mod 29.
  • A070380 (program): a(n) = 5^n mod 32.
  • A070381 (program): a(n) = 5^n mod 33.
  • A070382 (program): a(n) = 5^n mod 34.
  • A070383 (program): a(n) = 5^n mod 36.
  • A070384 (program): a(n) = 5^n mod 37.
  • A070385 (program): a(n) = 5^n mod 38.
  • A070386 (program): a(n) = 5^n mod 39.
  • A070387 (program): a(n) = 5^n mod 41.
  • A070388 (program): a(n) = 5^n mod 42.
  • A070389 (program): a(n) = 5^n mod 43.
  • A070390 (program): a(n) = 5^n mod 44.
  • A070391 (program): a(n) = 5^n mod 46.
  • A070392 (program): a(n) = 6^n mod 11.
  • A070393 (program): a(n) = 6^n mod 13.
  • A070394 (program): a(n) = 6^n mod 17.
  • A070395 (program): a(n) = 6^n mod 19.
  • A070396 (program): a(n) = 6^n mod 23.
  • A070397 (program): a(n) = 6^n mod 25.
  • A070398 (program): a(n) = 6^n mod 29.
  • A070399 (program): a(n) = 6^n mod 31.
  • A070400 (program): a(n) = 6^n mod 37.
  • A070401 (program): a(n) = 6^n mod 47.
  • A070402 (program): a(n) = 2^n mod 5.
  • A070403 (program): a(n) = 7^n mod 9.
  • A070404 (program): a(n) = 7^n mod 11.
  • A070405 (program): a(n) = 7^n mod 13.
  • A070406 (program): a(n) = 7^n mod 15.
  • A070407 (program): a(n) = 7^n mod 17.
  • A070408 (program): a(n) = 7^n mod 22.
  • A070409 (program): a(n) = 7^n mod 23.
  • A070410 (program): a(n) = 7^n mod 25.
  • A070411 (program): a(n) = 7^n mod 26.
  • A070412 (program): a(n) = 7^n mod 27.
  • A070413 (program): a(n) = 7^n mod 29.
  • A070414 (program): a(n) = 7^n mod 30.
  • A070415 (program): a(n) = 7^n mod 31.
  • A070416 (program): a(n) = 7^n mod 32.
  • A070417 (program): a(n) = 7^n mod 33.
  • A070419 (program): a(n) = 7^n mod 36.
  • A070420 (program): a(n) = 7^n mod 37.
  • A070421 (program): a(n) = 7^n mod 38.
  • A070422 (program): a(n) = 7^n mod 39.
  • A070423 (program): a(n) = 7^n mod 40.
  • A070424 (program): a(n) = 7^n mod 41.
  • A070425 (program): a(n) = 7^n mod 43.
  • A070426 (program): a(n) = 7^n mod 44.
  • A070427 (program): a(n) = 7^n mod 45.
  • A070429 (program): a(n) = 7^n mod 47.
  • A070430 (program): a(n) = n^2 mod 5.
  • A070431 (program): a(n) = n^2 mod 6.
  • A070432 (program): Period 4: repeat [0, 1, 4, 1]; a(n) = n^2 mod 8.
  • A070433 (program): a(n) = n^2 mod 9.
  • A070434 (program): a(n) = n^2 mod 11.
  • A070435 (program): a(n) = n^2 mod 12, or alternately n^4 mod 12.
  • A070436 (program): a(n) = n^2 mod 13.
  • A070437 (program): a(n) = n^2 mod 14.
  • A070438 (program): a(n) = n^2 mod 15.
  • A070439 (program): a(n) = n^2 mod 16.
  • A070440 (program): a(n) = n^2 mod 18.
  • A070441 (program): n^2 mod 19.
  • A070442 (program): a(n) = n^2 mod 20.
  • A070443 (program): a(n) = n^2 mod 21.
  • A070444 (program): a(n) = n^2 mod 22.
  • A070445 (program): a(n) = n^2 mod 23.
  • A070446 (program): a(n) = n^2 mod 24.
  • A070447 (program): a(n) = n^2 mod 25.
  • A070448 (program): a(n) = n^2 mod 26.
  • A070449 (program): a(n) = n^2 mod 27.
  • A070450 (program): a(n) = n^2 mod 28.
  • A070451 (program): a(n) = n^2 mod 29.
  • A070452 (program): a(n) = n^2 mod 30.
  • A070453 (program): a(n) = n^2 mod 31.
  • A070454 (program): a(n) = n^2 mod 32.
  • A070455 (program): a(n) = n^2 mod 33.
  • A070456 (program): a(n) = n^2 mod 34.
  • A070457 (program): a(n) = n^2 mod 35.
  • A070458 (program): a(n) = n^2 mod 36.
  • A070459 (program): a(n) = n^2 mod 37.
  • A070460 (program): a(n) = n^2 mod 38.
  • A070461 (program): a(n) = n^2 mod 39.
  • A070462 (program): a(n) = n^2 mod 40.
  • A070463 (program): a(n) = n^2 mod 41.
  • A070464 (program): a(n) = n^2 mod 42.
  • A070465 (program): a(n) = n^2 mod 43.
  • A070466 (program): a(n) = n^2 mod 44.
  • A070467 (program): a(n) = n^2 mod 45.
  • A070468 (program): a(n) = n^2 mod 46.
  • A070469 (program): a(n) = n^2 mod 47.
  • A070470 (program): a(n) = n^2 mod 48.
  • A070471 (program): a(n) = n^3 mod 5.
  • A070472 (program): a(n) = n^3 mod 7.
  • A070473 (program): a(n) = n^3 mod 11.
  • A070474 (program): a(n) = n^3 mod 12, n^5 mod 12.
  • A070475 (program): a(n) = n^3 mod 13.
  • A070476 (program): a(n) = n^3 mod 14.
  • A070477 (program): a(n) = n^3 mod 15.
  • A070478 (program): a(n) = n^3 mod 16.
  • A070479 (program): a(n) = n^3 mod 17.
  • A070480 (program): a(n) = n^3 mod 18.
  • A070481 (program): a(n) = n^3 mod 19.
  • A070482 (program): a(n) = n^3 mod 20.
  • A070483 (program): a(n) = n^3 mod 21.
  • A070484 (program): a(n) = n^3 mod 22.
  • A070485 (program): a(n) = n^3 mod 23.
  • A070486 (program): a(n) = n^3 mod 24 (or equivalently, n^5 mod 24).
  • A070487 (program): a(n) = n^3 mod 25.
  • A070488 (program): a(n) = n^3 mod 26.
  • A070489 (program): a(n) = n^3 mod 27.
  • A070490 (program): a(n) = n^3 mod 28.
  • A070491 (program): a(n) = n^3 mod 29.
  • A070492 (program): a(n) = n^3 mod 30.
  • A070493 (program): a(n) = n^3 mod 31.
  • A070494 (program): a(n) = n^3 mod 32.
  • A070495 (program): a(n) = n^3 mod 33.
  • A070496 (program): a(n) = n^3 mod 34.
  • A070497 (program): a(n) = n^3 mod 35.
  • A070498 (program): a(n) = n^3 mod 36.
  • A070499 (program): a(n) = n^3 mod 37.
  • A070500 (program): a(n) = n^3 mod 38.
  • A070501 (program): a(n) = n^3 mod 39.
  • A070502 (program): a(n) = n^3 mod 40.
  • A070503 (program): a(n) = n^3 mod 41.
  • A070504 (program): a(n) = n^3 mod 42.
  • A070505 (program): a(n) = n^3 mod 43.
  • A070506 (program): a(n) = n^3 mod 44.
  • A070507 (program): a(n) = n^3 mod 45.
  • A070508 (program): a(n) = n^3 mod 46.
  • A070509 (program): a(n) = n^3 mod 47.
  • A070510 (program): a(n) = n^3 mod 48.
  • A070511 (program): a(n) = n^4 mod 6.
  • A070512 (program): a(n) = n^4 mod 7.
  • A070513 (program): a(n) = n^4 mod 9.
  • A070514 (program): Final digit of n^4: n^4 mod 10.
  • A070515 (program): a(n) = n^4 mod 11.
  • A070517 (program): a(n) = n^4 mod 13.
  • A070532 (program): a(n) = n^4 mod 14.
  • A070533 (program): n^4 mod 15.
  • A070534 (program): a(n) = n^4 mod 17.
  • A070535 (program): a(n) = n^4 mod 18.
  • A070538 (program): a(n) = n^4 mod 19.
  • A070539 (program): a(n) = n^4 mod 20.
  • A070540 (program): a(n) = n^4 mod 21.
  • A070541 (program): a(n) = n^4 mod 22.
  • A070545 (program): a(n)=Card( k, 0<k<=n such that k is relatively prime to sigma(k)).
  • A070546 (program): a(n)=Card( k, 0<k<=n such that k is relatively prime to tau(k)=A000005(k)).
  • A070548 (program): a(n) = Cardinality k in range 1 <= k <= n such that Moebius(k) = 1 .
  • A070549 (program): a(n) = Card(k 0<k<=n such that mu(k)=-1).
  • A070550 (program): a(n) = a(n-1) + a(n-3) + a(n-4), starting with a(0..3) = 1, 2, 2, 3.
  • A070551 (program): n^4 mod 23.
  • A070553 (program): Rectangular array read by rows: n-th row gives the 7 numbers k*10^n mod 7 for 0 <= k < 7.
  • A070563 (program): a(n) = 0 if 3 divides the Ramanujan number tau(n) (A000594(n)), otherwise 1.
  • A070564 (program): Partial sums of A070563.
  • A070567 (program): a(n) = n^4 mod 24.
  • A070568 (program): n^4 mod 25.
  • A070569 (program): n^4 mod 26.
  • A070570 (program): n^4 mod 27.
  • A070571 (program): n^4 mod 28.
  • A070572 (program): n^4 mod 29.
  • A070573 (program): n^4 mod 30.
  • A070574 (program): n^4 mod 31.
  • A070575 (program): n^4 mod 32.
  • A070576 (program): n^4 mod 33.
  • A070577 (program): a(n) = n^4 mod 34.
  • A070578 (program): a(n) = n^4 mod 35.
  • A070579 (program): n^4 mod 36.
  • A070580 (program): a(n) = n^4 mod 37.
  • A070581 (program): n^4 mod 38.
  • A070582 (program): n^4 mod 39.
  • A070583 (program): n^4 mod 40.
  • A070584 (program): n^4 mod 41.
  • A070585 (program): n^4 mod 42.
  • A070586 (program): a(n) = n^4 mod 43.
  • A070587 (program): n^4 mod 44.
  • A070588 (program): a(n) = n^4 mod 45.
  • A070589 (program): n^4 mod 46.
  • A070590 (program): n^4 mod 47.
  • A070591 (program): n^4 mod 48.
  • A070593 (program): a(n) = n^5 mod 7.
  • A070595 (program): n^5 mod 9.
  • A070596 (program): n^5 mod 11.
  • A070598 (program): n^5 mod 13.
  • A070599 (program): n^5 mod 14.
  • A070601 (program): n^5 mod 17.
  • A070602 (program): n^5 mod 18.
  • A070603 (program): n^5 mod 19.
  • A070604 (program): n^5 mod 20.
  • A070605 (program): n^5 mod 21.
  • A070606 (program): n^5 mod 22.
  • A070607 (program): a(n) = n^5 mod 23.
  • A070609 (program): a(n) = n^5 mod 25.
  • A070611 (program): n^5 mod 27.
  • A070612 (program): n^5 mod 28.
  • A070613 (program): n^5 mod 29.
  • A070614 (program): a(n) = n^5 mod 31.
  • A070616 (program): n^5 mod 33.
  • A070617 (program): n^5 mod 34.
  • A070618 (program): a(n) = n^5 mod 35.
  • A070619 (program): n^5 mod 36.
  • A070620 (program): a(n) = n^5 mod 37.
  • A070621 (program): a(n) = n^5 mod 38.
  • A070622 (program): a(n) = n^5 mod 39.
  • A070623 (program): n^5 mod 40.
  • A070624 (program): n^5 mod 41.
  • A070625 (program): n^5 mod 42.
  • A070626 (program): n^5 mod 43.
  • A070627 (program): n^5 mod 44.
  • A070628 (program): n^5 mod 45.
  • A070629 (program): n^5 mod 46.
  • A070630 (program): n^5 mod 47.
  • A070631 (program): n^5 mod 48.
  • A070634 (program): n^6 mod 11.
  • A070636 (program): n^6 mod 13.
  • A070637 (program): n^6 mod 14.
  • A070638 (program): a(n) = n^6 mod 15.
  • A070640 (program): n^6 mod 17.
  • A070641 (program): n^6 mod 18.
  • A070642 (program): n^6 mod 19.
  • A070644 (program): n^6 mod 21.
  • A070645 (program): n^6 mod 22.
  • A070646 (program): n^6 mod 23.
  • A070648 (program): n^6 mod 25.
  • A070649 (program): n^6 mod 26.
  • A070650 (program): n^6 mod 27.
  • A070651 (program): n^6 mod 28.
  • A070652 (program): n^6 mod 29.
  • A070653 (program): a(n) = n^6 mod 30.
  • A070654 (program): n^6 mod 31.
  • A070656 (program): a(n) = n^6 mod 33.
  • A070657 (program): n^6 mod 34.
  • A070658 (program): n^6 mod 35.
  • A070659 (program): n^6 mod 36.
  • A070660 (program): n^6 mod 37.
  • A070661 (program): n^6 mod 38.
  • A070662 (program): n^6 mod 39.
  • A070663 (program): n^6 mod 40.
  • A070664 (program): n^6 mod 41.
  • A070665 (program): n^6 mod 42.
  • A070666 (program): n^6 mod 43.
  • A070684 (program): n^6 mod 44.
  • A070685 (program): n^6 mod 45.
  • A070686 (program): n^6 mod 46.
  • A070687 (program): n^6 mod 47.
  • A070688 (program): a(n) = n^6 mod 48.
  • A070690 (program): a(n) = n^7 mod 5.
  • A070691 (program): (Sum of digits of n)^n.
  • A070692 (program): a(n) = n^7 mod 9.
  • A070693 (program): a(n) = n^7 mod 11.
  • A070695 (program): a(n) = n^7 mod 13.
  • A070696 (program): a(n) = n mod 14.
  • A070697 (program): n^7 mod 15.
  • A070699 (program): a(n) = n^7 mod 17.
  • A070700 (program): a(n) = n^7 mod 18.
  • A070701 (program): a(n) = n^7 mod 19.
  • A070702 (program): a(n) = n^7 mod 20.
  • A070703 (program): a(n) = n^7 mod 22.
  • A070704 (program): a(n) = n^7 mod 23.
  • A070706 (program): a(n) = n^7 mod 25.
  • A070707 (program): n^7 mod 26.
  • A070708 (program): n^7 mod 27.
  • A070709 (program): n^7 mod 28.
  • A070710 (program): n^7 mod 29.
  • A070711 (program): n^7 mod 30.
  • A070712 (program): a(n) = n^7 mod 31.
  • A070714 (program): n^7 mod 33.
  • A070715 (program): n^7 mod 34.
  • A070716 (program): n^7 mod 35.
  • A070717 (program): a(n) = n^7 mod 36.
  • A070718 (program): n^7 mod 37.
  • A070719 (program): n^7 mod 38.
  • A070720 (program): n^7 mod 39.
  • A070721 (program): n^7 mod 40.
  • A070722 (program): a(n) = n^7 mod 41.
  • A070723 (program): n^7 mod 43.
  • A070724 (program): n^7 mod 44.
  • A070725 (program): n^7 mod 45.
  • A070726 (program): a(n) = n^7 mod 46.
  • A070727 (program): n^7 mod 47.
  • A070728 (program): n^7 mod 48.
  • A070734 (program): Order of the subgroup of the symmetric group S_n generated by the cycles (1,2,3) and (1,2,3,…,n).
  • A070750 (program): 0 if n-th prime is even, 1 if n-th prime is == 1 mod 4, and -1 if n-th prime is == 3 mod 4.
  • A070775 (program): a(n) = Sum_ k=0..n binomial(4n,4k).
  • A070777 (program): a(1) = 1; a(n) = (largest prime factor of n) - 1.
  • A070780 (program): Binomial((n+1)^2,n).
  • A070781 (program): a(n) = binomial((n+1)^2, n^2).
  • A070782 (program): a(n) = Sum_ k=0..n binomial(5n,5k).
  • A070800 (program): Smallest prime greater than phi(n): a(n) = nextprime(phi(n)).
  • A070801 (program): Largest prime <= sigma(n): a(n) = prevprime(sigma(n)), where prevprime(n) = A007917(n), the largest prime less than or equal to n.
  • A070803 (program): Number of primes not exceeding sum of divisors of n.
  • A070804 (program): Number of primes not exceeding phi(n).
  • A070820 (program): Difference between n-th prime and the value of commutator[phi,gpf] = commutator[A000010, A006530] at the same prime argument.
  • A070824 (program): Number of divisors of n which are > 1 and < n (nontrivial divisors).
  • A070825 (program): One half of product of first n+1 Lucas numbers A000032.
  • A070826 (program): One half of product of first n primes A000040.
  • A070832 (program): a(n) = Sum_ k=0..n binomial(8n,8k).
  • A070834 (program): Reverse(n)^n.
  • A070846 (program): Smallest prime == 1 (mod 2n).
  • A070847 (program): Smallest prime == 1 mod (3n).
  • A070848 (program): Smallest prime == 1 mod (4n).
  • A070849 (program): Smallest prime == 1 mod (5n).
  • A070850 (program): Smallest prime == 1 mod (6n).
  • A070851 (program): Smallest prime == 1 mod (7n).
  • A070852 (program): Smallest prime == 1 mod (8n).
  • A070853 (program): Smallest prime == 1 mod (9n).
  • A070864 (program): a(1) = a(2) = 1; a(n) = 2 + a(n - a(n-1)).
  • A070875 (program): Binary expansion is 1x100…0 where x = 0 or 1.
  • A070876 (program): Binary expansion is 1xx100…0 where xx = 00 or 11.
  • A070883 (program): Bitwise XOR of n and n-th prime.
  • A070884 (program): 7 + x where x is congruent to 0, 4, 6, 10, 12, 16, 22, 24 mod 30.
  • A070885 (program): a(n) = (3/2)a(n-1) if a(n-1) is even; (3/2)(a(n-1)+1) if a(n-1) is odd.
  • A070886 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 90”.
  • A070893 (program): Let r, s, t be three permutations of the set 1,2,3,..,n ; a(n) = value of Sum_ i=1..n r(i)s(i)t(i), with r= 1,2,3,..,n ; s= n,n-1,..,1 and t= n,n-2,n-4,…,1,…,n-3,n-1 .
  • A070909 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 28” and by “Rule 156”.
  • A070910 (program): Decimal expansion of BesselI(0,2).
  • A070923 (program): a(n) is the smallest value >= 0 of the form x^3 - n^2.
  • A070929 (program): Smallest integer >= 0 of the form x^2 - n^3.
  • A070930 (program): Smallest integer >= 0 of the form x^3 - n^4.
  • A070935 (program): Largest proper divisor of n^2.
  • A070939 (program): Length of binary representation of n.
  • A070940 (program): Number of digits that must be counted from left to right to reach the last 1 in the binary representation of n.
  • A070941 (program): Length of binary representation of 2n+1.
  • A070960 (program): a(1) = 1; a(n) = n!*(3/2) for n>=2.
  • A070967 (program): a(n) = Sum_ k=0..n binomial(6n,6k).
  • A070992 (program): Partial sums of A002487.
  • A070997 (program): a(n) = 8*a(n-1) - a(n-2), a(0)=1, a(-1)=1.
  • A070998 (program): a(n) = 9*a(n-1) - a(n-2) for n > 0, a(0)=1, a(-1)=1.
  • A071022 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 70” and by “Rule 198”.
  • A071023 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 78”.
  • A071024 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 92”.
  • A071026 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 188”.
  • A071028 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 50”.
  • A071030 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 54”.
  • A071041 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 246”.
  • A071042 (program): Number of 0’s in n-th row of triangle in A070886.
  • A071045 (program): Number of 0’s in n-th row of triangle in A071030.
  • A071050 (program): Number of 0’s in n-th row of triangle in A071035.
  • A071051 (program): Number of 1’s in n-th row of triangle in A071035.
  • A071054 (program): a(2n)=3n+1, a(2n+1)=2n+2.
  • A071055 (program): Number of 0’s in n-th row of triangle in A071038.
  • A071061 (program): Abjad values of the Arabic letters in the traditional order for abjad calculations.
  • A071072 (program): Minimal “multiples of 4” set in base 10.
  • A071089 (program): Remainder when sum of first n primes is divided by n-th prime.
  • A071099 (program): a(n) = (n-1)*(n+3) - 2^n + 4.
  • A071118 (program): Size of the automorphism group of the group Z X Z_n.
  • A071121 (program): a(n) = a(n-1) + sum of decimal digits of n^3.
  • A071122 (program): a(n) = a(n-1) + sum of decimal digits of 2^n.
  • A071148 (program): Partial sums of sequence of odd primes (A065091); a(n) = sum of the first n odd primes.
  • A071171 (program): L_2 norm of vertices of Permuto-Associahedron in R^n.
  • A071178 (program): Exponent of the largest prime factor of n.
  • A071187 (program): Smallest prime factor of number of divisors of n.
  • A071188 (program): Largest prime factor of number of divisors of n.
  • A071189 (program): Smallest prime factor of sum of divisors of n.
  • A071190 (program): Greatest prime factor of sum of divisors of n, for n >= 2; a(1) = 1.
  • A071222 (program): Smallest k such that gcd(n,k) = gcd(n+1,k+1).
  • A071228 (program): a(n) = n*(n-th composite number).
  • A071229 (program): a(n) = n(14n^2-21*n+13)/6.
  • A071230 (program): a(n) = n(6n^2 - 7*n + 3)/2.
  • A071231 (program): a(n) = (n^8 + n^4)/2.
  • A071232 (program): a(n) = (n^6 + n^3)/2.
  • A071233 (program): a(n) = 2(n-1)(n^2 + 1).
  • A071235 (program): a(n) = (n^12 + n^6)/2.
  • A071236 (program): a(n) = (n^10 + n^5)/2.
  • A071237 (program): a(n) = n(n+1)(n^2+1)/2.
  • A071238 (program): a(n) = n(n+1)(2*n^2+1)/6.
  • A071239 (program): a(n) = n(n+1)(n^2+2)/6.
  • A071244 (program): n(n-1)(n^2+2)/6.
  • A071245 (program): a(n) = n(n-1)(2*n^2+1)/6.
  • A071246 (program): a(n) = n(n - 1)(2*n^2 + n + 2)/6.
  • A071252 (program): a(n) = n(n - 1)(n^2 + 1)/2.
  • A071253 (program): a(n) = n^2*(n^2+1).
  • A071270 (program): a(n) = n^2(2n^2+1)/3.
  • A071273 (program): Concatenation of R(n) (A004086) and n, omitting leading 0’s.
  • A071274 (program): A071273 divided by 11.
  • A071279 (program): Kissing number of regular n-gon.
  • A071281 (program): Numerators of Peirce sequence of order 3.
  • A071282 (program): Denominators of Peirce sequence of order 3.
  • A071289 (program): a(n) = n(n^2 + 1) if n is even, otherwise (n - 1/2)(n^2 + 1).
  • A071317 (program): a(n) = a(n-1) + sum of digits of n^2.
  • A071324 (program): Alternating sum of all divisors of n; divisors nonincreasing, starting with n.
  • A071325 (program): Number of squares > 1 dividing n.
  • A071326 (program): Sum of squares > 1 dividing n.
  • A071328 (program): Smallest prime q such that q - prime(n) >= n.
  • A071355 (program): a(n) = 2n^2 + 11n + 12.
  • A071374 (program): 0 iff n is of the form 4^a*(8k+7), otherwise 1.
  • A071377 (program): Number of positive integers <= n which are the sum of 3 squares.
  • A071378 (program): Largest proper divisor of n^3.
  • A071396 (program): Rounded total surface area of a regular octahedron with edge length n.
  • A071398 (program): Rounded total surface area of a regular icosahedron with edge length n.
  • A071400 (program): Rounded volume of a regular octahedron with edge length n.
  • A071403 (program): Which squarefree number is prime? a(n)-th squarefree number equals n-th prime.
  • A071408 (program): a(n+1) - 2a(n) + a(n-1) = (2/3)(1 + w^(n+1) + w^(2*n+2)) with a(1)=0, a(2)=1, and where w is the imaginary cubic root of unity.
  • A071412 (program): A002487 mod 3.
  • A071413 (program): a(n) = if n=0 then 0 else a(floor(n/2))+n*(-1)^(n mod 2).
  • A071416 (program): a(n) = gcd(n, binomial(2*n, n)).
  • A071421 (program): a(n) = a(n-1) + sum of decimal digits of n^n.
  • A071422 (program): a(n) = a(n-1) + sum of decimal digits of sigma(n), the sum of divisors of n.
  • A071423 (program): a(n) = a(n-1) + number of decimal digits of 2^n. Number of decimal digits of concatenation of first n powers of 2.
  • A071424 (program): a(n) = a(n-1) + number of decimal digits of n!. Number of decimal digits of concatenation of first n factorials.
  • A071425 (program): Total number of 1-s in binary representation of all factorials from 1 to n.
  • A071520 (program): Number of 5-smooth numbers (A051037) <= n.
  • A071521 (program): Number of 3-smooth numbers <= n.
  • A071523 (program): Number of 11-smooth numbers <= n.
  • A071538 (program): Number of twin prime pairs (p, p+2) with p <= n.
  • A071542 (program): Number of steps to reach 0 starting with n and using the iterated process : x -> x - (number of 1’s in binary representation of x).
  • A071554 (program): Smallest x > 1 such that x^prime(n) == 1 mod(prime(i)) 2<=i<=n.
  • A071555 (program): Smallest x > 1 such that x^prime(n) == 1 mod(prime(i)) 3<=i<=n.
  • A071556 (program): Smallest x > 1 such that x^prime(n) == 1 mod(prime(i)) 4<=i<=n.
  • A071568 (program): Smallest k>n such that n^3+1 divides k*n^2+1.
  • A071575 (program): Number of iterations of cototient(n) needed to reach 1 (cototient(x) = x-phi(x)).
  • A071578 (program): Number of iterations of Pi(n) needed to reach 1, where Pi(x) denotes the number of primes <= x.
  • A071582 (program): Powers of 4 written backwards.
  • A071583 (program): Powers of 5 written backwards.
  • A071584 (program): Powers of 7 written backwards.
  • A071586 (program): Powers of 8 written backwards.
  • A071587 (program): Powers of 9 written backwards.
  • A071588 (program): Powers of 6 written backwards.
  • A071602 (program): Sum of the reverses of the first n primes.
  • A071604 (program): a(n) is the number of 7-smooth numbers <= n.
  • A071618 (program): a(n+1) - 3*a(n) + a(n-1) = (2/3)(1+w^(n+1)+w^(2n+2)), where w = exp(2 Pi I / 3).
  • A071619 (program): a(n) = ceiling( 2*n^2/3 ).
  • A071621 (program): Primes that can be written as “a * b + c * d”, where a, b, c and d are also primes.
  • A071679 (program): Least k such that the maximum number of elements among the continued fractions for k/1, k/2, k/3, k/4 …., k/k equals n.
  • A071683 (program): Nonprimes which are the average of two consecutive Fibonacci numbers.
  • A071701 (program): Number of twin prime pairs <= n of form (4k+1,4k+3), k>0.
  • A071716 (program): Expansion of (1+x^2C)C, where C = (1-(1-4x)^(1/2))/(2x) is g.f. for Catalan numbers, A000108.
  • A071720 (program): Number of spanning trees in K_ n -e, the complete graph on n nodes minus an edge (n > 1).
  • A071721 (program): Expansion of (1+x^2C^2)C^2, where C = (1-(1-4x)^(1/2))/(2x) is g.f. for Catalan numbers, A000108.
  • A071724 (program): a(n) = 3*binomial(2n, n-1)/(n+2), n > 0, with a(0)=1.
  • A071725 (program): Expansion of (1+x^2C^4)C, where C = (1 - sqrt(1-4x))/(2x) is g.f. for Catalan numbers, A000108.
  • A071735 (program): Expansion of (1+x^3C^3)C^2, where C = (1-(1-4x)^(1/2))/(2x) is g.f. for Catalan numbers, A000108.
  • A071738 (program): Expansion of (1+x^3C^4)C, where C = (1-(1-4x)^(1/2))/(2x) is g.f. for Catalan numbers, A000108.
  • A071773 (program): a(n) = gcd(rad(n), n/rad(n)), where rad(n) = A007947(n) is the squarefree kernel of n.
  • A071789 (program): Decimal expansion of the first (of 10) decimal selvage numbers; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071790 (program): Decimal expansion of the second (of 10) decimal selvage numbers; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071791 (program): Decimal expansion of the third (of 10) decimal selvage numbers; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071792 (program): Decimal expansion of the fourth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071793 (program): Decimal expansion of the fifth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071797 (program): Restart counting after each new odd integer (a fractal sequence).
  • A071816 (program): Number of ordered solutions to x+y+z = u+v+w, 0 <= x, y, z, u, v, w < n.
  • A071823 (program): Number of numbers x <= n with largest prime factor of the form 4k+3.
  • A071824 (program): Number of x with largest prime factor of the form 4k+1 less than or equal to n.
  • A071840 (program): Number of primes == 3 mod 8 <= n.
  • A071858 (program): (Number of 1’s in binary expansion of n) mod 3.
  • A071860 (program): Number of k 1<=k<=n such that sigma(k) is odd.
  • A071868 (program): Number of k (1 <= k <= n) such that k^2+1 is prime.
  • A071873 (program): Decimal expansion of the sixth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071874 (program): Decimal expansion of the seventh (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071875 (program): Decimal expansion of the eighth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071876 (program): Decimal expansion of the ninth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071877 (program): Decimal expansion of the tenth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.
  • A071903 (program): Number of x less than or equal to n and divisible only by primes congruent to 3 mod 4 (i.e., in A004614).
  • A071906 (program): Sum of digits of 2^n (mod 2).
  • A071910 (program): a(n) = t(n)t(n+1)t(n+2), where t() are the triangular numbers.
  • A071917 (program): Number of pairs (x,y) where x is even, y is odd, 1<=x<=n, 1<=y<=n and x+y is prime.
  • A071919 (program): Number of monotone nondecreasing functions [n]->[m] for n>=0, m>=0, read by antidiagonals.
  • A071928 (program): Kolakoski-(2,4) sequence: a(n) is length of n-th run.
  • A071930 (program): Number of words of length 2n in the two letters s and t that reduce to the identity 1 by using the relations ssTT=1, ststSS=1 and ststTT=1, where S and T are the inverses of s and t, respectively (i.e., sS=1 and tT=1). The generators s and t and the three stated relations generate the quaternion group Q4.
  • A071933 (program): a(n) = Sum_ i=1..n K(i,i+1), where K(x,y) is the Kronecker symbol (x/y).
  • A071934 (program): a(n) = Sum_ i=1..n K(i+1,i), where K(x,y) is the Kronecker symbol (x/y).
  • A071935 (program): K(n,n+1) where K(x,y) is the Kronecker symbol (x/y).
  • A071936 (program): K(n+1,n) where K(x,y) is the Kronecker symbol (x/y).
  • A071937 (program): Reverse(n)!.
  • A071953 (program): Diagonal T(n,n-2) of triangle in A071951.
  • A071954 (program): a(n) = 4*a(n-1) - a(n-2) - 4, with a(0) = 2, a(1) = 4.
  • A071955 (program): a(n) = remainder when n is reduced mod reverse(n).
  • A071960 (program): Largest k >= 0 such that Product_ i=0..k (n+i) divides n!.
  • A071981 (program): Parity of the digits of e in base 10.
  • A071982 (program): Parity of the decimal digits of sqrt(2).
  • A071986 (program): Parity of the prime-counting function pi(n).
  • A071991 (program): a(1) = a(2) = 1; a(n) = a(floor(n/3)) + a(n - floor(n/3)).
  • A071996 (program): a(1) = 0, a(2) = 1, a(n) = a(floor(n/3)) + a(n - floor(n/3)).
  • A071998 (program): Write n in binary, interpret that as a decimal number, convert back to binary.
  • A071999 (program): Determinant of n X n matrix whose element A(i,j) is 1 if i=j, i if n=i+j and 0 otherwise.
  • A072000 (program): Number of semiprimes (A001358) <= n.
  • A072003 (program): 10’s complement of final digit of n-th prime.
  • A072025 (program): a(n) = n^4 + 2n^3 + 4n^2 + 3n + 1 = ((n+1)^5+n^5) / (2n+1).
  • A072055 (program): a(n) = 2*prime(n)+1.
  • A072056 (program): Number of divisors of 2*prime(n)+1.
  • A072057 (program): Sum of divisors of 2*prime(n)+1.
  • A072058 (program): Squarefree kernel of 2*prime(n)+1.
  • A072065 (program): Define a “piece” to consist of 3 mutually touching pennies welded together to form a triangle; sequence gives side lengths of triangles that can be made from such pieces.
  • A072078 (program): Number of 3-smooth divisors of n.
  • A072100 (program): Column 2 of the array m(i,1)=m(1,j)=1 m(i,j)=m(i-1,j-1)+m(i-1,j+1) (a(n)=m(n,2)).
  • A072107 (program): a(n) = sum( k=1,n, A014963(k) ).
  • A072110 (program): a(n) = 4*a(n-1) - a(n-2) - 2, with a(0)=1, a(1)=2.
  • A072114 (program): Number of 3-almost primes (A014612) <= n.
  • A072126 (program): Parity of the decimal digits of log(2).
  • A072130 (program): a(n+1) -3a(n) + a(n-1) = (2/3)(1+w^(n+1)+w^(2*n+2)); a(1) = 0, a(2) = 1; where w is the cubic root of unity.
  • A072134 (program): Second generation sequence in which each number is skipped that can be written as sum of distinct previous entries. To make the first generation we start with all natural numbers: this gives the powers of 2 (A000079). For the second generation we start with the natural numbers from which are removed the numbers of the first generation.
  • A072154 (program): Coordination sequence for the planar net 4.6.12.
  • A072172 (program): a(n) = (2n+1)5^(2*n+1).
  • A072175 (program): a(1)=1, a(2)=2, a(n) = a(n-1) + 1 - 2*sign(a(n-2)) for n>2.
  • A072176 (program): Unimodal analog of Fibonacci numbers: a(n+1) = Sum_ k=0..floor(n/2) A071922(n-k,k).
  • A072195 (program): Replace all prime factors p of n with n/p.
  • A072196 (program): Multiples of 3 which on one operation of the Collatz function T (N -> 3N+1/2^r) yield the number 5.
  • A072197 (program): a(n) = 4*a(n-1) + 1 with a(0) = 3.
  • A072201 (program): a(n) = 4*a(n-1) + 1, a(1) = 15.
  • A072203 (program): (Number of oddly factored numbers <= n) - (number of evenly factored numbers <= n).
  • A072205 (program): a(n) = (p^2 - p + 2)/2 for p = prime(n); number of squares modulo p^2.
  • A072206 (program): Third terms of triple Peano sequence A071988.
  • A072211 (program): a(n) = p-1 if n=p, p if n=p^e and e<>1, 1 otherwise; p a prime.
  • A072219 (program): Any number n can be written uniquely in the form n = 2^k_1 - 2^k_2 + 2^k_3 - … + 2^k_ 2r+1 where the signs alternate, there are an odd number of terms, and k_1 > k_2 > k_3 > … > k_ 2r+1 >= 0; sequence gives number of terms 2r+1.
  • A072221 (program): a(n) = 6*a(n-1) - a(n-2) + 2, with a(0)=1, a(1)=4.
  • A072229 (program): Witt index of the standard bilinear form <1,1,1,…,1> over the 2-adic rationals.
  • A072230 (program): a(n) = n! (mod n^2), that is, n factorial modulo n^2.
  • A072251 (program): (3a(n)+1)/2^(2n + 1) = 23-6*n.
  • A072253 (program): Numbers n for which one step of the Collatz iteration (3n+1)/2^r gives rise to values 59,53,47,41,35,29,23,17,11 and 5 for r=1,3,5,..,19.
  • A072256 (program): a(n) = 10*a(n-1) - a(n-2) for n > 1, a(0) = a(1) = 1.
  • A072257 (program): a(n) = ((6n-17)4^n - 1)/3.
  • A072258 (program): a(n) = ((6n+1)4^n - 1)/3.
  • A072259 (program): a(n) = ((6n+37)4^n - 1)/3.
  • A072260 (program): a(n) = ((6n+19)4^n - 1)/3.
  • A072261 (program): a(n) = 4*a(n-1) + 1, a(1)=7.
  • A072262 (program): a(n) = 4*a(n-1) + 1, a(1)=11.
  • A072265 (program): Variant of Lucas numbers: a(n) = a(n-1) + 4*a(n-2) starting with a(0)=2 and a(1)=1.
  • A072277 (program): Smallest integer > 1 which is both n-gonal and centered n-gonal.
  • A072290 (program): Number of digits in the decimal expansion of the Champernowne constant that must be scanned to encounter all n-digit strings.
  • A072292 (program): Number of proper powers b^d <= n (b > 1, d > 1).
  • A072334 (program): Decimal expansion of e^2.
  • A072335 (program): Expansion of 1/((1-x^2)(1-4x+x^2)).
  • A072339 (program): Any number n can be written (in two ways, one with m even and one with m odd) in the form n = 2^k_1 - 2^k_2 + 2^k_3 - … + 2^k_m where the signs alternate and k_1 > k_2 > k_3 > … >k_m >= 0; sequence gives minimal value of m.
  • A072341 (program): a(n) = the least natural number k such that k*sigma(n) + 1 is prime.
  • A072342 (program): a(n) = the least natural number k such that k*reverse(n) + 1 is prime.
  • A072344 (program): a(n) = the least natural number k such that k*phi(n) + 1 is prime.
  • A072345 (program): Volume of n-dimensional sphere of radius r is V_nr^n = Pi^(n/2)r^n/(n/2)! = C_nPi^floor(n/2)r^n; sequence gives numerator of C_n.
  • A072346 (program): Volume of n-dimensional sphere of radius r is V_nr^n = Pi^(n/2)r^n/(n/2)! = C_nPi^floor(n/2)r^n; sequence gives denominator of C_n.
  • A072373 (program): Complexity of doubled cycle (regarding case n = 2 as a graph).
  • A072376 (program): a(n) = a(floor(n/2)) + a(floor(n/4)) + a(floor(n/8)) + … starting with a(0)=0 and a(1)=1.
  • A072379 (program): Sum_ k<=n (sigma(k)^2), where sigma(k) denotes the sum of the divisors of k A000203.
  • A072400 (program): (Factors of 4 removed from n) modulo 8.
  • A072401 (program): 1 iff n is of the form 4^m*(8k+7).
  • A072418 (program): Parity of floor(3^n/2^n).
  • A072436 (program): Remove prime factors of form 4*k+3.
  • A072438 (program): Remove prime factors of form 4*k+1.
  • A072442 (program): Least k such that Sum( Cos(1/Sqrt(i)) i=1..k) > n.
  • A072448 (program): Squares of the terms of the decimal expansion of Pi.
  • A072451 (program): Number of odd terms in the reduced residue system of 2*n-1.
  • A072464 (program): Code word lengths for non-redundant MML code for positive integers.
  • A072477 (program): (2n)!binomial(2*n,n)/8.
  • A072479 (program): Surface area of n-dimensional sphere of radius r is nV_nr^(n-1) = nPi^(n/2)r^(n-1)/(n/2)! = S_nPi^floor(n/2)r^(n-1); sequence gives denominator of S_n.
  • A072481 (program): a(n) = Sum_ k=1..n Sum_ d=1..k (k mod d).
  • A072486 (program): a(1) = 1, a(n) = a(n-1) times smallest prime factor of n.
  • A072490 (program): Number of squarefree numbers (excluding 1) less than n.
  • A072491 (program): Define f(1) = 0. For n>=2, let f(n) = n - p where p is the largest prime <= n. a(n) = number of iterations of f to reach 0, starting from n.
  • A072493 (program): a(1) = 1 and a(n) = ceiling((Sum_ k=1..n-1 a(k))/3) for n >= 2.
  • A072507 (program): Smallest start of n consecutive integers with n divisors, or 0 if no such number exists.
  • A072527 (program): Number of values of k such that n divided by k leaves a remainder 3.
  • A072547 (program): Main diagonal of the array in which first column and row are filled alternatively with 1’s or 0’s and then T(i,j) = T(i-1,j) + T(i,j-1).
  • A072557 (program): Let w(n) be defined by the following recurrence: w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3); sequence gives values of n such that w(n) is an integer.
  • A072561 (program): Denominators of w(n) equals 3 where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).
  • A072586 (program): Number of numbers <= n having prime factors with odd exponents only.
  • A072608 (program): Parity of remainder Mod[p(n),n]=A004648(n).
  • A072630 (program): Values of n where A072629 switches from 01010.. into 0000.. or back.
  • A072632 (program): Solutions to A072631[n]=0.
  • A072633 (program): Smallest positive integer m where 1^n+2^n+3^n+…+m^n is greater than or equal to (m+1)^n.
  • A072643 (program): Half of the binary width of the terms of A014486, the number of digits in A063171(n)/2.
  • A072648 (program): a(n) = [log_ Phi (n*sqrt(5))], where log_ Phi is logarithm in the base Phi ( = (sqrt(5)+1)/2) and [] stands for the floor function.
  • A072649 (program): n occurs Fibonacci(n) times (cf. A000045).
  • A072668 (program): Numbers one less than composite numbers.
  • A072670 (program): Number of ways to write n as i*j + i + j, 0 < i <= j.
  • A072674 (program): 3^n+2*2^n-3.
  • A072677 (program): a(n) = prime(prime(n)+1) where prime(k) is the k-th prime.
  • A072682 (program): Numbers congruent to 3, 36, 54, 57 mod 60.
  • A072689 (program): Difference between (least square >= n) and (largest square <= n).
  • A072690 (program): (n - A048760(n)) * (A048761(n) - n).
  • A072702 (program): Last digit of F(n) is 4 where F(n) is the n-th Fibonacci number.
  • A072703 (program): Indices of Fibonacci numbers whose last digit is 5.
  • A072708 (program): Last digit of F(n) is 6 where F(n) is the n-th Fibonacci number.
  • A072710 (program): Last digit of F(n) is 8 where F(n) is the n-th Fibonacci number.
  • A072731 (program): Difference of numbers of composite and prime numbers <= n.
  • A072805 (program): Primes of form 4k+3 written in base 3.
  • A072815 (program): Sum of proper divisors of 6n + 1.
  • A072818 (program): Possibly the only integers of the form sqrt(m^2(m^2-1)2/3) [only checked for the first 5 terms].
  • A072819 (program): Variance of time for a random walk starting at 0 to reach one of the boundaries at +n or -n for the first time.
  • A072831 (program): Number of bits in n!.
  • A072833 (program): Numbers that are congruent to 0, 5, 8, 9 mod 12.
  • A072834 (program): Exponents occurring in expansion of F_8(q^2).
  • A072835 (program): Exponents occurring in expansion of F_9(q^2).
  • A072861 (program): a(n) = sigma(n)^2.
  • A072863 (program): a(n) = 2^(n-3)(n^2+3n+8).
  • A072880 (program): A recurrence of order 6: a(1)=a(2)=a(3)=a(4)=a(5)=a(6)=1; a(n) = (a(n-1)^2 + a(n-2)^2 + a(n-3)^2 + a(n-4)^2 + a(n-5)^2)/a(n-6).
  • A072894 (program): Let c(k) be defined as follows: c(1)=1, c(2)=n, c(k+2) = c(k+1)/2 + c(k)/2 if c(k+1) and c(k) have the same parity; c(k+2) = c(k+1)/2 + c(k)/2 + 1/2 otherwise; a(n) = limit_ k -> infinity c(k).
  • A072900 (program): Discriminant of quadratic field Q(sqrt(prime(n))) where prime(n) is the n-th prime.
  • A072909 (program): Least k>0 such that n+k is squarefree.
  • A072912 (program): Number of Fibonacci numbers F(k) <= 10^n which end in 0.
  • A072917 (program): a(n) = p(n) - phi(n), where p(n) is the least prime greater than phi(n).
  • A072918 (program): a(n) = p(n) - sigma(n), where p(n) is the least prime greater than sigma(n).
  • A072920 (program): Sum(k=1,n, A034693(k)).
  • A072929 (program): a(n) = Sum_ d dividing n binomial(2d,d).
  • A072932 (program): Least k such that floor( (1+1/k)^n ) = floor( (1+1/n)^k ).
  • A072944 (program): a(1)=2, a(n+1) = 2*a(n) - phi(a(n)) where phi is the Euler totient function A000010.
  • A072946 (program): Coefficient of the highest power of q in the expansion of nu(0)=1, nu(1)=b and for n>=2, nu(n)=bnu(n-1)+lambda(n-1)_q*nu(n-2) with (b,lambda)=(2,2), where (n)_q=(1+q+…+q^(n-1)) and q is a root of unity.
  • A072988 (program): Coefficient of the highest power of q in the expansion of nu(0)=1, nu(1)=b and for n>=2, nu(n)=bnu(n-1)+lambda(n-1)_q*nu(n-2) with (b,lambda)=(3,1), where (n)_q=(1+q+…+q^(n-1)) and q is a root of unity.
  • A072996 (program): Coefficient of the highest power of q in the expansion of nu(0)=1, nu(1)=b and for n>=2, nu(n)=bnu(n-1)+lambda(n-1)_q*nu(n-2) with (b,lambda)=(2,1), where (n)_q=(1+q+…+q^(n-1)) and q is a root of unity.
  • A073010 (program): Decimal expansion of Pi/sqrt(27).
  • A073047 (program): Least k such that x(k)=0 where x(1)=n and x(k)=k*floor(x(k-1)/k).
  • A073059 (program): a(n) = (1/2)*(A073504(n+1) - A073504(n)).
  • A073065 (program): a(n) = prime(n) * prime(prime(n)).
  • A073080 (program): 3 appears three times, 23=6 appears six times, 26=12 appears twelve times etc.
  • A073089 (program): a(n) = (1/2)*(4n - 3 - Sum_ k=1..n A007400(k)).
  • A073093 (program): Number of prime power divisors of n.
  • A073094 (program): Final digit of C(2k,k) when not equal to zero.
  • A073121 (program): a(n) = ra(ceiling(n/2)) + sa(floor(n/2)) with a(1)=1 and (r,s)=(2,2).
  • A073122 (program): Minimal reversing binary representation of n. Converting sum of powers of 2 in binary representation of a(n) to alternating sum gives n. See A072339.
  • A073123 (program): a(n) is the largest number such that pi(a(n)) = prime(n).
  • A073124 (program): a(n) = prime(1+prime(n)) - prime(prime(n)).
  • A073136 (program): a(n) = prime(n) + prime(prime(n)).
  • A073169 (program): a(n)=A002808(n)-n, difference between n-th composite and n.
  • A073170 (program): a(1) = a(2) = 0; for n>2, a(n) = prime(n-1)-n+1.
  • A073171 (program): (n^2)-th composite number.
  • A073184 (program): Number of cubefree divisors of n.
  • A073185 (program): Sum of cubefree divisors of n.
  • A073188 (program): n appears 1+[n/3] times.
  • A073189 (program): Integers 0..k three times, then 0..k+1 three times, etc.
  • A073211 (program): Sum of two powers of 11.
  • A073216 (program): The terms of A055235 (sums of two powers of 3) divided by 2.
  • A073217 (program): The terms of A055237 (sums of two powers of 5) divided by 2.
  • A073218 (program): The terms of A055258 (sums of two powers of 7) divided by 2.
  • A073219 (program): The terms of A073211 (sums of two powers of 11) divided by 2.
  • A073225 (program): a(n) = ceiling(n^n/n!).
  • A073255 (program): Sum of divisors of n-th composite number.
  • A073256 (program): a(n) = phi(n-th composite number).
  • A073260 (program): Length of FixedPointList leading to value of [10^n]-th composite number.
  • A073267 (program): Number of compositions (ordered partitions) of n into exactly two powers of 2.
  • A073273 (program): a(n) = floor(sqrt(prime(n)*prime(n+2))).
  • A073333 (program): Decimal expansion of 1/(e - 1) = Sum_ k >= 1 exp(-k).
  • A073334 (program): The so-called “rhythmic infinity system” of Danish composer Per Nørgård [Noergaard].
  • A073353 (program): Sum of n and its squarefree kernel.
  • A073354 (program): Binomial coefficient ( n, squarefree kernel(n) ).
  • A073355 (program): Sum of squarefree kernels of numbers <= n.
  • A073357 (program): Binomial transform of tribonacci numbers.
  • A073359 (program): Nested floor product of n and fractions (2k+2)/(2k+1) for all k>=0, divided by 2.
  • A073360 (program): Nested floor product of n and fractions (k+1)/k for all k>0 (mod 3), divided by 3.
  • A073361 (program): Nested floor product of n and fractions (k+1)/k for all k>0 (mod 4), divided by 4.
  • A073362 (program): Nested floor product of n and fractions (k+1)/k for all k>0 (mod 5), divided by 5.
  • A073363 (program): Nested floor product of n and fractions (k+1)/k for all k>0 (mod 6), divided by 6.
  • A073371 (program): Convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0 with itself.
  • A073388 (program): Convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself.
  • A073423 (program): Sums of two powers of zero: triangle read by rows: T(m,n) = 0^n + 0^m, n >= 0, m = 0..n.
  • A073424 (program): Triangle read by rows: T(m,n) = parity of 0^n + 0^m, n = 0,1,2,3 …, m = 0,1,2,3, … n.
  • A073425 (program): a(0)=0; for n>0, a(n) = number of primes not exceeding n-th composite number.
  • A073497 (program): a(n) = n^2 - prime(n).
  • A073504 (program): A possible basis for finite fractal sequences: let u(1) = 1, u(2) = n, u(k) = floor(u(k-1)/2) + floor(u(k-2)/2); then a(n) = lim_ k->infinity u(k).
  • A073521 (program): The set of 16 consecutive primes with the property that they form a 4 X 4 magic square with the smallest magic constant (258).
  • A073522 (program): A set of 25 consecutive primes that form a 5 X 5 magic square with the (non-minimal) magic constant 1703.
  • A073523 (program): The set of 36 consecutive primes that form a 6 X 6 pandiagonal magic square with the smallest magic constant (930).
  • A073531 (program): Number of n-digit positive integers with all digits distinct.
  • A073548 (program): Number of Fibonacci numbers F(k), k <= 10^n, which end in 2.
  • A073549 (program): Number of Fibonacci numbers F(k), k <= 10^n, which end in 6.
  • A073550 (program): Number of Fibonacci numbers F(k), k <= 10^n, which end in 1.
  • A073551 (program): Number of Fibonacci numbers F(k), k <= 10^n, which end in 3.
  • A073553 (program): Number of Fibonacci numbers F(k), k <= 10^n, which end in 5.
  • A073554 (program): Number of Fibonacci numbers F(k), k <= 10^n, which end in 7.
  • A073555 (program): Number of Fibonacci numbers F(k), k <= 10^n, which end in 8.
  • A073556 (program): Number of Fibonacci numbers F(k), k <= 10^n, which end in 9.
  • A073575 (program): Sum of factorial numbers dividing n.
  • A073577 (program): a(n) = 4n^2 + 4n - 1.
  • A073578 (program): a(n) = Sum_ k=1..n mu(2*k).
  • A073579 (program): Signed primes: if prime(n) even, a(n) = 0; if prime(n) == 1 (mod 4), a(n) = prime(n); if prime(n) == -1 (mod 4), a(n) = -prime(n).
  • A073582 (program): Numbers n such that S(n) = n/2, where S(n) is the Kempner function A002034.
  • A073583 (program): Decimal expansion of 23/19.
  • A073587 (program): a(n)=a(n-1)*2^n+1 where a(0)=1.
  • A073588 (program): a(n) = a(n-1)*2^n-1 with a(1)=1.
  • A073591 (program): A000522(n)+1.
  • A073612 (program): Group the positive integers as (1, 2), (3, 4, 5), (6, 7, 8, 9, 10), (11, 12, 13, 14, 15, 16, 17), … the n-th group containing prime(n) elements. Except the first, all groups contain an odd number of elements and hence have a middle term. Sequence gives the middle terms starting from group 2.
  • A073636 (program): Period 3: repeat [1, 8, 9] ; Digital root of A000578(n) = n^3 for n >= 1.
  • A073637 (program): Digital root (cf. A010888) of prime(n)^3.
  • A073642 (program): Replace 2^k in the binary representation of n with k (i.e., if n = 2^a + 2^b + 2^c + … then a(n) = a + b + c + …).
  • A073663 (program): Total number of branches of length k (k>=1) in all ordered trees with n+k edges (it is independent of k).
  • A073675 (program): Rearrangement of natural numbers such that a(n) is the smallest proper divisor of n not included earlier but if no such divisor exists then a(n) is the smallest proper multiple of n not included earlier, subject always to the condition that a(n) is not equal to n.
  • A073717 (program): a(n)=T(2n+1), where T(n) are the tribonacci numbers A000073.
  • A073718 (program): Powers of 2 with composite exponents.
  • A073720 (program): Let b(1) = 1, b(k+1) = b(k) - k*trunc(k/b(k)+1), where trunc(x) = floor(x) if x>= 0, trunc(x) = ceiling(x) otherwise. Sequence a(n) gives the successive absolute values taken by b(k).
  • A073724 (program): a(n) = (4^(n+1) + 6n + 5)/9.
  • A073729 (program): Concatenation of initial and final digits of n in decimal representation.
  • A073731 (program): Least k such that A073729(k) = n.
  • A073738 (program): Sum of every other prime <= n-th prime down to 2 or 1; equals the partial sums of A036467 (in which sums of two consecutive terms form the primes).
  • A073744 (program): Decimal expansion of tanh(1).
  • A073747 (program): Decimal expansion of coth(1).
  • A073750 (program): Factors of 2 in the denominators of the fractional coefficients of the square-root of the prime power series: sum_ n=0..inf p_n x^n, where p_n is the n-th prime and p_0 is defined to be 1.
  • A073757 (program): Number of numbers “related” to n: either divisors or terms in RRS of n.
  • A073759 (program): Largest number that is neither a divisor of nor relatively prime to n, or 0 if no such number exists.
  • A073760 (program): Integers m such that A073758(m) = 4.
  • A073762 (program): a(n) = 24*n - 12.
  • A073763 (program): Least number of unrelated set belonging to these numbers is odd.
  • A073773 (program): Number of plane binary trees of size n+2 and height n.
  • A073775 (program): Polynomial (1/3)n^3 + (9/2)n^2 + (85/6)*n - 2.
  • A073779 (program): Number of 0’s in base-3 representation of n-th prime.
  • A073780 (program): Number of 1’s in base 3 representation of n-th prime.
  • A073781 (program): Number of 2’s in base-3 representation of n-th prime.
  • A073783 (program): First differences of composite numbers.
  • A073784 (program): Number of primes between successive composite numbers.
  • A073795 (program): Replace 8^k with (-8)^k in base 8 expansion of n.
  • A073796 (program): Replace 9^k with (-9)^k in base 9 expansion of n.
  • A073802 (program): Number of common divisors of n and sigma(n).
  • A073806 (program): Number of divisors of sum of square of divisors.
  • A073807 (program): Number of divisors of sum of cube of divisors.
  • A073811 (program): Number of common divisors of n and phi(n).
  • A073813 (program): Difference between n and largest unrelated number belonging to n, when n runs over composite numbers. For primes and for 4, unrelated set is empty.
  • A073829 (program): 4*((n-1)!+1)+n.
  • A073835 (program): Replace 10^k with (-10)^k in decimal expansion of n.
  • A073849 (program): Cumulative sum of initial digits of (n base 3).
  • A073850 (program): Cumulative sum of initial digits of (n base 4).
  • A073851 (program): Cumulative sum of initial digits of (n base 5).
  • A073855 (program): Number of steps to reach 0 starting with n and applying the process x ->bigomega(x), where bigomega = A001222.
  • A073869 (program): a(n) = Sum_ i=0..n A002251(i)/(n+1).
  • A073881 (program): a(n) = smallest number m (obviously prime) such that pi(m) = 2*pi(n).
  • A073890 (program): Numerator of n/floor(sqrt(n)).
  • A073933 (program): Number of terms in n-th row of triangle in A073932.
  • A073941 (program): a(n) = ceiling((Sum_ k=1..n-1 a(k)) / 2) for n >= 2 starting with a(1) = 1.
  • A074039 (program): If (n, n+2) is the k-th twin prime pair then k else 0.
  • A074057 (program): 2*phi(n-2)-(n-1).
  • A074065 (program): Numerators a(n) of fractions slowly converging to sqrt(3): let a(1) = 0, b(n) = n - a(n); if (a(n) + 1) / b(n) < sqrt(3), then a(n+1) = a(n) + 1, else a(n+1)= a(n).
  • A074066 (program): Zigzag modulo 3.
  • A074067 (program): Zigzag modulo 5.
  • A074092 (program): Number of plane binary trees of size n+3 and contracted height n.
  • A074116 (program): Largest n-digit power of 2.
  • A074143 (program): a(1) = 1; a(n) = n * Sum_ k=1..n-1 a(k).
  • A074147 (program): (2n-1) odd numbers followed by 2n even numbers.
  • A074148 (program): a(n) = n + floor(n^2/2).
  • A074149 (program): Sum of terms in each group in A074147.
  • A074155 (program): Group the natural numbers so that the product of members of a group is a multiple of the sum: (1),(2,3,4,5,6),(7,8,9),(10,11,12),(13,14,15),(16,17,18),(19,20,21),(22,23,24),…. This is the sequence of the ratio of product /sum.
  • A074171 (program): a(1) = 1. For n >= 2, a(n) is either a(n-1)+n or a(n-1)-n; we only use the minus sign if a(n-1) is prime. E.g. since a(2)=3 is prime, a(3)=a(2)-3=0.
  • A074209 (program): a(n) = Sum_ i=n+1..2n i^n.
  • A074225 (program): a(n) = n * Sum_ d n d*2^(d-1).
  • A074229 (program): Numbers n such that Kronecker(6,n)==mu(gcd(6,n)).
  • A074231 (program): Numbers n such that Kronecker(8,n) = mu(gcd(8,n)).
  • A074232 (program): Positive numbers that are not 3 or 6 (mod 9).
  • A074239 (program): Related to cumulative number of non-twin primes.
  • A074279 (program): n appears n^2 times.
  • A074284 (program): Sum of the aliquot divisors of n-th triangular number.
  • A074285 (program): Sum of the divisors of n-th triangular number.
  • A074294 (program): Integers 1 to 2k followed by integers 1 to 2k + 2 and so on.
  • A074313 (program): a(n) = the maximal length of a sequence of primes s_1 = prime(n), s_2 = f(s1), s_3 = f(s_2), …. formed by repeated application of f(m) = Floor(m/2) on prime(n).
  • A074322 (program): 0 if pronounced name of n-th letter of English alphabet begin with a vowel sound, otherwise 1. Different from A054638.
  • A074323 (program): Coefficient of the highest power of q in the expansion of nu(0)=1, nu(1)=b and for n>=2, nu(n)=bnu(n-1)+lambda(n-1)_q*nu(n-2) with (b,lambda)=(1,2), where (n)_q=(1+q+…+q^(n-1)) and q is a root of unity.
  • A074324 (program): a(2n+1) = 3^n, a(2n) = 4*3^(n-1) except for a(0) = 1.
  • A074330 (program): a(n) = Sum_ k=1..n 2^b(k) where b(k) denotes the number of 1’s in the binary representation of k.
  • A074331 (program): a(n) = Fibonacci(n+1) - (1 + (-1)^n)/2.
  • A074335 (program): In music, with 0 = C natural, 1 = C#, etc.: The unfolding of a semitonal interval cycle, alternating the ascending and descending aspects of the cycle from a common point or axis of symmetry. Any regularly occurring alignment may be used, with predictable even or odd results.
  • A074337 (program): 18 primes in arithmetic progression.
  • A074358 (program): Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n >= 2, nu(n) = bnu(n-1) + lambda(1 + q + q^2 + … + q^(n-2))*nu(n-2) with (b,lambda)=(2,2).
  • A074367 (program): (p^2-5)/4 for odd primes p.
  • A074369 (program): Number of divisors of Sum_ i=1..n prime(i).
  • A074370 (program): Sum of the divisors of Sum_ i=1..n prime(i).
  • A074372 (program): 1 + the sum of the distinct primes dividing n.
  • A074373 (program): Square of the sum of the prime factors of n (with repetition).
  • A074374 (program): s(s+1)/2 where s is the sum of the prime factors of n (with repetition).
  • A074375 (program): s(s+3)/2 where s is the sum of the prime factors of n (with repetition).
  • A074377 (program): Generalized 10-gonal numbers: m(4m - 3) for m = 0, +- 1, +- 2, +- 3, …
  • A074378 (program): Even triangular numbers halved.
  • A074392 (program): a(n) = Lucas(n+1) + (3*(-1)^n - 1)/2.
  • A074399 (program): a(n) is the largest prime divisor of n(n+1).
  • A074400 (program): Sum of the even divisors of 2n.
  • A074461 (program): Average digit (rounded down) in the decimal expansion of the n-th prime number.
  • A074462 (program): Average digit (rounded up) in the decimal expansion of a prime number.
  • A074494 (program): Number of 2-input gates used to synthesize parity function in disjunctive normal form (DNF) with n inputs.
  • A074495 (program): a(n) = the first prime > sigma(n).
  • A074501 (program): a(n) = 1^n + 2^n + 5^n.
  • A074502 (program): 1^n + 2^n + 6^n.
  • A074503 (program): a(n) = 1^n + 2^n + 7^n.
  • A074504 (program): a(n) = 1^n + 2^n + 8^n.
  • A074505 (program): a(n) = 1^n + 2^n + 9^n.
  • A074506 (program): a(n) = 1^n + 3^n + 4^n.
  • A074507 (program): a(n) = 1^n + 3^n + 5^n.
  • A074508 (program): 1^n + 3^n + 6^n.
  • A074509 (program): a(n) = 1^n + 3^n + 7^n.
  • A074510 (program): a(n) = 1^n + 3^n + 8^n.
  • A074511 (program): a(n) = 1^n + 4^n + 5^n.
  • A074512 (program): a(n) = 1^n + 4^n + 6^n.
  • A074513 (program): a(n) = 1^n + 4^n + 7^n.
  • A074514 (program): 1^n + 4^n + 8^n.
  • A074515 (program): a(n) = 1^n + 4^n + 9^n.
  • A074516 (program): a(n) = 1^n + 5^n + 6^n.
  • A074517 (program): a(n) = 1^n + 5^n + 7^n.
  • A074518 (program): a(n) = 1^n + 5^n + 8^n.
  • A074519 (program): a(n) = 1^n + 5^n + 9^n.
  • A074520 (program): 1^n + 6^n + 7^n.
  • A074521 (program): a(n) = 1^n + 6^n + 8^n.
  • A074522 (program): a(n) = 1^n + 6^n + 9^n.
  • A074523 (program): a(n) = 1^n + 7^n + 8^n.
  • A074524 (program): a(n) = 1^n + 7^n + 9^n.
  • A074525 (program): a(n) = 1^n + 8^n + 9^n.
  • A074526 (program): a(n) = 2^n + 3^n + 4^n.
  • A074527 (program): a(n) = 2^n + 3^n + 5^n.
  • A074528 (program): a(n) = 2^n + 3^n + 6^n.
  • A074529 (program): a(n) = 2^n + 3^n + 7^n.
  • A074532 (program): a(n) = 2^n + 4^n + 5^n.
  • A074533 (program): a(n) = 2^n + 4^n + 6^n.
  • A074534 (program): a(n) = 2^n + 4^n + 7^n.
  • A074535 (program): a(n) = 2^n + 4^n + 8^n.
  • A074537 (program): a(n) = 2^n + 5^n + 6^n.
  • A074538 (program): a(n) = 2^n + 5^n + 7^n.
  • A074541 (program): a(n) = 2^n + 6^n + 7^n.
  • A074547 (program): a(n) = 3^n + 4^n + 5^n.
  • A074548 (program): a(n) = 3^n + 4^n + 6^n.
  • A074549 (program): a(n) = 3^n + 4^n + 7^n.
  • A074552 (program): a(n) = 3^n + 5^n + 7^n.
  • A074555 (program): a(n) = 3^n + 6^n + 7^n.
  • A074561 (program): a(n) = 4^n + 5^n + 6^n.
  • A074562 (program): a(n) = 4^n + 5^n + 7^n.
  • A074565 (program): a(n) = 4^n + 6^n + 7^n.
  • A074571 (program): a(n) = 5^n + 6^n + 7^n.
  • A074581 (program): a(n)=T(3n+1), where T(n) are tribonacci numbers A000073.
  • A074591 (program): If n is a prime power then 0 else n.
  • A074600 (program): a(n) = 2^n + 5^n.
  • A074601 (program): a(n) = 2^n + 6^n.
  • A074602 (program): a(n) = 2^n + 7^n.
  • A074603 (program): a(n) = 2^n + 8^n.
  • A074604 (program): a(n) = 2^n + 9^n.
  • A074605 (program): a(n) = 3^n + 4^n.
  • A074606 (program): a(n) = 3^n + 5^n.
  • A074607 (program): a(n) = 3^n + 6^n.
  • A074608 (program): a(n) = 3^n + 7^n.
  • A074609 (program): a(n) = 3^n + 8^n.
  • A074610 (program): a(n) = 3^n + 9^n.
  • A074611 (program): 4^n + 5^n.
  • A074612 (program): a(n) = 4^n + 6^n.
  • A074613 (program): a(n) = 4^n + 7^n.
  • A074614 (program): a(n) = 4^n + 9^n.
  • A074615 (program): a(n) = 5^n + 6^n.
  • A074616 (program): a(n) = 5^n + 7^n.
  • A074617 (program): a(n) = 5^n + 8^n.
  • A074618 (program): a(n) = 5^n + 9^n.
  • A074619 (program): a(n) = 6^n + 7^n.
  • A074620 (program): a(n) = 6^n + 8^n.
  • A074621 (program): a(n) = 6^n + 9^n.
  • A074622 (program): a(n) = 7^n + 8^n.
  • A074623 (program): a(n) = 7^n + 9^n.
  • A074624 (program): a(n) = 8^n + 9^n.
  • A074677 (program): a(n) = Sum_ i = 0..floor(n/2) (-1)^(i + floor(n/2)) F(2*i + e), where F = A000045 (Fibonacci numbers) and e = (1-(-1)^n)/2.
  • A074695 (program): Greatest common divisor of n and floor(n^(1/2))^2.
  • A074700 (program): a(n) = tau(F(2^n)) where tau(x) is the number of divisors of x (A000005(x)) and F(k) the k-th Fibonacci number (A000045(k)).
  • A074701 (program): Numbers k such that k = Sum_ d phi(k) mu(phi(d))*phi(k)/d.
  • A074715 (program): Number of prime factors of F(2^n) where F(m) is the m-th Fibonacci number.
  • A074719 (program): ip(n): the number of primes not exceeding reverse(n).
  • A074721 (program): Concatenate the primes as 2357111317192329313…, then insert commas from left to right so that between each pair of successive commas is a prime, always making the new prime as small as possible.
  • A074723 (program): Largest power of 2 dividing F(3n) where F(k) is the k-th Fibonacci number.
  • A074724 (program): Largest power of 3 dividing F(4n) where F(k) is the k-th Fibonacci number.
  • A074741 (program): Sum of squares of gaps between consecutive primes.
  • A074742 (program): a(n) = (n^3 + 6n^2 - n + 12)/6.
  • A074745 (program): a(n) = sum_ k=1..n prime(k)*prime(k+1).
  • A074764 (program): Numbers of smaller squares into which a square may be dissected.
  • A074784 (program): a(n) = a(n-1) + square of the sum of digits of n.
  • A074787 (program): Sum of squares of the number of unitary divisors of k from 1 to n.
  • A074793 (program): Sum of prime powers less than or equal to n.
  • A074794 (program): Number of numbers k <= n such that tau(k) == 1 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.
  • A074795 (program): Number of numbers k <= n such that tau(k) == 0 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.
  • A074796 (program): Number of numbers k <= n such that tau(k) == 2 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.
  • A074800 (program): a(n) = denominator( (4n+1)(Product_ i=1..n (2i-1)/Product_ i=1..n (2i))^5 ).
  • A074802 (program): Number of numbers k <= n such that tau(k)=tau(k+1) where tau(x)=A000005(x) is the number of divisors of x.
  • A074805 (program): n mod 19 + 1 (“Golden Number”).
  • A074816 (program): a(n) = 3^A001221(n) = 3^omega(n).
  • A074823 (program): a(n) = 2^omega(n)*mu(n)^2.
  • A074828 (program): a(1) = 1; for n>1, a(n) = smallest composite multiple of n if n is a prime else the smallest prime divisor of n if n is composite.
  • A074837 (program): Numbers k such that the penultimate 3 divisors of k sum to k.
  • A074840 (program): Numerators a(n) of fractions slowly converging to sqrt(2): let a(1) = 0, b(n) = n - a(n); if (a(n) + 1) / b(n) < sqrt(2), then a(n+1) = a(n) + 1, else a(n+1)= a(n).
  • A074842 (program): Triplets: base 10 representation is the juxtaposition of three identical strings.
  • A074843 (program): Quadruplets: base 10 representation is the juxtaposition of four identical strings.
  • A074854 (program): a(n) = Sum_ d n (2^(n-d)).
  • A074872 (program): Inverse BinomialMean transform of the Fibonacci sequence A000045 (with the initial 0 omitted).
  • A074909 (program): Running sum of Pascal’s triangle (A007318), or beheaded Pascal’s triangle read by beheaded rows.
  • A074922 (program): Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 2 simple intersections.
  • A074927 (program): a(n) such that p(n)*p(n+1)+a(n) is a minimal square.
  • A074929 (program): a(n)>0 such that p(n)*p(n+1)-a(n) is a maximal square.
  • A074930 (program): Number of integers in 1, 2, …, n! that are coprime to n.
  • A074937 (program): Let c(1) = c(2) = 1, c(n+2) = 1/(c(n+1)+c(n)); then a(n) = (1+sign(c(n)-sqrt(1/2))/2.
  • A074938 (program): Odd numbers such that base 3 representation contains no 2.
  • A074939 (program): Even numbers such that base 3 representation contains no 2.
  • A074941 (program): a(n) = sigma(n) mod 3.
  • A074942 (program): a(n) = phi(n) mod 3.
  • A074943 (program): tau(n) (mod 3).
  • A074972 (program): a(n) == - prime(n) (modulo 20).
  • A074992 (program): a(n) = (10^(2*n)+10^n+1)/3.
  • A074993 (program): a(n) = floor((concatenation of n, n+1)/2).
  • A075084 (program): Number of composite numbers between n and 2n.
  • A075089 (program): Smallest prime == 1 mod n-th composite number.
  • A075091 (program): Sum of Lucas numbers and reflected Lucas numbers (comment to A061084).
  • A075101 (program): Numerator of 2^n/n.
  • A075104 (program): Greatest common divisor of n and integer part of log_2(n).
  • A075105 (program): Numerator of n/floor(log_2(n)); denominator is A075106(n).
  • A075110 (program): Concatenation of n-th prime and n in decimal notation.
  • A075111 (program): a(n)=Sum((-1)^(i+Floor(n/2))T(2i+e),(i=0,..,Floor(n/2))), where T(n) are tribonacci numbers (A000073) and e=(1/2)(1-(-1)^n).
  • A075118 (program): Variant on Lucas numbers: a(n) = a(n-1) + 3*a(n-2) with a(0)=2 and a(1)=1.
  • A075123 (program): a(n) is the least positive integer > a(n-1) and a(n) is not 2*a(i)+a(j) for 1<=i<j<n.
  • A075155 (program): Cubes of Lucas numbers.
  • A075193 (program): Expansion of (1-2*x)/(1+x-x^2).
  • A075254 (program): a(n) = n + (sum of primes factors of n taken with repetition).
  • A075255 (program): a(n) = n - (sum of primes factors of n (with repetition)).
  • A075269 (program): Product of Lucas numbers and inverted Lucas numbers: a(n)=A000032(n)*A075193(n).
  • A075312 (program): Products of Wythoff pairs: [nr][n*r^2], where [] is the floor function and r is the golden ratio, (1+sqrt(5))/2.
  • A075317 (program): Pair the odd numbers such that the k-th pair is (r, r+2k) where r is the smallest odd number not included earlier: (1,3),(5,9),(7,13),(11,19),(15,25),(17,29),(21,35),(23,39),(27,45),… This is the sequence of the first member of pairs.
  • A075318 (program): Pair the odd numbers such that the k-th pair is (r, r+2k) where r is the smallest odd number not included earlier: (1,3),(5,9),(7,13),(11,19),(15,25),(17,29),(21,35),(23,39),(27,45),… This is the sequence of the second member of pairs.
  • A075319 (program): Pair the odd numbers such that the k-th pair is (r, r+2k) where r is the smallest odd number not included earlier: (1,3),(5,9),(7,13),(11,19),(15,25),(17,29),(21,35),(23,39),(27,45),… This is the sequence of the sum of the members of pairs.
  • A075325 (program): Pair the natural numbers such that the m-th pair is (r, s) where r, s and s-r are the smallest numbers which have not occurred earlier and also are not equal to the difference of any earlier pair: (1, 3), (4, 9), (6, 13), (8, 18), (11, 23), (14, 29), (16, 33), (19, 39), (21, 43), (24, 49), (26, 53), (28, 58), … Sequence gives first term of each pair.
  • A075326 (program): Anti-Fibonacci numbers: start with a(0) = 0, and extend by rule that the next term is the sum of the two smallest numbers that are not in the sequence nor were used to form an earlier sum.
  • A075327 (program): Sum of n-th pair in A075325.
  • A075328 (program): Difference between n-th pair in A075325.
  • A075349 (program): a(1) = 1; first differences follow the pattern 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,…, i.e., the next n differences are n.
  • A075353 (program): Initial term of n-th group in A075352.
  • A075354 (program): Final term of n-th group in A075352.
  • A075362 (program): Triangle read by rows with the n-th row containing the first n multiples of n.
  • A075363 (program): Triangle read by rows, in which n-th row gives n smallest powers of n.
  • A075365 (program): Smallest k such that (n+1)(n+2)…(n+k) is divisible by the product of all the primes up to n.
  • A075408 (program): Perfect powers pp such that pp+1 is prime.
  • A075411 (program): Squares of A002276.
  • A075412 (program): Squares of A002277.
  • A075413 (program): Squares of A002278.
  • A075414 (program): Squares of A002279: a(n) = (5*(10^n - 1)/9)^2.
  • A075415 (program): Squares of A002280 or numbers (666…6)^2.
  • A075416 (program): Squares of A002281.
  • A075417 (program): Squares of A002282: a(n) = (8*(10^n - 1)/9)^2.
  • A075423 (program): rad(n) - 1, where rad(n) is the squarefree kernel of n (A007947).
  • A075425 (program): Number of steps to reach 1 starting with n and iterating the map n ->rad(n)-1, where rad(n) is the squarefree kernel of n (A007947).
  • A075427 (program): a(0) = 1; a(n) = if n is even then a(n-1)+1 else 2*a(n-1).
  • A075438 (program): Triangle read by rows giving successive iterations of the Rule 60 elementary cellular automaton starting with a single ON cell where row n is of length 2n+1.
  • A075439 (program): Triangle read by rows giving successive iterations of the Rule 102 elementary cellular automaton starting with a single ON cell where row n is of length 2n+1.
  • A075518 (program): a(n) = floor(prime(n)/4).
  • A075520 (program): 4*prime(n) + (prime(n) mod 4).
  • A075526 (program): A008578(n+2) - A008578(n+1).
  • A075527 (program): A008578(n+3) - A008578(n+1).
  • A075528 (program): Triangular numbers that are half other triangular numbers.
  • A075543 (program): a[n] = a[n-1] + digit sum(n) - 1.
  • A075553 (program): Numerators in the Maclaurin series for arctan(1+x).
  • A075561 (program): Domination number for kings’ graph K(n).
  • A075576 (program): Smaller of two consecutive squares with a prime sum.
  • A075643 (program): Group the natural numbers so that the n-th group contains n numbers one each of a multiple of numbers from 1 to n so that the group sum is a multiple of (n+1): (2), (1, 8), (3, 4, 9), (5, 6, 12, 32), (7, 10, 15, 16, 30), (11, 14, 18, 20, 25, 24), … Sequence gives initial terms of groups.
  • A075653 (program): a(n) = n + sum of distinct prime factors of n.
  • A075656 (program): n + product of prime factors of n.
  • A075677 (program): Reduced Collatz function R applied to the odd integers: a(n) = R(2n-1), where R(k) = (3k+1)/2^r, with r as large as possible.
  • A075680 (program): For odd numbers 2n-1, the minimum number of iterations of the reduced Collatz function R required to yield 1. The function R is defined as R(k) = (3k+1)/2^r, with r as large as possible.
  • A075681 (program): Difference between (n-1)*(n-2)^3 and A003878(n).
  • A075682 (program): First differences of A075681.
  • A075683 (program): 2nd differences of A075681.
  • A075692 (program): Upper irredundance number for queens graph Q_n on n^2 nodes.
  • A075709 (program): Upper irredundance number for kings graph K_n on n^2 nodes.
  • A075727 (program): a(n) = 2 Pi * n rounded off.
  • A075743 (program): For all numbers of the form 6 +- 1 starting with 5,7,11,13,…, ‘1’ indicates prime and ‘0’ indicates composite.
  • A075794 (program): a(n) = the least positive integer k such that phi(k) > phi(1) + … + phi(n).
  • A075795 (program): Number of k, 0<k<=n, such that the resultant of the k-th cyclotomic polynomial and the n-th cyclotomic polynomial is equal to 1.
  • A075796 (program): Numbers k such that 5*k^2 + 5 is a square.
  • A075802 (program): Characteristic function of perfect powers, A001597.
  • A075835 (program): Numbers n such that 13*n^2 + 4 is a square.
  • A075839 (program): Numbers k such that 11*k^2 - 2 is a square.
  • A075841 (program): Numbers k such that 2*k^2 - 9 is a square.
  • A075843 (program): Numbers k such that 99*k^2 + 1 is a square.
  • A075844 (program): Numbers n such that 11*n^2 + 4 is a square.
  • A075847 (program): Difference between n^2 and the largest cube <= n^2.
  • A075848 (program): Numbers k such that 2*k^2 + 9 is a square.
  • A075858 (program): n followed by n 1’s.
  • A075860 (program): a(n) is the fixed point reached by the sum of divisors of n without multiplicity (with the convention a(1)=0).
  • A075861 (program): Least k such that (n-k) divides (n+k).
  • A075869 (program): Numbers k such that 5*k^2 - 9 is a square.
  • A075870 (program): Numbers k such that 2*k^2 - 4 is a square.
  • A075871 (program): Numbers n such that 13*n^2 + 1 is a square.
  • A075878 (program): Sum of coefficients of (x1)^(2i(1))(x2)^(2i(2))(x3)^(2i(3))*(x4)^(2i(4)) for (i1),(i2),(i3),(i4) =0,1,2,… : sum(i)=2n in the expansion of (x1+x2+x3+x4)^(2n) where n=1,2,3,…
  • A075881 (program): a(n) = the sum of the prime factors of Sum_ i=1..n prime(i).
  • A075882 (program): a(n) = phi(Sum_ i=1,…,n prime(i)).
  • A075884 (program): Image of n at the second step of the 3x+1 algorithm.
  • A075885 (program): a(n) = 1 + n + n[n/2] + n[n/2][n/3] + n[n/2][n/3][n/4] +… where [x]=floor(x).
  • A075888 (program): Difference of successive primes squared divided by 24, (prime(n+1)^2-prime(n)^2)/24.
  • A075890 (program): Either of the twin middle(greatest) terms in p(n)-th row of Pascal’s triangle,p(n) being the n-th prime.
  • A075891 (program): Quotient C[p(n), p(n)+-1 /2]/p(n), where p(n)=n-th prime.
  • A075897 (program): 1 if binary weight of n is 1 or 2, otherwise 0.
  • A075921 (program): Second column of triangle A075502.
  • A075989 (program): Number of k satisfying 1<=k<=n and n/k >= 1/2, where n/k is the fractional part of n/k, i.e., n/k = n/k - floor(n/k).
  • A075995 (program): a(n) = Sum_ k=1..floor(n/2) floor(n/k) for n >= 2, with a(1) = 1.
  • A075997 (program): a(n) = [n/2]-[n/3]+[n/4]-[n/5]+[n/6]-…, where [n/k] = floor(n/k).
  • A076000 (program): a(n) = Product_ k=1..n k/floor(n/k).
  • A076014 (program): Triangle in which m-th entry of n-th row is m^(n-1).
  • A076015 (program): Row sums of triangle A076014.
  • A076024 (program): a(n) = (2^n + 4)*(2^n - 1)/6.
  • A076040 (program): a(n) = (-1)^n * (3^n - 1)/2.
  • A076049 (program): Numbers k such that the sum of the k-th triangular number and (k+2)-nd triangular number is a triangular number.
  • A076051 (program): Sum of product of odd numbers <= n and the product of even numbers <= n.
  • A076054 (program): Sum(k=1,n, A006513(k)).
  • A076074 (program): Initial members of groups in A076077.
  • A076079 (program): Largest multiple of n < the n-th prime.
  • A076080 (program): a(n) = A076079(n)/n.
  • A076095 (program): Initial terms of rows in A076099.
  • A076110 (program): Triangle (read by rows) in which the n-th row contains first n terms of an arithmetic progression with first term 1 and common difference (n-1).
  • A076111 (program): Product of terms in n-th row of A076110.
  • A076112 (program): Triangle (read by rows) in which the n-th row contains first n terms of n geometric progression with first term 1 and common ratio (n-1).
  • A076118 (program): a(n) = sum_k n/2<=k<=n k * (-1)^(n-k) * C(k,n-k).
  • A076121 (program): Complete list of possible cribbage hands.
  • A076128 (program): Difference between the product of numbers up to n and the sum of numbers up to n.
  • A076131 (program): a(n) = 2^n*a(n-1)+1, a(0) = 0.
  • A076139 (program): Triangular numbers that are one-third of another triangular number: T(m) such that 3*T(m)=T(k) for some k.
  • A076140 (program): Triangular numbers T(k) that are three times another triangular number: T(k) such that T(k) = 3*T(m) for some m.
  • A076178 (program): a(n) = 2*n^2 - A077071(n).
  • A076182 (program): a(n) = A006666(n) mod 2.
  • A076237 (program): Remainder when 2nd order composite cc[n]=A050435[n] is divided by n.
  • A076240 (program): Remainder when 2nd order prime pp(n) = A006450(n) is divided by n-th prime = A000040(n).
  • A076264 (program): Number of ternary (0,1,2) sequences without a consecutive ‘012’.
  • A076273 (program): a(0) = 1, a(1) = 2; for n>1, a(n) = prime(n)+prime(n-1)-1.
  • A076274 (program): 2p-1 where p is 1 or a prime.
  • A076301 (program): Related to number of labeled partially ordered sets.
  • A076309 (program): a(n) = floor(n/10) - 2*(n mod 10).
  • A076310 (program): a(n) = floor(n/10) + 4*(n mod 10).
  • A076311 (program): a(n) = floor(n/10) - 5*(n mod 10).
  • A076312 (program): a(n) = floor(n/10) + 2*(n mod 10).
  • A076313 (program): a(n) = floor(n/10) - (n mod 10).
  • A076314 (program): a(n) = floor(n/10) + (n mod 10).
  • A076332 (program): Rad(n)+n/rad(n), where rad(n) is the squarefree kernel of n = A007947(n).
  • A076338 (program): a(n) = 512*n + 1.
  • A076342 (program): a(n) = A076340(A000040(n)), real part of primes mapped as defined in A076340, A076341.
  • A076367 (program): Primes with subscripts from the Bonse sequence.
  • A076368 (program): a(1) = 1; for n > 1, a(n) = prime(n) - prime(n-1) + 1.
  • A076369 (program): n + mu(n), where mu is the Moebius-function (A008683).
  • A076389 (program): Sum of squares of numbers that cannot be written as tn + u(n+1) for nonnegative integers t,u.
  • A076411 (program): Number of perfect powers < n.
  • A076454 (program): Sum of numbers that can be written as tn + u(n+1) for nonnegative integers t,u in exactly one way.
  • A076455 (program): Sum of numbers that can be written as tn + u(n+1) for nonnegative integers t,u in exactly two ways.
  • A076456 (program): Sum of numbers that can be written as tn + u(n+1) for nonnegative integers t,u in exactly three ways.
  • A076457 (program): Sum of numbers that can be written as tn + u(n+1) for nonnegative integers t,u in exactly four ways.
  • A076458 (program): Sum of numbers that can be written as tn + u(n+1) for nonnegative integers t,u in exactly five ways.
  • A076459 (program): Sum of numbers that can be written as tn + u(n+1) for nonnegative integers t,u in exactly n ways.
  • A076479 (program): a(n) = mu(rad(n)), where mu is the Moebius-function (A008683) and rad is the radical or squarefree kernel (A007947).
  • A076480 (program): n + mu(rad(n)), where mu is the Moebius-function (A008683) and rad is the squarefree kernel (A007947).
  • A076505 (program): 3 people at a party are saying Hello to each other. Person 1 says Hello. Person 2 counts the times Hello has been said and says Hello twice that number. Person 3 says Hello 3 times the sum of Hello’s and then it is Person 1 again. This is how many Hello’s each person says.
  • A076506 (program): Expansion of x(1+3x+12x^2)/(1-24x^3).
  • A076507 (program): Three people (P1, P2, P3) are in a circle and are saying Hello to each other. They start with P2 saying “Hello, Hello”. Thereafter Pn says “Hello” for n times the total number of Hello’s so far.
  • A076508 (program): Expansion of 2x(1+4x+8x^2)/(1-24*x^3).
  • A076509 (program): Expansion of 3x(1-x)(1+2x+6x^2)/(1-24x^3).
  • A076510 (program): Expansion of 3(1+2x+6 x^2)/(1-24*x^3).
  • A076523 (program): Maximal number of halving lines for 2n points in plane.
  • A076535 (program): a(n) = A064405 (2^m+n) - 2^m (for m large enough this difference appears to be constant).
  • A076538 (program): Numerators a(n) of fractions slowly converging to e: let a(1) = 0, b(n) = n - a(n); if (a(n) + 1) / b(n) < e then a(n+1) = a(n) + 1, else a(n+1)= a(n).
  • A076539 (program): Numerators a(n) of fractions slowly converging to Pi: let a(1) = 0, b(n) = n - a(n); if (a(n) + 1) / b(n) < Pi, then a(n+1) = a(n) + 1, otherwise a(n+1) = a(n).
  • A076540 (program): Number of branches in all ordered trees with n edges.
  • A076544 (program): mu(n)+sqf(n): mu(n) is Moebius function; sqf(n)=1 if n is squarefree, sqf(n)=-1 otherwise.
  • A076545 (program): sum[k=1 to n] mu(k)+sqf(k): mu(k) is Moebius function; sqf(k)=1 if k is squarefree, sqf(k)=-1 otherwise.
  • A076555 (program): Greatest prime divisor of n-th prime + 2.
  • A076556 (program): Greatest prime divisor of n-th prime + n.
  • A076563 (program): a(n>1) = n - greatest prime divisor of n.
  • A076565 (program): Greatest prime divisor of 2n+1 (sum of two successive integers).
  • A076566 (program): Greatest prime divisor of 3n+3 (sum of three successive integers).
  • A076567 (program): Greatest prime divisor of 4n+6 (sum of four successive integers).
  • A076568 (program): Greatest prime divisor of 5n+10 (sum of five successive integers).
  • A076569 (program): Greatest prime divisor of 6n+15 (sum of six successive integers).
  • A076570 (program): Greatest prime divisor of sum of first n primes.
  • A076577 (program): Sum of squares of divisors d of n such that n/d is odd.
  • A076597 (program): Numbers k such that sqrt(k(k-1)(k-2)*(k-3)+1) is a prime.
  • A076605 (program): Largest prime divisor of n^2 - 1.
  • A076616 (program): Number of permutations of 1,2,…,n that result in a binary search tree (when elements of the permutation are inserted in that order) of height n-1 (i.e., the second largest possible height).
  • A076618 (program): Least x>1 such that x^d == 1 (mod d) for each divisor d of n.
  • A076621 (program): Least square greater than the product of two successive primes.
  • A076627 (program): a(n) = tau(n)*(n-tau(n)), where tau(n) = number of divisors of n (A000005).
  • A076631 (program): Solve 2^n - 2 = 7(x^2 - x) + (y^2 - y) for (x,y) with x>0, y>0; a(n) = value of y.
  • A076632 (program): Solve 2^n - 2 = 7(x^2 - x) + (y^2 - y) for (x,y) with x>0, y>0; sequence gives value of x.
  • A076634 (program): Coefficient of x^a(n) in (x+1/2)(x+2/2)…*(x+n/2) is the largest one.
  • A076640 (program): a(1)=1, a(n) = a(n-phi(n)) + 1.
  • A076644 (program): a(1)=1; for n>1, a(n) = a(n-floor(sqrt(n))) + n.
  • A076662 (program): First differences of A007066.
  • A076664 (program): a(n) = Sum_ k=1..n antisigma(k), where antisigma(i) = sum of the nondivisors of i that are between 1 and i.
  • A076677 (program): a(0)=a(1)=1 a(n)=a(n-1)+floor(sqrt(a(n-2))).
  • A076684 (program): Odd terms in A027941.
  • A076694 (program): a(n) = n - sum of the distinct prime factors of n.
  • A076708 (program): Numbers n such that triangular numbers T(n) and T(n+1) sum to another triangular number (that is also a perfect square).
  • A076728 (program): a(n) = (n-1)^2 * n^(n-2).
  • A076736 (program): Let u(1) = u(2) = u(3) = 2, u(n) = (1 + u(n-1)*u(n-2))/u(n-3); then a(n) is the denominator of u(n).
  • A076737 (program): Let u(1)=u(2)=u(3)=2, u(n)=(1+u(n-1)u(n-2))/u(n-3); then a(n) is the numerator of u(n).
  • A076765 (program): Partial sums of Chebyshev sequence S(n,8) = U(n,4) = A001090(n+1).
  • A076767 (program): Triangular numbers with square pyramidal indices.
  • A076770 (program): Even numbers representable as the sum of two odd composites.
  • A076793 (program): a(n) = Sum_ k=1..n 2^prime(k).
  • A076795 (program): Partial sums of (2n-1)!!.
  • A076816 (program): Squares modulo triangular numbers: n^2 minus the greatest triangular number smaller than or equal to n^2.
  • A076820 (program): Second-largest distinct prime dividing n (or 1 if n is a power of a prime).
  • A076821 (program): Squares of the differences between consecutive primes.
  • A076824 (program): Let a(1)=a(2)=1, a(n)=(2^ceiling(a(n-1)/2)+1)/a(n-2).
  • A076826 (program): a(n) = 2*(Sum_ k=0..n A010060(k)) - n, where A010060 is a Thue-Morse sequence.
  • A076835 (program): Coefficients in expansion of Eisenstein series -q*E’_2.
  • A076839 (program): A simple example of the Lyness 5-cycle: a(1) = a(2) = 1; a(n) = (a(n-1)+1)/a(n-2) (for n>2).
  • A076840 (program): a(1) = a(2) = 1; a(n) = (a(n-1) + 1)/a(n-2) (for n>2, n odd), (a(n-1)^2 + 1)/a(n-2) (for n>2, n even).
  • A076844 (program): a(1) = a(2) = a(3) = 1; a(n) = (a(n-1) + a(n-2) + 1)/a(n-3) (for n>3).
  • A076874 (program): n - floor ( ( 4*n + 1 )^(1/2) ).
  • A076877 (program): a(n) = A020330(n) / n.
  • A076878 (program): a(n) = ceiling(n^(1/n))^n - n.
  • A076883 (program): Let u(0)=1, u(n) = 5/2 * floor(u(n-1)); then a(n) = (2/5)*u(n).
  • A076885 (program): Let u(0)=1, u(1)=1 u(n) = u(n-1) + u(n-2) - n*z where z = (5-sqrt(5))/10 =0.27…, then a(n)=floor(u(n)).
  • A076895 (program): a(1) = 1, a(n) = n - a(ceiling(n/2)).
  • A076896 (program): a(1)=1, a(n)=n-a(floor(2n/3)).
  • A076897 (program): a(1)=1, a(n)=n-a(floor(3n/4)).
  • A076921 (program): Smallest number such that the highest common factor of pair of successive terms follows the pattern 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, …, i.e., b(2n-1) = b(2n) = n given by A004526.
  • A076934 (program): Smallest integer of the form n/k!.
  • A076936 (program): a(1) = 1; then the smallest number different from its predecessor such that the n-th partial product is an n-th power.
  • A076981 (program): Smallest k such that n(n+1)(n+2)(n+k) is divisible by the product of primes up to n.
  • A076982 (program): Number of triangular numbers that divide the n-th triangular number.
  • A076984 (program): Number of Fibonacci numbers that are divisors of the n-th Fibonacci number.
  • A077008 (program): Legendre symbol (-1,p) where p is the n-th prime.
  • A077017 (program): a(1) = 2, a(n+1) = smallest positive integer divisible by the n-th prime that also has a nontrivial common divisor with a(n).
  • A077020 (program): a(n) is the unique odd positive solution x of 2^n = 7x^2+y^2.
  • A077021 (program): a(n) is the unique odd positive solution y of 2^n = 7x^2 + y^2.
  • A077024 (program): Sum Floor(n/k + 1/2): k=1,2,…,n .
  • A077025 (program): Sum Floor(n/(k + 1/2)): k=1,2,…,n .
  • A077026 (program): a(n) = Sum_ k=1..n floor(n/k + 1)-floor(n/k + 1/2).
  • A077028 (program): The rascal triangle, read by rows: T(n,k) (n >= 0, 0 <= k <= n) = k(n-k) + 1.
  • A077043 (program): “Three-quarter squares”: a(n) = n^2 - A002620(n).
  • A077049 (program): Left summatory matrix, T, by antidiagonals upwards.
  • A077051 (program): Right summatory matrix, T, by antidiagonals.
  • A077063 (program): Squarefree kernel of prime(n) - 1.
  • A077066 (program): Squarefree kernel of prime(n) + 1.
  • A077071 (program): Row sums of A077070.
  • A077106 (program): Largest integer cube <= n^2.
  • A077107 (program): Least integer cube >= n^2.
  • A077109 (program): A077107(n) - n^2.
  • A077113 (program): Number of integer cubes <= n^2.
  • A077115 (program): Least integer square >= n^3.
  • A077116 (program): n^3 - A065733(n).
  • A077118 (program): Nearest integer square to n^3.
  • A077121 (program): Number of integer squares <= n^3.
  • A077126 (program): Sum of even-indexed primes.
  • A077128 (program): Smallest number greater than the previous term which is relatively prime to each of the group of the next n numbers.
  • A077131 (program): Sum of odd-indexed primes.
  • A077133 (program): Difference between the sum of odd-indexed primes and even-indexed primes.
  • A077140 (program): a(1) = 1 and then add n to the previous term if n is coprime to the previous term, otherwise subtract n from the previous term. a(1) = 1 and a(n) = a(n-1) + n if gcd(n, a(n-1)) = 1, otherwise a(n) = a(n-1) - n.
  • A077152 (program): Smallest k such that there are n primes between n and k.
  • A077163 (program): n-th power of next n numbers.
  • A077169 (program): Initial terms of rows of A077168.
  • A077221 (program): a(0) = 0 and then alternately even and odd numbers in increasing order such that the sum of any two successive terms is a square.
  • A077234 (program): Bisection (odd part) of Chebyshev sequence with Diophantine property.
  • A077235 (program): Bisection (odd part) of Chebyshev sequence with Diophantine property.
  • A077236 (program): a(n) = 4*a(n-1) - a(n-2) with a(0) = 4 and a(1) = 11.
  • A077239 (program): Bisection (odd part) of Chebyshev sequence with Diophantine property.
  • A077240 (program): Bisection (even part) of Chebyshev sequence with Diophantine property.
  • A077243 (program): Bisection (odd part) of Chebyshev sequence with Diophantine property.
  • A077244 (program): Bisection (odd part) of Chebyshev sequence with Diophantine property.
  • A077245 (program): Bisection (even part) of Chebyshev sequence with Diophantine property.
  • A077249 (program): Bisection (odd part) of Chebyshev sequence with Diophantine property.
  • A077251 (program): Bisection (even part) of Chebyshev sequence with Diophantine property.
  • A077252 (program): Sum of digits squared minus sum of digits of n.
  • A077253 (program): Sum of digits squared plus sum of digits of n.
  • A077259 (program): First member of the Diophantine pair (m,k) that satisfies 5*(m^2 + m) = k^2 + k; a(n) = m.
  • A077260 (program): Triangular numbers that are 1/5 of a triangular number.
  • A077261 (program): Triangular numbers that are 5 times another triangular number.
  • A077262 (program): Second member of the Diophantine pair (m,k) that satisfies 5*(m^2 + m) = k^2 + k; a(n) = k.
  • A077265 (program): Number of cycles in the n-th order prism graph.
  • A077267 (program): Number of zeros in base-3 expansion of n.
  • A077268 (program): Number of bases in which n requires at least one zero to be written.
  • A077373 (program): Fibonacci numbers whose external digits as well as internal digits form a Fibonacci number.
  • A077386 (program): Sums of rows of triangle in A077385.
  • A077412 (program): Chebyshev U(n,x) polynomial evaluated at x=8.
  • A077413 (program): Bisection (odd part) of Chebyshev sequence with Diophantine property.
  • A077414 (program): a(n) = n(n - 1)(n + 2)/2.
  • A077415 (program): a(n) = n(n+2)(n-2)/3.
  • A077416 (program): Chebyshev S-sequence with Diophantine property.
  • A077417 (program): Chebyshev T-sequence with Diophantine property.
  • A077420 (program): Bisection of Chebyshev sequence T(n,3) (odd part) with Diophantine property.
  • A077421 (program): Chebyshev sequence U(n,11)=S(n,22) with Diophantine property.
  • A077423 (program): Chebyshev sequence U(n,12)=S(n,24) with Diophantine property.
  • A077425 (program): a(n) == 1 (mod 4) (see A016813), but not a square (i.e., not in A000290).
  • A077429 (program): a(n) = floor(log_10(n^2)).
  • A077430 (program): a(n) = floor(log_10(2*n^2)) + 1.
  • A077431 (program): n repeated in decimal representation, but separated by enough zeros that the square has the pattern (n^2)(2n^2)(n^2).
  • A077432 (program): Squares of the form u’v’w, where in decimal representation u=n^2, v=2*n^2 and w=n^2 possibly with a leading zero.
  • A077433 (program): Number of separating zeros to represent A077431.
  • A077444 (program): Numbers k such that (k^2 + 4)/2 is a square.
  • A077445 (program): Numbers k such that (k^2 - 8)/2 is a square.
  • A077446 (program): Numbers n such that 2*n^2 + 14 is a square.
  • A077447 (program): Numbers n such that (n^2 - 14)/2 is a square.
  • A077450 (program): Continued fraction expansion of (29+sqrt(145))/12.
  • A077467 (program): Sum of binary digits of A077465(n).
  • A077552 (program): Consider the following triangle in which the n-th row contains n distinct numbers whose product is the smallest and has the least possible number of divisors. 1 is a member of only the first row. Sequence contains the final term of the rows (the leading diagonal).
  • A077588 (program): Maximum number of regions into which the plane is divided by n triangles.
  • A077591 (program): Maximum number of regions into which the plane can be divided using n (concave) quadrilaterals.
  • A077597 (program): Coefficient of x in the n-th Moebius polynomial (A074586), M(n,x), which satisfies M(n,-1)=mu(n) the Moebius function of n.
  • A077605 (program): Left summing matrix, S.
  • A077612 (program): Number of adjacent pairs of form (even,even) among all permutations of 1,2,…,n .
  • A077613 (program): Number of adjacent pairs of form (even,odd) among all permutations of 1,2,…,n . Also, number of adjacent pairs of form (odd,even).
  • A077616 (program): Binomial transform of n^2*2^n/2.
  • A077625 (program): Largest term in periodic part of continued fraction expansion of square root of -1+2^n.
  • A077648 (program): Initial digits of prime numbers.
  • A077649 (program): Initial digit of composite numbers.
  • A077650 (program): Initial decimal digit of sigma(n), the sum of divisors of n.
  • A077651 (program): Initial digit of phi(n), where phi is Euler totient function, A000010.
  • A077653 (program): a(1)=1, a(2)=2, a(3)=2, a(n) = abs(a(n-1)-a(n-2)-a(n-3)).
  • A077659 (program): a(n) = smallest k>1 such that the sum n^k + (n+1)^k is prime, or -1 if no such k exists.
  • A077726 (program): Smallest number beginning with n and having a digit sum n.
  • A077750 (program): Least significant digit of A077749(n).
  • A077802 (program): Sum of products of parts increased by 1 in hook partitions of n, where hook partitions are of the form h*1^(n-h).
  • A077814 (program): a(n) = # 0<=k<=n: mod(kn,4)=2 .
  • A077834 (program): Expansion of 1/(1 - 2x - 2x^2 - 3*x^3).
  • A077842 (program): Expansion of (1-x)/(1-2x-2x^2-3*x^3).
  • A077846 (program): Expansion of 1/(1 - 3x + 2x^3).
  • A077847 (program): Expansion of (1-x)^(-1)/(1-2x-2x^2+2*x^3).
  • A077849 (program): Expansion of (1-x)^(-1)/(1 - 2*x - x^2 - x^3).
  • A077850 (program): Expansion of (1-x)^(-1)/(1 - 2*x - x^2 + x^3).
  • A077852 (program): Expansion of (1-x)^(-1)/(1-2*x-x^3).
  • A077854 (program): Expansion of 1/((1-x)(1-2x)*(1+x^2)).
  • A077855 (program): Expansion of (1-x)^(-1)/(1 - 2*x + x^2 - x^3).
  • A077856 (program): Expansion of (1-x)^(-1)/(1-2*x+x^2+x^3).
  • A077858 (program): Expansion of (1-x)^(-1)/(1-2x+2x^2-2*x^3).
  • A077859 (program): Expansion of (1-x)^(-1)/(1-2x+2x^2-x^3).
  • A077860 (program): Expansion of 1/((1 - 2x + 2x^2)*(1-x)).
  • A077861 (program): Expansion of (1-x)^(-1)/(1-2x+2x^2+x^3).
  • A077864 (program): Expansion of (1-x)^(-1)/(1-x-2*x^2-x^3).
  • A077865 (program): Expansion of (1-x)^(-1)/(1-x-2*x^2+x^3).
  • A077866 (program): Expansion of (1-x)^(-1)/(1 - x - 2x^2 + 2x^3).
  • A077868 (program): Expansion of (1-x)^(-1)/(1-x-x^3).
  • A077870 (program): Expansion of (1-x)^(-1)/(1-x+2*x^3).
  • A077871 (program): Expansion of (1-x)^(-1)/(1-x+x^2-2*x^3).
  • A077872 (program): Expansion of 1 / ((1-x)*(1-x+x^2+x^3)).
  • A077873 (program): Expansion of (1-x)^(-1)/(1-x+x^2+2*x^3).
  • A077874 (program): Expansion of (1-x)^(-1)/(1-x+2x^2-2x^3).
  • A077875 (program): Expansion of (1-x)^(-1)/(1-x+2*x^2-x^3).
  • A077876 (program): Expansion of (1-x)^(-1)/(1-x+2*x^2).
  • A077880 (program): Expansion of (1-x)^(-1)/(1-2*x^2+x^3).
  • A077885 (program): Expansion of (1-x)^(-1)/(1-2*x^3).
  • A077886 (program): Expansion of (1-x)^(-1)/(1+2*x^3).
  • A077891 (program): Expansion of (1-x)^(-1)/(1+2x^2-2x^3).
  • A077896 (program): Expansion of (1-x)^(-1)/(1+x-2x^2-2x^3).
  • A077898 (program): Expansion of (1 - x)^(-1)/(1 + x - 2*x^2).
  • A077904 (program): Expansion of (1-x)^(-1)/(1+x-2*x^3).
  • A077912 (program): Expansion of 1/(1+x^2-2*x^3).
  • A077917 (program): Expansion of (1-x)^(-1)/(1+2x-2x^2).
  • A077921 (program): Expansion of (1-x)^(-1)/(1+2*x-x^2).
  • A077925 (program): Expansion of 1/((1-x)(1+2x)).
  • A077937 (program): Expansion of 1/(1-2x-2x^2+2*x^3).
  • A077939 (program): Expansion of 1/(1 - 2*x - x^2 - x^3).
  • A077940 (program): Expansion of 1/(1-2x+2x^3).
  • A077941 (program): Expansion of 1/(1-2*x+x^2+x^3).
  • A077943 (program): Expansion of 1/(1-2x+2x^2-2*x^3).
  • A077944 (program): Expansion of 1/(1-2x+2x^2+x^3).
  • A077947 (program): Expansion of 1/(1 - x - x^2 - 2*x^3).
  • A077950 (program): Expansion of 1/(1-x+2*x^3).
  • A077952 (program): Expansion of 1/(1 - x + x^2 + 2*x^3).
  • A077953 (program): Expansion of 1/(1-x+2x^2-2x^3).
  • A077954 (program): Expansion of 1/(1-x+2*x^2-x^3) in powers of x.
  • A077957 (program): Powers of 2 alternating with zeros.
  • A077958 (program): Expansion of 1/(1-2*x^3).
  • A077959 (program): Expansion of 1/(1+2*x^3).
  • A077964 (program): Expansion of 1/(1+2x^2-2x^3).
  • A077965 (program): Expansion of 1/(1+2*x^2-x^3).
  • A077966 (program): Expansion of 1/(1+2*x^2).
  • A077973 (program): Expansion of 1/(1+x-2*x^3).
  • A077978 (program): Expansion of 1/(1+x+2*x^2-x^3).
  • A077985 (program): Expansion of 1/(1 + 2*x - x^2).
  • A077997 (program): Expansion of (1-x)/(1-2*x-x^2-x^3).
  • A077998 (program): Expansion of (1-x)/(1-2*x-x^2+x^3).
  • A078002 (program): Expansion of (1-x)/(1-2x+x^2+2x^3).
  • A078003 (program): Expansion of (1-x)/(1-2x+2x^2-2*x^3).
  • A078004 (program): Expansion of (1-x)/(1-2x+2x^2+x^3).
  • A078007 (program): Expansion of (1-x)/(1-x-2*x^2-x^3).
  • A078008 (program): Expansion of (1-x)/( (1+x)(1-2x) ).
  • A078010 (program): Expansion of (1-x)/(1 - x - x^2 - 2*x^3).
  • A078012 (program): Expansion of (1 - x) / (1 - x - x^3) in powers of x.
  • A078014 (program): Expansion of (1-x)/(1-x+2*x^3).
  • A078016 (program): Expansion of (1-x)/(1-x+x^2+x^3).
  • A078017 (program): Expansion of (1-x)/(1-x+x^2+2*x^3).
  • A078019 (program): Expansion of (1-x)/(1-x+2*x^2-x^3).
  • A078020 (program): Expansion of (1-x)/(1-x+2*x^2).
  • A078034 (program): Expansion of (1-x)/(1+2x^2-2x^3).
  • A078035 (program): Expansion of (1-x)/(1+2*x^2-x^3).
  • A078046 (program): Expansion of (1-x)/(1 + x + x^2 - x^3).
  • A078049 (program): Expansion of (1-x)/(1+x+2*x^2-x^3).
  • A078050 (program): Expansion of (1-x)/(1+x+2*x^2).
  • A078057 (program): Expansion of (1+x)/(1-2*x-x^2).
  • A078107 (program): Numbers n such that it is not possible to arrange the numbers from 1 to n in a chain with adjacent links summing to a square.
  • A078111 (program): a(n) = floor((n+2)^(n+2)/n^n).
  • A078112 (program): Coefficients a(n) in the unique expansion sin(1) = Sum[a(n)/n!, n>=1], where a(n) satisfies 0<=a(n)<n.
  • A078113 (program): Let u(1)=u(2)=1, u(3)=n, u(k) = (1/2)abs(2u(k-1) -u(k-2)-u(k-3)); sequence gives values of n such that sum(k>=1, u(k)) is an integer.
  • A078126 (program): Negative determinant of n X n matrix M_ i,j =1 if i=j or i+j=1 (mod 2).
  • A078135 (program): Numbers which cannot be written as a sum of squares > 1.
  • A078137 (program): Numbers which can be written as sum of squares>1.
  • A078138 (program): Primes which can be written as sum of squares > 1.
  • A078163 (program): a(n)=A051201[n^2].
  • A078171 (program): a(n)=A055086[A000040(n)].
  • A078181 (program): Sum_ d n, d=1 mod 3 d.
  • A078182 (program): a(n) = Sum_ d n, d=2 mod 3 d.
  • A078306 (program): a(n) = Sum_ d divides n (-1)^(n/d+1)*d^2.
  • A078308 (program): a(n) = Sum_ d divides n d^(n/d + 1).
  • A078309 (program): Numbers that are congruent to 1, 4, 7 mod 10.
  • A078310 (program): a(n) = n*rad(n) + 1, where rad = A007947 (squarefree kernel).
  • A078343 (program): a(0) = -1, a(1) = 2; a(n) = 2*a(n-1) + a(n-2).
  • A078349 (program): Number of primes in sequence h(m) defined by h(1) = n, h(m+1) = Floor(h(m)/2).
  • A078358 (program): Non-oblong numbers: Complement of A002378.
  • A078362 (program): A Chebyshev S-sequence with Diophantine property.
  • A078364 (program): A Chebyshev S-sequence with Diophantine property.
  • A078366 (program): A Chebyshev S-sequence with Diophantine property.
  • A078368 (program): A Chebyshev S-sequence with Diophantine property.
  • A078370 (program): a(n) = 4(n+1)n + 5.
  • A078371 (program): a(n) = (2n+5)(2*n+1).
  • A078427 (program): Sum of all the decimal digits of numbers from 1 to 10^n.
  • A078428 (program): Partial sums of A035187.
  • A078430 (program): Sum of gcd(k^2,n) for 1 <= k <= n.
  • A078435 (program): Number of composites <= n^2.
  • A078442 (program): a(p) = a(n) + 1 if p is the n-th prime, prime(n); a(n)=0 if n is not prime.
  • A078444 (program): Floor of geometric mean of consecutive primes.
  • A078469 (program): Number of different compositions of the ladder graph L_n.
  • A078471 (program): Sum of all odd divisors of all positive integers <= n.
  • A078476 (program): Time taken to get n people from one side of a bridge to the other where (a) the only flashlight must be carried when crossing; (b) only one or two people may cross at the same time; (c) a pair crosses at the speed of the slowest member; and (d) the k-th person’s speed requires k seconds to cross the bridge.
  • A078484 (program): G.f.: -x(1-2x+2x^2)/(2x^3-4x^2+4x-1).
  • A078485 (program): Number of irreducible indecomposable permutations of degree n.
  • A078488 (program): First differences of coefficients of g.f. (1-x)^24.
  • A078489 (program): a(n)=j such that binomial(n,j)<binomial(n-1,j-2).
  • A078501 (program): a(n) = sum(k=1,n^2, A078446(k)).
  • A078522 (program): Numbers n such that (n+1)(2n+1) is a perfect square.
  • A078545 (program): Largest prime dividing tau(n), the number of divisors of n.
  • A078565 (program): Number of zeros in the binary expansion of n!.
  • A078567 (program): Number of arithmetic subsequences of [1..n] with length > 1.
  • A078584 (program): a(n) = prime(2n) - prime(2n-1).
  • A078588 (program): a(n) = 1 if the integer multiple of phi nearest n is greater than n, otherwise 0, where phi = (1+sqrt(5))/2.
  • A078599 (program): Product of squarefree divisors of n.
  • A078607 (program): Least positive integer x such that 2*x^n > (x+1)^n.
  • A078608 (program): a(n) = ceiling( 2/(2^(1/n)-1)).
  • A078609 (program): Least positive integer x such that 2*x^n>(x+3)^n.
  • A078614 (program): Differences of A072633.
  • A078615 (program): a(n) = rad(n)^2, where rad is the squarefree kernel of n (A007947).
  • A078617 (program): Floor(average of first n squares).
  • A078618 (program): a(n) = floor(average of first n cubes).
  • A078619 (program): Floor(average of first n factorials).
  • A078627 (program): Write n in binary; repeatedly sum the “digits” until reaching 1; a(n) = 1 + number of steps required.
  • A078632 (program): Number of geometric subsequences of [1,…,n] with integral successive-term ratio and length > 1.
  • A078633 (program): Smallest number of sticks of length 1 needed to construct n squares with sides of length 1.
  • A078636 (program): rad n(n+1) .
  • A078642 (program): Numbers with two representations as the sum of two Fibonacci numbers.
  • A078644 (program): a(n) = tau(2*n^2)/2.
  • A078651 (program): Number of geometric subsequences of [1,…,n] with integral successive-term ratio and length >= 1.
  • A078654 (program): a(n) = prime(k) where k = n-th prime congruent to 3 mod 4.
  • A078677 (program): Write n in binary; repeatedly sum the “digits” until reaching 1; a(n) = sum of these sums (including ‘1’ and n itself).
  • A078683 (program): Least prime of the form n*2^m+1 for m>0, or 0 if there is no such prime.
  • A078684 (program): a(n) = 3^floor(n^2/4).
  • A078685 (program): Minimum value of prime(n) - 2^x .
  • A078688 (program): Continued fraction expansion of e^(1/4).
  • A078689 (program): Continued fraction expansion of e^(1/3).
  • A078696 (program): a(n+1)=a(n)+a(n-1) if a(n-1) odd, a(n+1)=a(n)+a(n-1)/2 if a(n-1) even.
  • A078701 (program): Least odd prime factor of n, or 1 if no such factor exists.
  • A078703 (program): Number of ways of subtracting twice a triangular number from a perfect square to obtain the integer n.
  • A078704 (program): Integer part of the square root of phi(n).
  • A078705 (program): Integer part of the square root of sigma(n).
  • A078707 (program): Number of vectors of length n that are symmetric about the middle, where each element is drawn from a set of n distinct elements.
  • A078709 (program): Integer part of the mean subinterval length in the partition of [0,n] by the divisors of n.
  • A078711 (program): Sequence is S(infinity), where S(1)= 1,2,3 , S(n+1)=S(n)S’(n) and S’(n) is obtained from S(n) by changing last term using the cyclic permutation 1->2->3->1.
  • A078716 (program): Sequence has period 9 and differences between successive terms are 4, -3, 4, -3, 4, -3, 4, -3, -4.
  • A078719 (program): Number of odd terms among n, f(n), f(f(n)), …., 1 for the Collatz function (that is, until reaching “1” for the first time), or -1 if 1 is never reached.
  • A078723 (program): a(n) = prime(n*(n+1)/2 + n).
  • A078734 (program): Start with 1,2, concatenate 2^k previous terms and change last term as follows: 1->2, 2->3, 3->1.
  • A078761 (program): Sum of the digits of all n-digit numbers.
  • A078766 (program): Number of primes less than n*phi(n).
  • A078767 (program): Let f(n) = A003434(n) be the number of iterations of phi needed to reach 1. Then a(n) = max(f(1), f(2), …, f(n)).
  • A078772 (program): a(n) = phi(n-p) where p is largest prime < n, a(1) = a(2) = 1 by convention.
  • A078782 (program): Nonprimes (A018252) with prime (A000040) subscripts.
  • A078787 (program): a(n) = 101*n + 1.
  • A078788 (program): Smallest m such that (n-1)*m+1 mod n = 0, or 0 if no such number exists.
  • A078789 (program): Expansion of (1-4x+2x^2)/(1-7x+13x^2-4*x^3).
  • A078796 (program): a(n) = 2ceiling(ntau) - ceiling(n*sqrt(5)) where tau=(1+sqrt(5))/2 is the Golden ratio.
  • A078809 (program): Number of divisors of the average of consecutive odd primes.
  • A078832 (program): Smallest prime contained as binary substring in binary representation of n>1, a(1)=1.
  • A078835 (program): Sum of the divisors of the average of consecutive odd primes.
  • A078836 (program): a(n) = n*2^(n-6).
  • A078837 (program): a(n)=sum(k=1,p(n)-1, floor(k^3/p(n))) where p(n) denotes the n-th prime.
  • A078838 (program): a(n)=sum(k=1,(p(n)-1)(p(n)-2),floor((kp(n))^(1/3))) where p(n) denotes the n-th prime.
  • A078876 (program): a(n) = n^4*(n^4-1)/240.
  • A078881 (program): Size of the largest subset S of 1,2,3,…,n with the property that if i and j are distinct elements of S then i XOR j is not in S, where XOR is the bitwise exclusive-OR operator.
  • A078903 (program): a(n) = n^2 - Sum_ u=1..n Sum_ v=1..u valuation(2*v, 2).
  • A078904 (program): a(n) = 4a(n-1) + 3n with a(0) = 0.
  • A078916 (program): a(n) = prime(n) + 2*n.
  • A078922 (program): a(n) = 11*a(n-1) - a(n-2) with a(1)=1, a(2) = 10.
  • A078934 (program): Smallest semiperimeter of integral rectangle with area n*(n+1)/2.
  • A078935 (program): Largest divisor of n(n+1)/2 that is <= sqrt(n(n+1)/2).
  • A078936 (program): Smallest divisor of n(n+1)/2 that is >= sqrt(n(n+1)/2).
  • A078941 (program): Flipping burnt pancakes. Maximum number of spatula flips to sort a stack of n pancakes of different sizes, each burnt on one side, so that the smallest ends up on top, …, the largest at the bottom and each has its burnt side down.
  • A078978 (program): Sequence is S(infinity), where S(1)= 1,2,3,4 , S(n+1)=S(n)S’(n) and S’(n) is obtained from S(n) by changing last term using the cyclic permutation 1->2->3->4->1.
  • A078979 (program): a(n) = A078711(n) - 1.
  • A078986 (program): Chebyshev T(n,19) polynomial.
  • A078987 (program): Chebyshev U(n,x) polynomial evaluated at x=19.
  • A079000 (program): a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition “n is a member of the sequence if and only if a(n) is odd”.
  • A079001 (program): Digital equivalents of letters A, B, C, …, Z on touch-tone telephone keypad.
  • A079003 (program): Least k >= 3 such that Fibonacci(k) == -1 (mod 3^n).
  • A079004 (program): Least x>=3 such that F(x)==1 (mod 3^n) where F(x) denotes the x-th Fibonacci number (A000045).
  • A079027 (program): a(n) = det(M(n)) where M(n) is the n X n matrix defined by m(i,i)=6, m(i,j)=i/j.
  • A079028 (program): a(0) = 1, a(n) = (n+4)*4^(n-1) for n >= 1.
  • A079034 (program): Determinant of M(n), the n X n matrix defined by m(i,i)=1, m(i,j)=i-j.
  • A079044 (program): Numbers k such that Sum_ j=0..k sin(j/Pi) < 0.
  • A079057 (program): a(n)=sum(k=1,n,bigomega(tau(k))).
  • A079065 (program): In prime factorization of n replace odd primes with 3.
  • A079079 (program): a(n) = (prime(n)+1)*(prime(n+1)+1)/4.
  • A079086 (program): Total number of prime factors of (prime(n)+1)*(prime(n+1)+1)/4.
  • A079097 (program): Mix odd numbers and squares.
  • A079102 (program): a(2n) = 2^n, a(2n+1) = 2^(2n).
  • A079208 (program): Number of isomorphism classes of associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n, listed by class size.
  • A079247 (program): Number of pairs (p,q), 0 <= p < q, such that p+q divides n.
  • A079250 (program): Even numbers in A079000.
  • A079252 (program): Even numbers not in A079000.
  • A079253 (program): a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition “n is a member of the sequence if and only if a(n) is even”.
  • A079260 (program): Characteristic function of primes of form 4n+1 (1 if n is prime of form 4n+1, 0 otherwise).
  • A079261 (program): Characteristic function of primes of form 4n+3 (1 if n is prime of form 4n+3, 0 otherwise).
  • A079272 (program): a(n) = ((2n+1)*3^n - 1)/2.
  • A079273 (program): Octo numbers (a polygonal sequence): a(n) = 5n^2 - 6n + 2 = (n-1)^2 + (2*n-1)^2.
  • A079275 (program): Number of divisors of n that are semiprimes with distinct factors.
  • A079291 (program): Squares of Pell numbers.
  • A079295 (program): (D(p)-6)/(12p) where D(p) denotes the denominator of the 2p-th Bernoulli number and p runs through the primes.
  • A079297 (program): Triangle read by rows: the k-th column is an arithmetic progression with difference 2k-1 and the top entry is the hexagonal number k(2k-1) (A000384).
  • A079309 (program): a(n) = C(1,1) + C(3,2) + C(5,3) + … + C(2*n-1,n).
  • A079314 (program): Number of first-quadrant cells (including the two boundaries) born at stage n of the Holladay-Ulam cellular automaton.
  • A079316 (program): Number of first-quadrant cells (including the two boundaries) That are ON at stage n of the cellular automaton described in A079317.
  • A079317 (program): Number of ON cells after n generations of cellular automaton on square grid in which cells which share exactly one edge with an ON cell change their state.
  • A079318 (program): a(0) = 1; for n > 0, a(n) = (3^(A000120(n)-1) + 1)/2.
  • A079319 (program): a(0) = 1; for n > 1, a(n) = 4*a(n-1) - (2^n-1).
  • A079326 (program): a(n) = the largest number m such that if m monominoes are removed from an n X n square then an L-triomino must remain.
  • A079343 (program): Period 6: repeat [0, 1, 1, 2, 3, 1]; also F(n) mod 4, where F(n) = A000045(n).
  • A079344 (program): F(n) mod 8, where F(n) = A000045(n) is the n-th Fibonacci number.
  • A079345 (program): Fibonacci(n) mod 16.
  • A079351 (program): a(1)=3; for n > 1, a(n) is the smallest integer greater than a(n-1) consistent with the condition “n is in the sequence if and only if a(n) is congruent to 0 (mod 5)”.
  • A079360 (program): Sequence of sums of alternating increasing powers of 2.
  • A079362 (program): Sequence of sums of alternating powers of 3.
  • A079395 (program): a(n) = prime(n)^11.
  • A079414 (program): a(n) = 4n^4 - 3n^2.
  • A079424 (program): A bisection of A024675. Cf. A058296.
  • A079429 (program): a(0) = 2, a(1) = 3, a(2) = 5; a(n) = a(n-1) + [a(n-1)-a(n-2)] * [a(n-2)-a(n-3)].
  • A079450 (program): a(n) = 2^(n-1)u(n) where u(1)=1 and u(n) = frac(3/2u(n-1)) + 1.
  • A079472 (program): Number of perfect matchings on an n X n L-shaped graph.
  • A079484 (program): a(n) = (2n-1)!! * (2n+1)!!, where the double factorial is A006882.
  • A079496 (program): a(0) = a(1) = 1; thereafter a(2n+1) = 2a(2n) - a(2n-1), a(2n) = 4a(2n-1) - a(2n-2).
  • A079498 (program): Numbers whose sum of digits in base b gives 0 (mod b), for b = 3.
  • A079503 (program): a(n) = (n-1)^3((n-2)^2 - 2(n-3)).
  • A079504 (program): a(n) = 8n^3((2n-1)^2 - 4n + 4).
  • A079505 (program): The last number for which a determinant of base-n numbers is nonzero.
  • A079511 (program): a(n) = constant arising in game of n-times nim.
  • A079524 (program): Expansion of (x + bx^2 - bx^3)/((1 - x^2)*(1 - x)^2) with b=2.
  • A079535 (program): a(n) = phi(n)*d(n) - n.
  • A079547 (program): a(n) = ((n^6 - (n-1)^6) - (n^2 - (n-1)^2))/60.
  • A079552 (program): Record values in A079551.
  • A079553 (program): a(n) = floor( d(n^2) / d(n) ), where d() = A000005.
  • A079559 (program): Number of partitions of n into distinct parts of the form 2^j-1, j=1,2,….
  • A079578 (program): Least coprime to n, greater than n+1.
  • A079579 (program): Totally multiplicative with p -> (p-1)*p, p prime.
  • A079583 (program): a(n) = 3*2^n - n - 2.
  • A079584 (program): Number of ones in the binary expansion of n!.
  • A079585 (program): Decimal expansion of c = (7-sqrt(5))/2 = 2.3819660112501…
  • A079588 (program): a(n) = (n+1)(2n+1)(4n+1).
  • A079589 (program): a(n) = C(5n+1,n).
  • A079590 (program): C(6n+1,n).
  • A079598 (program): a(n) = 2^(4n+1)-2^(2n).
  • A079610 (program): a(n) = (5n+1)(5n+3)(5*n+5).
  • A079632 (program): a(n) = floor(n/floor(sqrt(n)))-floor(sqrt(n)).
  • A079643 (program): a(n) = floor(n/floor(sqrt(n))).
  • A079644 (program): n (mod sqrtint(n)).
  • A079667 (program): a(n) = (1/2) * Sum_ d divides n abs(n/d-d).
  • A079675 (program): a(1)=1; a(n)=sum(u=1,n-1,sum(v=1,u,sum(w=1,v,sum(x=1, w,sum(y=1,x,a(y)))))).
  • A079696 (program): Numbers one more than composite numbers.
  • A079704 (program): 2p^2 where p runs through the primes.
  • A079705 (program): 3p^2 where p runs through the primes.
  • A079719 (program): a(n) = n + floor[sum_k k<n a(k)/2] with a(0)=0.
  • A079725 (program): Sum of composite numbers less than n-th prime.
  • A079727 (program): a(n) = 1 + C(2,1)^3 + C(4,2)^3 + … + C(2n,n)^3.
  • A079728 (program): sum(k=0,p,binomial(2*k,k)) (mod p) where p runs through the primes.
  • A079750 (program): Operation count to create all permutations of n distinct elements using the “streamlined” version of Algorithm L (lexicographic permutation generation) from Knuth’s The Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives number of comparisons required to find j in step L2.2’.
  • A079751 (program): Operation count to create all permutations of n distinct elements using the “streamlined” version of Algorithm L (lexicographic permutation generation) from Knuth’s The Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives number of cases where the j search loop runs beyond j=n-3.
  • A079752 (program): Operation count to create all permutations of n distinct elements using the “streamlined” version of Algorithm L lexicographic permutation generation) from Knuth’s The Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives number of times the search for an element exchangeable with a_j has to be started.
  • A079757 (program): Periodic sequence 1 0 -2 3 -2 0,…
  • A079772 (program): Let C(n) be the n-th composite number; then a(n) is the smallest number > C(n) and not coprime to C(n).
  • A079773 (program): a(n) = 2a(n-1)+15a(n-2) with n>0, a(0)=0, a(1)=1.
  • A079813 (program): n 0’s followed by n 1’s.
  • A079824 (program): Sum of numbers in n-th upward diagonal of triangle in A079823.
  • A079859 (program): a(n) = n*2^(n-4).
  • A079861 (program): a(n) is the number of occurrences of 7’s in the palindromic compositions of 2n-1, or also, the number of occurrences of 8’s in the palindromic compositions of 2n.
  • A079862 (program): a(i) = the number of occurrences of 9’s in the palindromic compositions of n=2i-1 = the number of occurrences of 10’s in the palindromic compositions of n=2i.
  • A079863 (program): a(n) is the number of occurrences of 11s in the palindromic compositions of m=2n-1 = the number of occurrences of 12s in the palindromic compositions of m=2n.
  • A079878 (program): a(1)=1, then a(n)=2a(n-1) if 2a(n-1)<=n, a(n)=2*a(n-1)-n otherwise.
  • A079882 (program): A run of 2^n 1’s followed by a run of 2^n 2’s, for n=0, 1, 2, …
  • A079901 (program): Triangle of powers, T(n,k) = n^k, 0<=k<=n, read by rows.
  • A079903 (program): a(n) = (9n^4 - 18n^3 + 18n^2 - 9n + 2)/2.
  • A079904 (program): Triangle read by rows: T(n, k) = n*k, 0<=k<=n.
  • A079905 (program): a(1)=1; then a(n) is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n+1 for n>1.
  • A079908 (program): Solution to the Dancing School Problem with 3 girls and n+3 boys: f(3,n).
  • A079921 (program): Solution to the Dancing School Problem with n girls and n+2 boys: f(n,2).
  • A079929 (program): a(n)=(3n+1)!/(n!3^n).
  • A079935 (program): a(n) = 4*a(n-1) - a(n-2) with a(1) = 1, a(2) = 3.
  • A079944 (program): A run of 2^n 0’s followed by a run of 2^n 1’s, for n=0, 1, 2, …
  • A079945 (program): Partial sums of A079882.
  • A079946 (program): Binary expansion of n has form 11*…0.
  • A079947 (program): Partial sums of A030300.
  • A079948 (program): First differences of A079000.
  • A079951 (program): Number of primes p with prime(n) == 1 (modulo 2*p).
  • A079952 (program): Number of primes less than prime(n)/2.
  • A079953 (program): Smallest prime p such that prime(n) mod 2*p = prime(n).
  • A079954 (program): Partial sums of A030301.
  • A079962 (program): Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i=1..n, with k=1, r=5, I= 1,3 .
  • A079977 (program): Fibonacci numbers interspersed with zeros.
  • A079978 (program): Characteristic function of multiples of three.
  • A079979 (program): Characteristic function of multiples of six.
  • A079998 (program): The characteristic function of the multiples of five.
  • A080023 (program): log_phi(n) is closer to an integer than is log_phi(m) for any m with 2<=m<n, where phi=(1+sqrt(5))/2 is the golden ratio.
  • A080029 (program): a(n) is taken to be the smallest positive integer not already present which is consistent with the condition “n is a member of the sequence if and only if a(n) is a multiple of 3”.
  • A080030 (program): a(n) is taken to be the smallest positive integer not already present which is consistent with the condition “n is a member of the sequence if and only if a(n) is congruent to 1 mod 3”.
  • A080031 (program): a(n) is taken to be the smallest positive integer not already present which is consistent with the condition “n is a member of the sequence if and only if a(n) is congruent to 2 mod 3”.
  • A080036 (program): a(n) = n + round(sqrt(2*n)) + 1.
  • A080037 (program): a(0)=2; for n > 0, a(n) = n + floor(sqrt(4n-3)) + 2.
  • A080039 (program): a(n) = floor((1+sqrt(2))^n).
  • A080040 (program): a(n) = 2a(n-1) + 2a(n-2) for n > 1; a(0)=2, a(1)=2.
  • A080041 (program): a(n)=floor((1+sqrt(3))^n).
  • A080047 (program): Operation count to create all permutations of n distinct elements using Algorithm L (lexicographic permutation generation) from Knuth’s The Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives number of times l has to be repeatedly decreased in step L3.
  • A080063 (program): n mod (spf(n)+1), where spf(n) is the smallest prime dividing n (A020639).
  • A080075 (program): Proth numbers: of the form k*2^m + 1 for k odd, m >= 1 and 2^m > k.
  • A080079 (program): Least number causing the longest carry sequence when adding numbers <= n to n in binary representation.
  • A080084 (program): Number of prime factors in the factorial of the n-th prime, counted with multiplicity.
  • A080085 (program): Number of factors of 2 in the factorial of the n-th prime, counted with multiplicity.
  • A080086 (program): Number of factors of 3 in the factorial of the n-th prime, counted with multiplicity.
  • A080087 (program): Number of factors of 5 in the factorial of the n-th prime, counted with multiplicity.
  • A080095 (program): Let sum(k>=0, k^n/(2k+1)!) = (x(n)e + y(n)/e)/z(n), where x(n) and z(n) are >0, then a(n)=z(n).
  • A080096 (program): a(1)=a(2)=1; a(3)=2; a(n)=abs(a(n-1)-a(n-2)-a(n-3)).
  • A080097 (program): a(n) = Fibonacci(n+2)^2 - 1.
  • A080100 (program): a(n) = 2^(number of 0’s in binary representation of n).
  • A080109 (program): Square of primes of the form 4k+1 (A002144).
  • A080121 (program): a(n) is the smallest k > 0 such that n^2^k + (n+1)^2^k is prime, or -1 if no such k exists.
  • A080141 (program): (3^(n-1))*(n!)^2.
  • A080143 (program): a(n) = F(3)F(n)F(n+1) + F(4)F(n+1)^2 - F(4) if n even, F(3)F(n)F(n+1) + F(4)F(n+1)^2 if n odd, where F(n) is the n-th Fibonacci number (A000045).
  • A080144 (program): a(n) = F(4)F(n)F(n+1) + F(5)F(n+1)^2 if n odd, a(n) = F(4)F(n)F(n+1) + F(5)F(n+1)^2 - F(5) if n even, where F(n) is the n-th Fibonacci number (A000045).
  • A080145 (program): a(n) = Sum_ m=1..n Sum_ i=1..m F(i)*F(i+1) where F(n)=Fibonacci numbers A000045.
  • A080147 (program): Positions of primes of the form 4*k+1 (A002144) among all primes (A000040).
  • A080148 (program): Positions of primes of the form 4*k+3 (A002145) among all primes (A000040).
  • A080150 (program): Let m = Wonderful Demlo number A002477(n); a(n) = square of the sum of digits of m.
  • A080151 (program): Let m = Wonderful Demlo number A002477(n); a(n) = sum of digits of m.
  • A080169 (program): Numbers that are cubes of primes of the form 4k+1 (A002144).
  • A080175 (program): Fourth power of primes of the form 4k+1 (A002144).
  • A080211 (program): a(n) = binomial(n, smallest prime factor of n).
  • A080213 (program): a(n) = binomial(n, greatest prime factor of n).
  • A080239 (program): Antidiagonal sums of triangle A035317.
  • A080256 (program): Sum of numbers of distinct and of all prime factors of n.
  • A080260 (program): a(n)=1+(1/12)(n(n+1)(n+3)*(4-n)).
  • A080276 (program): Variation on Connell sequence (A001614). In this one, a(1)=1, terms a(n) onwards are generated in “blocks” as the next a(n-1) odd numbers > a(n-1) if the previous block ends with a(n-1) even and the next a(n-1) even numbers > a(n-1) if the previous block ends with a(n-1) odd.
  • A080277 (program): Partial sums of A038712.
  • A080278 (program): a(n) = (3^(v_3(n) + 1) - 1)/2, where v_3(n) = highest power of 3 dividing n = A007949(n).
  • A080304 (program): Numerator of n^mu(n), where mu is the Moebius function (A008683).
  • A080305 (program): Denominator of n^mu(n), where mu is the Moebius function (A008683).
  • A080323 (program): a(n) = mu(n)^n, where mu is the Moebius function (A008683).
  • A080333 (program): Partial sums of A080278.
  • A080334 (program): n^2 read backwards, for n = 51, 50, 49, …
  • A080335 (program): Diagonal in square spiral or maze arrangement of natural numbers.
  • A080339 (program): Characteristic function of 1 union primes : 1 if n is 1 or a prime, else 0.
  • A080340 (program): First known infinite sequence containing no odd integer of the form 2^m+p (p prime).
  • A080341 (program): Sum of the first n terms that are congruent to 1, 4 or 5 mod 6 (A047259).
  • A080342 (program): Number of weighings required to identify a single bad coin out of n coins, using a two-pan balance.
  • A080343 (program): a(n) = round(sqrt(2n)) - floor(sqrt(2n)).
  • A080344 (program): Partial sums of A023969.
  • A080352 (program): Partial sums of A080343.
  • A080353 (program): a(1)=5; for n>1, a(n)=a(n-1)+1 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.
  • A080354 (program): First differences of A080353.
  • A080355 (program): a(1)=1; thereafter, a(n+1) = a(n) + 2^(prime(n)-1).
  • A080378 (program): Residues mod 4 of the n-th difference between consecutive primes.
  • A080396 (program): Largest squarefree numbers dividing the binomial coefficients C(n,k) read by row, 0<=k<=n. Squarefree kernel of Pascal triangle.
  • A080398 (program): Largest squarefree number dividing sum of divisors of n.
  • A080400 (program): Largest squarefree number dividing phi of n.
  • A080412 (program): Exchange rightmost two binary digits of n > 1; a(0)=0, a(1)=2.
  • A080420 (program): a(n) = (n+1)(n+6)3^n/6.
  • A080424 (program): a(n) = 3a(n-1) + 18a(n-2), a(0)=0, a(1)=1.
  • A080425 (program): Period 3: repeat [0, 2, 1].
  • A080455 (program): a(1)=1; for n>1, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.
  • A080456 (program): a(1) = a(2) = 2; for n > 2, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.
  • A080457 (program): a(1)=3; for n>1, a(n)=a(n-1) if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
  • A080458 (program): a(1)=4; for n>1, a(n)=a(n-1) if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
  • A080460 (program): a(1) = 2; for n > 1, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.
  • A080468 (program): a(n) = A080578(n)-2n.
  • A080476 (program): Floor( geometric mean of next n numbers ).
  • A080500 (program): a(n) = (n-1)(n-4)(n-9)…(n-k^2) where k^2 < n <= (k+1)^2.
  • A080512 (program): a(n) = n if n is odd, a(n) = 3*n/2 if n is even.
  • A080513 (program): a(n) = round(n/2) + 1 = ceiling(n/2) + 1 = floor((n+1)/2) + 1.
  • A080522 (program): Leading diagonal of triangle in A080521.
  • A080523 (program): a(n) = n^n - n(n-1)/2.
  • A080525 (program): First column of triangle in A080524.
  • A080526 (program): Final entry in n-th row of triangle in A080524.
  • A080529 (program): Number of nucleons in longest known radioactive decay series ending with Lead 206 (“uranium series”), reversed.
  • A080530 (program): Number of nucleons in longest known radioactive decay series ending with Lead 207 (“actinium series”), reversed.
  • A080531 (program): Number of nucleons in longest known radioactive decay series ending with Lead 208 (“thorium series”), reversed.
  • A080532 (program): Number of nucleons in longest known radioactive decay series ending with Lead 209, reversed.
  • A080534 (program): Number of protons in longest known radioactive decay series ending with Lead 207 (“actinium series”), reversed.
  • A080538 (program): Number of neutrons in longest known radioactive decay series ending with Lead 207 (“actinium series”), reversed.
  • A080540 (program): Number of neutrons in longest known radioactive decay series ending with Lead 209, reversed.
  • A080545 (program): Characteristic function of 1 union odd primes : 1 if n is 1 or an odd prime, else 0.
  • A080565 (program): Binary expansion of n has form 11*…1.
  • A080566 (program): Partial sums of A079000.
  • A080567 (program): 1 + Sum_ k=2..n 2^((prime(k)-1)/2).
  • A080572 (program): Number of ordered pairs (i,j), 0 <= i,j < n, for which (i & j) is nonzero, where & is the bitwise AND operator.
  • A080578 (program): a(1)=1; for n > 1, a(n) = a(n-1) + 1 if n is already in the sequence, a(n) = a(n-1) + 3 otherwise.
  • A080579 (program): a(1)=1; for n>1, a(n)=a(n-1)+1 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
  • A080584 (program): A run of 32^n 0’s followed by a run of 32^n 1’s, for n=0, 1, 2, …
  • A080585 (program): Partial sums of A080584.
  • A080586 (program): A run of 32^n 1’s followed by a run of 32^n 2’s, for n=0, 1, 2, …
  • A080587 (program): Partial sums of A080586.
  • A080590 (program): a(1)=1; for n>1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
  • A080595 (program): Consider the standard game of Nim with 3 heaps and make a list of the losing positions (x,y,z) with x <= y <= z in reverse lexicographic order; sequence gives z values.
  • A080596 (program): a(1)=1; for n >= 2, a(n) is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n+3.
  • A080600 (program): a(n) = ceiling(n*(3 + sqrt(13))/2).
  • A080610 (program): Partial sums of Jacobsthal gap sequence.
  • A080612 (program): Numbers n such that 1/p(2n+1)sum(k=1,n,p(2k+1)-p(2k)) >= 1/p(2n)*sum(k=1,n,p(2k)-p(2k-1)) where p(k) denotes the k-th prime.
  • A080633 (program): a(1)=3; for n > 1, a(n) is the smallest integer greater than a(n-1) consistent with the condition “n is in the sequence if and only if a(n) is congruent to 1 (mod 4)”.
  • A080637 (program): a(n) is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(1)=2, a(a(n)) = 2n+1 for n>1.
  • A080639 (program): a(1) = 1; for n>1, a(n) is taken to be the smallest integer greater than a(n-1) which is consistent with the condition “for n>1, n is a member of the sequence if and only if a(n) is even”.
  • A080643 (program): a(0)=0; for n>0, a(n) = 4^n - 2*3^(n-1).
  • A080645 (program): a(1) = 1; for n>1, a(n) is taken to be the smallest integer greater than a(n-1) which is consistent with the condition “for n>1, if n is a member of the sequence then a(n) is even”.
  • A080646 (program): a(1) = 3; for n>1, a(n) is taken to be the smallest integer greater than a(n-1) which is consistent with the condition “if n is a member of the sequence then a(n) is divisible by 3”.
  • A080649 (program): Sum of prime factors of sigma(n).
  • A080652 (program): a(1)=2; for n>1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.
  • A080653 (program): a(1) = 2; for n>1, a(n) is taken to be the smallest integer greater than a(n-1) such that the condition “a(a(n)) is always even” is satisfied.
  • A080663 (program): a(n) = 3*n^2 - 1.
  • A080667 (program): a(1)=3; for n>1, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.
  • A080668 (program): Numbers of the form n!+n^3.
  • A080674 (program): a(n) = (4/3)*(4^n - 1).
  • A080675 (program): a(n) = (5*4^n - 8)/6.
  • A080676 (program): a(1) = 1; for n>1, a(n) is the smallest number > a(n-1) such that the first n terms of the sequence contain a total of a(n) digits.
  • A080680 (program): Integer part of the square root of the n-th prime of the form 4k+1.
  • A080684 (program): Number of 13-smooth numbers <= n.
  • A080685 (program): Number of 17-smooth numbers <= n.
  • A080697 (program): a(n) = n * prime(prime(n)).
  • A080702 (program): a(1)=3; for n>1, a(n) = smallest number > a(n-1) such that the condition “if n is in the sequence then a(n) is even” is satisfied.
  • A080703 (program): a(1)=5; for n>1, a(n) = smallest number > a(n-1) such that the condition “if n is in the sequence then a(n) is a multiple of 4” is satisfied.
  • A080722 (program): a(0) = 0; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition “n is a member of the sequence if and only if a(n) == 1 mod 3”.
  • A080723 (program): a(0) = 1; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition “n is a member of the sequence if and only if a(n) == 1 mod 3”.
  • A080724 (program): a(0) = 2; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition “n is a member of the sequence if and only if a(n) == 1 mod 3”.
  • A080727 (program): a(0) = 1; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition “n is a member of the sequence if and only if a(n) == 2 mod 3”.
  • A080734 (program): a(1)=1, then a(n)=a(n-1)+2 if the final decimal digit of a(n) is 0, a(n)=a(n-1)+3 otherwise.
  • A080746 (program): Inverse Aronson transform of lower Wythoff sequence A000201.
  • A080750 (program): a(n) = largest number greater than a(n-1) such that the first n terms of the sequence contain a total of a(n) base-10 digits.
  • A080751 (program): a(n) is smallest number greater than a(n-1) such that the sequence contains a total of a(n) base 10 digits + commas through n terms (assuming one comma between each pair of terms).
  • A080754 (program): a(n) = ceiling(n*(1+sqrt(2))).
  • A080755 (program): a(n) = ceiling(n*(1+1/sqrt(2))).
  • A080757 (program): First differences of Beatty sequence A022838(n) = floor(n sqrt(3)).
  • A080763 (program): Exchange 1’s and 2’s in the eta-sequence A006337.
  • A080764 (program): First differences of A049472, floor(n/sqrt(2)).
  • A080770 (program): a(n)=[e(n+3)! ]-(n+3)(n+2)(n+1)(n)[e*(n-1)! ].
  • A080775 (program): Number of n X n monomial matrices whose nonzero entries are unit Hurwitz quaternions.
  • A080776 (program): Oscillating sequence which rises to 2^(k-1) in k-th segment (k>=1) then falls back to 0.
  • A080782 (program): a(1)=1, a(n)=a(n-1)-1 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.
  • A080787 (program): a(1)=a(2)=1; a(n) = a(n-1) + last decimal digit of a(n-2).
  • A080791 (program): Number of nonleading 0’s in binary expansion of n.
  • A080799 (program): Number of divide by 2 and add 1 operations required to reach …,7,8,4,2,1 when started at n.
  • A080800 (program): Similar to A080799 but count only division steps.
  • A080801 (program): Similar to A080799 but count only addition steps.
  • A080804 (program): Least number of connected subgraphs of the binary cube GF(2)^n such that every vertex of GF(2)^n lies in at least one of the subgraphs and no two vertices lie in the same set of subgraphs (such a collection is called an identifying set).
  • A080813 (program): Lexicographically largest overlap-free binary sequence.
  • A080817 (program): Leading diagonal of triangle in A080818.
  • A080819 (program): Row sums from triangle in A080818.
  • A080820 (program): Least m such that m^2 >= n*(n+1)/2.
  • A080827 (program): Rounded up staircase on natural numbers.
  • A080838 (program): Orchard crossing number of complete bipartite graph K_ 1,n .
  • A080846 (program): Fixed point of the morphism 0->010, 1->011, starting from a(1) = 0.
  • A080847 (program): mu(n)+2, where mu is the Moebius function (A008683).
  • A080848 (program): a(n) = n*(mu(n)+2), where mu is the Moebius function (A008683).
  • A080849 (program): (mu(n)+2)*n^2, where mu is the Moebius function (A008683).
  • A080855 (program): a(n) = (9n^2 - 3n + 2)/2.
  • A080856 (program): a(n) = 8n^2 - 4n + 1.
  • A080857 (program): (25n^2 - 15n + 2)/2.
  • A080859 (program): a(n) = 6n^2 + 4n + 1.
  • A080860 (program): 10n^2 + 5n + 1.
  • A080861 (program): 15n^2 + 6n + 1.
  • A080880 (program): a(n)a(n+3) - a(n+1)a(n+2) = 2^n, given a(0)=1, a(1)=2, a(2)=2.
  • A080883 (program): Distance of n to next square.
  • A080884 (program): Sum of (0,1) versions of Thue-Morse word (A010060) and Fibonacci word (A003849).
  • A080885 (program): Boolean AND of (0,1) versions of Thue-Morse word (A010060) and Fibonacci word (A003849).
  • A080886 (program): Boolean OR of (0,1) versions of Thue-Morse word (A010060) and Fibonacci word (A003849).
  • A080887 (program): Boolean XOR of (0,1) versions of Thue-Morse word (A010060) and Fibonacci word (A003849).
  • A080891 (program): Period 5: repeat [0, 1, -1, -1, 1].
  • A080921 (program): a(n) = 2a(n-1) + 48a(n-2), a(0)=0, a(1)=1.
  • A080923 (program): First differences of A003946.
  • A080924 (program): Jacobsthal gap sequence.
  • A080925 (program): Binomial transform of Jacobsthal gap sequence (A080924).
  • A080926 (program): Partial sums of A080925.
  • A080929 (program): Sequence associated with a(n) = 2a(n-1) + k(k+2)*a(n-2).
  • A080930 (program): a(n) = 2^(n-3)(n+2)(n+3)*(n+4)/3.
  • A080937 (program): Number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 2*n steps with all values <= 5.
  • A080940 (program): Smallest proper divisor of n which is a suffix of n in binary representation; a(n) = 0 if no such divisor exists.
  • A080951 (program): Sequence associated with recurrence a(n) = 2a(n-1) + k(k+2)*a(n-2).
  • A080952 (program): a(n) = 2^(n-4)(n+2)(n+3)(n+4)(n+5)*(n+6)/15.
  • A080954 (program): E.g.f. exp(5x)/(1-x).
  • A080956 (program): a(n) = (n+1)*(2-n)/2.
  • A080957 (program): Expansion of (5 - 9x + 6x^2)/(1-x)^4.
  • A080960 (program): Third binomial transform of A010685 (period 2: repeat 1,4).
  • A080961 (program): Fourth binomial transform of A010686 (period 2: repeat 1,5).
  • A080978 (program): a(n) = 2*A006046(n) + 1.
  • A080995 (program): Characteristic function of generalized pentagonal numbers A001318.
  • A081002 (program): a(n) = Fibonacci(4n) + 1, or Fibonacci(2n-1)*Lucas(2n+1).
  • A081003 (program): a(n) = Fibonacci(4n+1) + 1, or Fibonacci(2n+1)*Lucas(2n).
  • A081004 (program): a(n) = Fibonacci(4n+2) + 1, or Fibonacci(2n+2)*Lucas(2n).
  • A081005 (program): a(n) = Fibonacci(4n+3) + 1, or Fibonacci(2n+1)*Lucas(2n+2).
  • A081006 (program): a(n) = Fibonacci(4n) - 1, or Fibonacci(2n+1)*Lucas(2n-1).
  • A081007 (program): a(n) = Fibonacci(4n+1) - 1, or Fibonacci(2n)*Lucas(2n+1).
  • A081008 (program): a(n) = Fibonacci(4n+2) - 1, or Fibonacci(2n)*Lucas(2n+2).
  • A081009 (program): a(n) = Fibonacci(4n+3) - 1, or Fibonacci(2n+2)*Lucas(2n+1).
  • A081010 (program): a(n) = Fibonacci(4n+1) + 2, or Fibonacci(2n-1)*Lucas(2n+2).
  • A081011 (program): a(n) = Fibonacci(4n+3) + 2, or Fibonacci(2n+3)*Lucas(2n).
  • A081012 (program): a(n) = Fibonacci(4n+1) - 2, or Fibonacci(2n+2)*Lucas(2n-1).
  • A081013 (program): a(n) = Fibonacci(4n+3) - 2, or Fibonacci(2n)Lucas(2n+3).
  • A081014 (program): a(n) = Lucas(4n+1) + 1, or Lucas(2n)Lucas(2n+1).
  • A081015 (program): a(n) = Lucas(4n+3) + 1, or 5Fibonacci(2n+1)Fibonacci(2n+2).
  • A081016 (program): a(n) = (Lucas(4n+3) + 1)/5, or Fibonacci(2n+1)Fibonacci(2n+2), or A081015(n)/5.
  • A081017 (program): a(n) = Lucas(4n+1) - 1, or 5Fibonacci(2n)Fibonacci(2n+1).
  • A081018 (program): a(n) = (Lucas(4n+1)-1)/5, or Fibonacci(2n)*Fibonacci(2n+1), or A081017(n)/5.
  • A081019 (program): a(n) = Lucas(4n+3) - 1, or Lucas(2n+1)*Lucas(2n+2).
  • A081026 (program): Variation on Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = smallest (n odd) or largest (n even) number > a(n-1) that is a unique sum of two distinct earlier terms.
  • A081031 (program): Positions of white keys on piano keyboard, start with A0 = the 1st key.
  • A081032 (program): Positions of black keys on piano keyboard, start with A0 = the 1st key.
  • A081038 (program): 3rd binomial transform of (1,2,0,0,0,0,0,0….).
  • A081039 (program): 4th binomial transform of (1,3,0,0,0,0,0,…..).
  • A081040 (program): 5th binomial transform of (1,4,0,0,0,0,….).
  • A081041 (program): 6th binomial transform of (1,5,0,0,0,0,0,0,…..).
  • A081042 (program): 7th binomial transform of (1,6,0,0,0,0,0,0,…..).
  • A081043 (program): 8th binomial transform of (1,7,0,0,0,0,0,…).
  • A081044 (program): 9th binomial transform of (1,8,0,0,0,0,0,0,…..).
  • A081045 (program): 10th binomial transform of (1,9,0,0,0,0,0,…..).
  • A081057 (program): E.g.f.: Sum_ n>=0 a(n)x^n/n! = Sum_ n>=0 F(n+1)x^n/n! ^2, where F(n) is the n-th Fibonacci number.
  • A081065 (program): Numbers n such that n^2 = (1/3)(n+floor(sqrt(3)nfloor(sqrt(3)n))).
  • A081067 (program): Lucas(4n+2)+2, or 5*Fibonacci(2n+1)^2.
  • A081068 (program): a(n) = (Lucas(4n+2) + 2)/5, or Fibonacci(2n+1)^2, or A081067(n)/5.
  • A081069 (program): Lucas(4n)+2, or Lucas(2n)^2.
  • A081070 (program): Lucas(4n)-2, or 5*Fibonacci(2n)^2.
  • A081071 (program): a(n) = Lucas(4n+2)-2, or Lucas(2n+1)^2.
  • A081072 (program): Fibonacci(4n) + 3, or Fibonacci(2n+2)*Lucas(2n-2).
  • A081073 (program): Fibonacci(4n+2)+3, or Fibonacci(2n-1)*Lucas(2n+3).
  • A081074 (program): Fibonacci(4n)-3, or Fibonacci(2n-2)*Lucas(2n+2).
  • A081075 (program): a(n) = Fibonacci(4n+2) - 3.
  • A081076 (program): a(n) = Lucas(4n) + 3, or 5Fibonacci(2n-1)Fibonacci(2n+1).
  • A081077 (program): a(n) = Lucas(4n+2) + 3, or Lucas(2n)Lucas(2n+2).
  • A081078 (program): a(n) = Lucas(4n) - 3, or Lucas(2n-1)*Lucas(2n+1).
  • A081079 (program): Lucas(4n+2) - 3, or 5Fibonacci(2n)Fibonacci(2n+2).
  • A081105 (program): 5th binomial transform of (1,1,0,0,0,0,…..).
  • A081106 (program): 6th binomial transform of (1,1,0,0,0,0,…).
  • A081107 (program): 7th binomial transform of (1,1,0,0,0,0,…….).
  • A081108 (program): 8th binomial transform of (1,1,0,0,0,0,………).
  • A081109 (program): 9th binomial transform of (1,1,0,0,0,0,0,….).
  • A081115 (program): (p^2 - 1)/12 where p > 3 runs through the primes.
  • A081118 (program): Triangle of first n numbers per row having exactly n 1’s in binary representation.
  • A081122 (program): 10th binomial transform of (1,1,0,0,0,0,……).
  • A081123 (program): a(n) = floor(n/2)!.
  • A081125 (program): a(n) = n! / floor(n/2)!.
  • A081127 (program): 11th binomial transform of (0,1,0,0,0,0,0,……).
  • A081128 (program): 12th binomial transform of (0,1,0,0,0,0,0,0,…).
  • A081129 (program): Differences of Beatty sequence for cube root of 3.
  • A081131 (program): a(n) = n^(n-2) * binomial(n,2).
  • A081132 (program): a(n) = (n+1)^n*binomial(n+2,2).
  • A081133 (program): a(n) = n^n*binomial(n+2, 2).
  • A081134 (program): Distance to nearest power of 3.
  • A081135 (program): 5th binomial transform of (0,0,1,0,0,0, …).
  • A081136 (program): 6th binomial transform of (0,0,1,0,0,0, …).
  • A081138 (program): 8th binomial transform of (0,0,1,0,0,0, …).
  • A081139 (program): 9th binomial transform of (0,0,1,0,0,0,…).
  • A081140 (program): 10th binomial transform of (0,0,1,0,0,0,…).
  • A081141 (program): 11th binomial transform of (0,0,1,0,0,0,…).
  • A081142 (program): 12th binomial transform of (0,0,1,0,0,0,…).
  • A081143 (program): 5th binomial transform of (0,0,0,1,0,0,0,0,……).
  • A081144 (program): Starting at 1, four-fold convolution of A000400 (powers of 6).
  • A081147 (program): Differences of Beatty sequence for square root of 5.
  • A081168 (program): Differences of Beatty sequence for square root of 10.
  • A081179 (program): 3rd binomial transform of (0,1,0,2,0,4,0,8,0,16,…).
  • A081180 (program): 4th binomial transform of (0,1,0,2,0,4,0,8,0,16,…).
  • A081181 (program): Staircase on Pascal’s triangle.
  • A081186 (program): 4th binomial transform of (1,0,1,0,1,…), A059841.
  • A081187 (program): 5th binomial transform of (1,0,1,0,1,…), A059841.
  • A081188 (program): 6th binomial transform of (1,0,1,0,1,…..), A059841.
  • A081189 (program): 7th binomial transform of (1,0,1,0,1,…), A059841.
  • A081190 (program): 8th binomial transform of (1,0,1,0,1,…..), A059841.
  • A081192 (program): 10th binomial transform of (1,0,1,0,1,……), A059841.
  • A081193 (program): a(n) = 6a(n-1)-8a(n-2) for n>1, a(0)=1, a(1)=9.
  • A081196 (program): a(n) = (n+4)^n*binomial(n+2,2).
  • A081199 (program): 5th binomial transform of (0,1,0,1,…), A000035.
  • A081200 (program): 6th binomial transform of (0,1,0,1,0,1,…), A000035.
  • A081201 (program): 7th binomial transform of (0,1,0,1,0,1,….), A000035.
  • A081202 (program): 8th binomial transform of (0,1,0,1,0,1,….), A000035.
  • A081203 (program): 9th binomial transform of (0,1,0,1,0,1,…..), A000035.
  • A081204 (program): Staircase on Pascal’s triangle.
  • A081205 (program): Staircase on Pascal’s triangle.
  • A081209 (program): a(n) = Sum_ k=0..n (-1)^(n-k)*n^k.
  • A081215 (program): a(n) = (n^(n+1)+(-1)^n)/(n+1)^2.
  • A081216 (program): a(n) = (n^n-(-1)^n)/(n+1).
  • A081219 (program): One sixtieth the product of primitive Pythagorean triangles’ sides whose odd values differ by 2.
  • A081221 (program): Number of consecutive numbers >= n having at least one square divisor > 1.
  • A081223 (program): Smallest k such that floor(k*gamma) begins with n (gamma=0.5772156649…).
  • A081241 (program): Position in B of reversal of n-th term of B, where B is the logic-binary sequence, A007931.
  • A081242 (program): Left-to-right binary enumeration.
  • A081243 (program): a(n) = Mod[n+(Mod[Prime[n],3]-1),10]
  • A081245 (program): Number of days in months in the Haab year of Mayan/Mesoamerican calendars.
  • A081249 (program): Partial sums of A081134.
  • A081250 (program): Numbers k such that A081249(m)/m^2 has a local minimum for m = k.
  • A081251 (program): Numbers n such that A081249(m)/m^2 has a local maximum for m = n.
  • A081252 (program): Partial sums of A053646.
  • A081253 (program): Numbers n such that A081252(m)/m^2 has a local minimum for m = n.
  • A081254 (program): Numbers k such that A081252(m)/m^2 has a local maximum for m = k.
  • A081256 (program): Greatest prime factor of n^3 + 1.
  • A081257 (program): Greatest prime factor of n^3-1.
  • A081259 (program): a(n) is the smallest k such that C(3n,n) divides k!.
  • A081266 (program): Staggered diagonal of triangular spiral in A051682.
  • A081267 (program): Diagonal of triangular spiral in A051682.
  • A081268 (program): Diagonal of triangular spiral in A051682.
  • A081270 (program): Diagonal of triangular spiral in A051682.
  • A081271 (program): Vertical of triangular spiral in A051682.
  • A081272 (program): Downward vertical of triangular spiral in A051682.
  • A081275 (program): Shallow diagonal of triangular spiral in A051682.
  • A081276 (program): Floor(n^3/8).
  • A081282 (program): Generalized centered polygonal numbers.
  • A081283 (program): An interleaved sequence of pyramidal and polygonal numbers.
  • A081284 (program): An interleaved sequence of pyramidal and polygonal numbers.
  • A081288 (program): a(n) is the minimal i such that A000108(i) > n.
  • A081293 (program): a(n) = A000108(n) + A014137(n).
  • A081294 (program): Expansion of (1-2x)/(1-4x).
  • A081304 (program): Number of numbers m <= n with prime factors less than 2*spf(m), where spf(m) is the smallest prime factor of m (A020639).
  • A081305 (program): Number of numbers m <= n with at least one prime factor greater than 2*spf(m), where spf(m) is the smallest prime factor of m (A020639).
  • A081307 (program): G.f.: Sum_ k=1..n Sum_ m=1..k 1/(1-x^m).
  • A081325 (program): sigma(n^2) modulo 4.
  • A081334 (program): sigma(2*n^2) modulo 4.
  • A081335 (program): a(n) = (6^n + 2^n)/2.
  • A081336 (program): a(n) = (7^n + 3^n)/2.
  • A081337 (program): (8^n+4^n)/2.
  • A081338 (program): (9^n+5^n)/2.
  • A081340 (program): (5^n+(-1)^n)/2.
  • A081341 (program): Expansion of exp(3x)cosh(3*x).
  • A081342 (program): a(n) = (8^n + 2^n)/2.
  • A081343 (program): a(n) = (10^n + 4^n)/2.
  • A081345 (program): First row in maze arrangement of natural numbers A081344.
  • A081346 (program): First column in maze arrangement of natural numbers A081344.
  • A081347 (program): First column in maze arrangement of natural numbers.
  • A081348 (program): First row in maze arrangement of natural numbers.
  • A081350 (program): First column in maze array of natural numbers A081349.
  • A081351 (program): First row in square maze array of natural numbers A081349.
  • A081352 (program): Main diagonal of square maze arrangement of natural numbers A081349.
  • A081353 (program): Diagonal of square maze arrangement of natural numbers A081349.
  • A081369 (program): Binomial(n^2, n) reduced mod n^2.
  • A081374 (program): Size of “uniform” Hamming covers of distance 1, that is, Hamming covers in which all vectors of equal weight are treated the same, included or excluded from the cover together.
  • A081403 (program): a(n) = A008475(n^2).
  • A081404 (program): a(n) = A008475(prime(n)-1).
  • A081405 (program): a(n) = (n+1)*a(n-2) with a(0) = a(1) = 1.
  • A081406 (program): a(n) = (n+1)*a(n-3), a(0)=a(1)=a(2)=1 for n>1.
  • A081407 (program): 4th-order non-linear (“factorial”) recursion: a(0)=a(1)=a(2)=a(3)=1, a(n) = (n+1)*a(n-4).
  • A081408 (program): a(n) = (n+1)*a(n-5), with a(0)=a(1)=a(2)=a(3)=a(4)=1.
  • A081417 (program): A000720 applied to Pascal-triangle: Pi[C(n,j)], j,0..n and n=0,1,2,…
  • A081421 (program): Quotient after one division by 2 of numbers of the form 3^(2n) + 5^(2n).
  • A081423 (program): Subdiagonal of array of n-gonal numbers A081422.
  • A081431 (program): RevBinary(RevDecimal(n)), where RevBinary(m) is the binary reversal of m (A030101) and RevDecimal(m) is the decimal reversal of m (A004086).
  • A081432 (program): RevDecimal(RevBinary(n)), where RevDecimal(m) is the decimal reversal of m (A004086) and RevBinary(m) is the binary reversal of m (A030101).
  • A081435 (program): Diagonal in array of n-gonal numbers A081422.
  • A081436 (program): Fifth subdiagonal in array of n-gonal numbers A081422.
  • A081437 (program): Diagonal in array of n-gonal numbers A081422.
  • A081438 (program): Diagonal in array of n-gonal numbers A081422.
  • A081441 (program): a(n) = (2*n^3 - n^2 - n + 2)/2.
  • A081475 (program): Consider the mapping f(x/y) = (x+y)/(2xy) where x/y is a reduced fraction. Beginning with x_0 = 1 and y_0 = 2, repeated application of this mapping produces a sequence of fractions x_n/y_n; a(n) is the n-th numerator.
  • A081477 (program): Complement of A086377.
  • A081478 (program): Consider the mapping f(a/b) = (a - b)/(ab). Taking a = 2 b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 2/1,1/2,-1/2,-3/-2,-1/6,… Sequence contains the denominators.
  • A081489 (program): a(n) = n(2n^2 -3n +7)/6 = C(n, 1) + C(n, 2) + 2C(n, 3).
  • A081490 (program): Leading term of n-th row of A081491.
  • A081491 (program): Triangle read by rows in which the n-th row contains n terms of an arithmetic progression with a common difference of (n-1) and the first term of (n+1)-th row is 1 more than the last term of the n-th row.
  • A081492 (program): Sum of terms in n-th row of A081491.
  • A081493 (program): Triangle read by rows in which the n-th row begins with n and contains n terms of an Arithmetic progression with a common difference of (n-1).
  • A081494 (program): Start with Pascal’s triangle; form a triangle by sliding down n steps from top on both sides and including the horizontal row, deleting the inner numbers; a(n) = sum of entries on perimeter of triangle.
  • A081495 (program): Start with Pascal’s triangle; form a rhombus by sliding down n steps from top on both sides then sliding down inwards to complete the rhombus and then deleting the inner numbers; a(n) = sum of entries on perimeter of rhombus.
  • A081498 (program): Consider the triangle in which the n-th row starts with n, contains n terms and the difference of successive terms is 1,2,3,… up to n-1. Sequence gives row sums.
  • A081499 (program): Sum at 45 degrees to horizontal in triangle of A081498.
  • A081502 (program): Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 3x+y.
  • A081503 (program): Number of steps to reach a single digit when map in A081502 is iterated.
  • A081515 (program): Sum of terms in n-th row of A081517.
  • A081552 (program): Leading terms of rows in A081551.
  • A081554 (program): a(n) = sqrt(2)( (3+2sqrt(2))^n - (3-2*sqrt(2))^n ).
  • A081555 (program): a(n) = 6*a(n-1) - a(n-2) - 4, a(0)=3, a(1)=7.
  • A081567 (program): Second binomial transform of F(n+1).
  • A081583 (program): Third row of Pascal-(1,2,1) array A081577.
  • A081585 (program): Third row of Pascal-(1,3,1) array A081578.
  • A081586 (program): Fourth row of Pascal-(1,3,1) array A081578.
  • A081587 (program): Third row of Pascal-(1,4,1) array A081579.
  • A081588 (program): Fourth row of the Pascal-(1,4,1) array A081579.
  • A081589 (program): Third row of Pascal-(1,5,1) array A081580.
  • A081590 (program): Fourth row of Pascal-(1,5,1) array A081580.
  • A081591 (program): Third row of Pascal-(1,6,1) array A081581.
  • A081592 (program): A self generating sequence: “there are n a(n)’s in the sequence”. Start with 1,2 and use the rule : “a(n)=k implies there are n following k’s (k is 1 or 2)”.
  • A081593 (program): Third row of Pascal-(1,7,1) array A081582.
  • A081594 (program): Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 2x+y.
  • A081595 (program): Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 4x+y.
  • A081596 (program): Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 5x+y.
  • A081597 (program): Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 6x + y.
  • A081598 (program): Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 7x+y.
  • A081599 (program): Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 8x+y.
  • A081600 (program): Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 9x+y.
  • A081601 (program): Numbers n such that 3 does not divide Sum_ k=0..n binomial(2k,k) = A006134(n).
  • A081603 (program): Number of 2’s in ternary representation of n.
  • A081604 (program): Number of digits in ternary representation of n.
  • A081607 (program): Number of numbers <= n having at least one 0 in their ternary representation.
  • A081608 (program): Number of numbers <= n having no 0 in their ternary representation.
  • A081609 (program): Number of numbers <= n having at least one 1 in their ternary representation.
  • A081610 (program): Number of numbers <= n having at least one 2 in their ternary representation.
  • A081611 (program): Number of numbers <= n having no 2 in their ternary representation.
  • A081623 (program): Number of ways in which the points on an n X n square lattice can be equally occupied with spin “up” and spin “down” particles. If n is odd, we arbitrarily take the lattice to contain one more spin “up” particle than the number of spin “down” particles.
  • A081625 (program): a(n) = 2*5^n - 3^n.
  • A081626 (program): 2*6^n-4^n.
  • A081628 (program): a(n) = 2*(-1)^n - (-5)^n.
  • A081630 (program): 2-(-3)^n.
  • A081631 (program): 2*2^n-(-2)^n.
  • A081632 (program): 2*3^n-(-1)^n.
  • A081654 (program): a(n) = 2*4^n - 0^n.
  • A081655 (program): 2*5^n-1.
  • A081656 (program): 2*6^n-2^n.
  • A081659 (program): a(n) = n + Fibonacci(n+1).
  • A081660 (program): n+A001045(n+1).
  • A081661 (program): Partial sums of A081660.
  • A081662 (program): Partial sums of n + Fibonacci(n+1).
  • A081667 (program): a(n) = Fibonacci(binomial(n+2,2)).
  • A081668 (program): Expansion of 2sinh(x) + BesselI_0(2x).
  • A081670 (program): 3^n-1+C(2n,n).
  • A081672 (program): Expansion of exp(2x) - exp(0) + BesselI_0(2x).
  • A081674 (program): Generalized Poly-Bernoulli numbers.
  • A081676 (program): Largest perfect power <= n.
  • A081688 (program): 0 followed by A030124 - 1.
  • A081689 (program): A005228 - 1.
  • A081690 (program): From P-positions in a certain game.
  • A081704 (program): Let f(0)=1, f(1)=t, f(n+1) = (f(n)^2+t^n)/f(n-1). f(t) is a polynomial with integer coefficients. Then a(n) = f(n) when t=3.
  • A081714 (program): a(n) = F(n)*L(n+1) where F=Fibonacci and L=Lucas numbers.
  • A081728 (program): Length of periods of Euler numbers modulo prime(n).
  • A081737 (program): a(n) = (n-1)*10 + n-th decimal digit of Pi=3.14159…
  • A081738 (program): Sum_ 2 <= p <= n, p prime p^2.
  • A081743 (program): a(1)=1 then a(n)=a(n/2^k)+1 if n is even and 2^k is the largest power of 2 dividing n, a(n)=a(n-1) otherwise.
  • A081753 (program): a(n) = floor(n/12) if n==2 (mod 12); a(n)=floor(n/12)+1 otherwise.
  • A081759 (program): Numbers n such that 5n+6 is prime.
  • A081808 (program): Numbers n such that the largest prime power in the factorization of n equals phi(n).
  • A081839 (program): a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.
  • A081840 (program): a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
  • A081841 (program): a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.
  • A081842 (program): a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.
  • A081848 (program): Number of numbers whose base-3/2 expansion (see A024629) has n digits.
  • A081854 (program): (8n-3)(4n-1)(8n^2-5n+1).
  • A081861 (program): (1/24)*(sigma_3(2n-1)-sigma_1(2n-1)).
  • A081864 (program): Sum of 5th powers of the divisors of odd numbers: a(n) = sigma_5(2n-1).
  • A081865 (program): a(n) = sigma_7(2n-1).
  • A081866 (program): a(n)=sigma_9(2n-1).
  • A081867 (program): a(n)=sigma_11(2n-1).
  • A081892 (program): Second binomial transform of C(n+2,2).
  • A081908 (program): a(n) = 2^n*(n^2 - n + 8)/8.
  • A081909 (program): a(n) = 3^n(n^2 - n + 18)/18.
  • A081910 (program): 4^n*(n^2-n+32)/32.
  • A081913 (program): a(n) = 2^n*(n^3 - 3n^2 + 2n + 48)/48.
  • A081955 (program): a(n) = 2^r*3^s where r = n(n+1)/2 and s = n(n-1)/2.
  • A082019 (program): Diagonal of square array T(n,k) with T(1,1) = 1 where antidiagonals are filled alternating upwards and downwards with the smallest number not already used such that the n-th antidiagonal sum is a multiple of n.
  • A082023 (program): Number of partitions of n into 2 parts which are not relatively prime.
  • A082028 (program): Expansion of exp(x)*(1+x)/(1-x)^2.
  • A082030 (program): Expansion of e.g.f. exp(x)/(1-x)^3.
  • A082032 (program): Expansion of e.g.f.: exp(2x)/(1-2x).
  • A082033 (program): a(n) = (3n+1)*n!.
  • A082034 (program): a(n) = (4n + 1)n!.
  • A082039 (program): Symmetric square array defined by T(n,k)=(k^2*n^2 + kn + 1), read by antidiagonals.
  • A082040 (program): a(n) = 9n^2 + 3n + 1.
  • A082041 (program): 16n^2+4n+1.
  • A082042 (program): (n^2+1)n!.
  • A082043 (program): A symmetric square array of numbers, read by antidiagonals.
  • A082044 (program): Main diagonal of A082043: a(n) = n^4 + 2n^2 + 1.
  • A082045 (program): Diagonal sums of number array A082043.
  • A082046 (program): A symmetric square array of numbers, read by antidiagonals.
  • A082047 (program): Diagonal sums of number array A082046.
  • A082050 (program): Sum of divisors of n that are not of the form 3k+1.
  • A082051 (program): Sum of divisors of n that are not of the form 3k+2.
  • A082052 (program): Sum of divisors of n that are not of the form 4k+1.
  • A082061 (program): Greatest common prime-divisor of n and phi(n)=A000010(n); a(n)=1 if no common prime-divisor was found.
  • A082062 (program): Greatest common prime-divisor of n and sigma(n)=A000203(n); a(n)=1 if no common prime-divisor was found.
  • A082067 (program): Smallest prime that divides n and phi(n)=A000010(n), or 1 if n and phi(n) are relatively prime.
  • A082068 (program): Smallest common prime-divisor of n and sigma(n) = A000203(n); a(n)=1 if no common prime-divisor was found.
  • A082073 (program): First difference set of primes with 4k+1 form: A002144.
  • A082074 (program): One quarter of first differences of primes of the form 4*k+1 (A002144).
  • A082075 (program): First differences of primes of the form 4*k+3 (A002145).
  • A082076 (program): First differences of primes of the form 4*k+3 (A002145), divided by 4.
  • A082091 (program): a(n) = one more than the number of iterations of A005361 needed to reach 1 from the starting value n.
  • A082105 (program): A symmetric square array of numbers, read by antidiagonals.
  • A082106 (program): Main diagonal of number array A082105.
  • A082107 (program): Diagonal sums of number array A082105.
  • A082108 (program): a(n) = 4n^2 + 6n + 1.
  • A082109 (program): Third row of number array A082105.
  • A082110 (program): Array T(n,k) = k^2n^2+5k*n+1, read by antidiagonals.
  • A082111 (program): a(n) = n^2 + 5*n + 1.
  • A082112 (program): a(n) = 4n^2 + 10n + 1.
  • A082113 (program): n^4+5n^2+1.
  • A082114 (program): Diagonal sums of number array A082110.
  • A082115 (program): Fibonacci sequence (mod 3).
  • A082116 (program): Fibonacci sequence (mod 5).
  • A082117 (program): Fibonacci sequence (mod 6).
  • A082133 (program): Expansion of e.g.f. xexp(2x)*cosh(x).
  • A082134 (program): Expansion of e.g.f. xexp(3x)*cosh(x).
  • A082138 (program): A transform of C(n,3).
  • A082139 (program): A transform of binomial(n,5).
  • A082140 (program): A transform of binomial(n,6).
  • A082141 (program): A transform of C(n,7).
  • A082143 (program): First subdiagonal of number array A082137.
  • A082144 (program): A subdiagonal of number array A082137.
  • A082149 (program): A transform of C(n,2).
  • A082186 (program): 1 + sum of first n terms of A001221.
  • A082204 (program): Begin with a 1, then place the smallest (as far as possible distinct) digits, such that, beginning from the n-th term, n terms form a palindrome.
  • A082206 (program): Digit sum of A082205(n).
  • A082245 (program): Sum of (n-1)-th powers of divisors of n.
  • A082285 (program): a(n) = 16n + 13.
  • A082286 (program): a(n) = 18*n + 10.
  • A082289 (program): Expansion of x^4(2+x)/((1+x)(1-x)^5).
  • A082290 (program): Expansion of (1+x+x^2)/((1+x^2)(1+x)^4(1-x)^5).
  • A082291 (program): Expansion of x(2 + 5x - x^2)/((1 - x)(1 - 6x + x^2)).
  • A082296 (program): Solutions to 13^x+17^x == 19 mod 23.
  • A082306 (program): Expansion of e.g.f. (1+x)exp(2x)*cosh(x).
  • A082311 (program): A Jacobsthal sequence trisection.
  • A082365 (program): A Jacobsthal number sequence.
  • A082369 (program): Numbers congruent to 13 mod 30.
  • A082375 (program): Irregular triangle read by rows: row n begins with n and decreases by 2 until 0 or 1 is reached, for n >= 0.
  • A082388 (program): a(1) = 1, a(2) = 2; further terms are defined by rules that for k >= 2, a(2^k-i) = a(2^k+i) for 1 <= i <= 2^k-1 and a(2^k) = a(2^(k-1)) + Sum_ i < 2^k a(i).
  • A082389 (program): a(n) = floor((n+2)phi) - floor((n+1)phi) where phi=(1+sqrt(5))/2.
  • A082392 (program): Expansion of (1/x) * sum(k>=0, x^2^k/(1-2x^2^(k+1))).
  • A082398 (program): Number of directed, diagonally convex polyominoes with n cells.
  • A082405 (program): a(n) = 34*a(n-1) - a(n-2); a(0)=0, a(1)=6.
  • A082410 (program): a(1)=0. Thereafter, the sequence is constructed using the rule: for any k >= 0, if a(1), a(2), …, a(2^k+1) are known, the next 2^k terms are given as follows: a(2^k+1+i) = 1 - a(2^k+1-i) for 1 <= i <= 2^k.
  • A082412 (program): a(n) = (2*8^n + 2^n)/3.
  • A082413 (program): a(n) = (2*9^n + 3^n)/3.
  • A082416 (program): Parity of A073941(n).
  • A082425 (program): a(1)=1, a(n) = n*(a(n-1) + a(n-2) + … + a(2) + a(1)) - 1.
  • A082426 (program): a(1)=1, a(n)=n*(a(n-1)+a(n-2)+…+a(2)+a(1)) + 2.
  • A082429 (program): a(n) is the cardinality of the smallest subset S1 of S= 1,2,3,…,n such that every element of S is either in S1 or is the sum of two elements of S1.
  • A082446 (program): a(0)=0, a(1)=1, a(2)=0; thereafter, if k>=0 and a block of the first 32^k terms is known, then a(32^k+i)=1-a(i) for 0<=i<3*2^k.
  • A082447 (program): a(n) = the number k such that s(k)=0 where s(0)=n and s(i)=s(i-1)-(s(i-1) modulo i).
  • A082450 (program): a(n) = 5*(n^2-n+2)/2.
  • A082458 (program): Multiply by 1, add 1, multiply by 2, add 2, etc., starting with 0.
  • A082460 (program): a(n) = pi(n) - a(n - 1) = A000720(n) - a(n - 1).
  • A082462 (program): Let chi(k) = 1 if prime(k+1) - prime(k) = 2, = 0 otherwise; sequence gives a(n) = sum_ k <= n chi(k).
  • A082472 (program): a(1) = 1, a(n) = Sum_ k=1..n-1 a(k)*2^k.
  • A082476 (program): a(n) = Sum_ d n mu(d)^2*tau(d)^2.
  • A082477 (program): Number of divisors d of n such that d+1 is also a divisor of n+1.
  • A082481 (program): Number of 1’s in binary representation of C(2n,n).
  • A082482 (program): Floor of (2^n-1)/n.
  • A082485 (program): Numbers n such that 1/(2-s(n)) is an integer where s(k)=sum(i=1,k,1/3^floor(sqrt(i))).
  • A082486 (program): Decimal expansion of the constant c satisfying sum(k>=1,1/c^sqrtint(k))=1 where sqrtint(x)=floor(sqrt(x)).
  • A082493 (program): a(n) = n*ceiling(2^n/n) - 2^n.
  • A082494 (program): a(n) = n - (2^n (mod n)).
  • A082495 (program): a(n) = (2^n - 1) mod n.
  • A082505 (program): a(n) = sum of (n-1)-th row terms of triangle A134059.
  • A082507 (program): Generated by a 3rd-order formal recursion with suitable initial values as follows: a(n) = n - a(n-1) - a(n-2) - a(n-3); a(0)=a(1)=a(2)=0.
  • A082511 (program): a(n) = 3^n mod 2n.
  • A082514 (program): a(n)=A000720(n)+A000005(n).
  • A082524 (program): a(1)=1, a(2)=2, then use the rule when a(n) is the end of a run, n appears a(n) times.
  • A082528 (program): Least k such that x(k)=0 where x(1)=n x(k)=k^3*floor(x(k-1)/k^3).
  • A082532 (program): a(n) = n^2 - 2*floor(n/sqrt(2))^2.
  • A082541 (program): a(n) = (73^n - 40^n)/3.
  • A082542 (program): a(n) = prime(n) + 2 - (prime(n) mod 4).
  • A082543 (program): Take a string of n x’s and insert n-1 ^’s and n-1 pairs of parentheses in all possible ways. Sequence gives number of distinct integer values when x=sqrt(2).
  • A082548 (program): a(n) is the number of values of k such that k can be expressed as the sum of distinct primes with largest prime in the sum equal to prime(n).
  • A082551 (program): Denote sigma(n)-n by s(n); a(n)=1 if s(n)>n, a(n)=0 if s(n)=n, a(n)=-1 if s(n)<n.
  • A082562 (program): a(n) = number of values of m such that m can be expressed as the sum of distinct odd numbers with largest odd number in the sum = 2n+1.
  • A082569 (program): a(1)=2; a(n)=ceiling(n*(a(n-1)-1/a(n-1))).
  • A082570 (program): a(1)=1, a(n)=ceiling(n*(a(n-1)+1/a(n-1))).
  • A082574 (program): a(1)=1, a(n) = ceiling(r(3)a(n-1)) where r(3) = (1/2)(3 + sqrt(13)) is the positive root of X^2 = 3*X + 1.
  • A082575 (program): Nonnegative numbers in (3A005836) union (3A005836 - 2) [A005836 lists the numbers with base-3 representation containing no 2].
  • A082577 (program): a(n) = first digit to the right of decimal point of n*(sqrt(5)-1)/2.
  • A082578 (program): A binomial sum.
  • A082585 (program): a(1)=1, a(n) = ceiling(r(5)a(n-1)) where r(5) = (1/2)(5 + sqrt(29)) is the positive root of X^2 = 5*X + 1.
  • A082605 (program): Using Euler’s 6-term sequence A014556, we define the partial recurrence relation a(0)=2, a(1)=3, a(2)=5; a(k) = 2a(k-1) - 1 + (-1)^(k-1)2^(k-2), 3 <= k <= 5.
  • A082630 (program): Limit of the sequence obtained from S(0) = (1,1) and, for n > 0, S(n) = I(S(n-1)), where I consists of inserting, for i = 1, 2, 3…, the term a(i) + a(i+1) between any two terms for which 7a(i+1) <= 11a(i).
  • A082639 (program): Numbers n such that 2n(n+2) is a square.
  • A082642 (program): Expansion of Molien series for 5-dimensional representation of dihedral group of order 10.
  • A082643 (program): a(n) = ceiling(n*(n+1/2)/2).
  • A082644 (program): a(n) = floor(n*(n-1/2)/2).
  • A082645 (program): a(n) = floor((2*n^2 + n - 4)/4).
  • A082648 (program): Consider f(m) = Sum_ k=1..m k! (A007489) when m is very large; a(n) = n-th digit from end.
  • A082655 (program): Number of distinct letters needed to spell English names of numbers 1 through n.
  • A082662 (program): Numbers k such that the odd part of k is less than sqrt(2k).
  • A082667 (program): a(n) = floor(2n/3) * ceiling(2n/3) / 2.
  • A082679 (program): Number of Lego towers, one piece per floor, where every floor is perpendicular to the one below it (so we have a kind of 3-dimensional zigzag pattern).
  • A082685 (program): (2*5^n + 2^n)/3.
  • A082691 (program): a(1)=1, a(2)=2, then if 32^k-1 first terms are a(1),a(2),………,a(32^k - 1) we have the 32^(k+1)-1 first terms as : a(1),a(2),………,a(32^k - 1),a(1),a(2),………,a(32^k - 1),a(32^k-1)+1.
  • A082692 (program): Partial sums of A082691.
  • A082693 (program): Pyramidal sequence built with powers of 2.
  • A082694 (program): Partial sums of A082693.
  • A082742 (program): Indices of occurrences of 2 in A004738.
  • A082761 (program): Trinomial transform of the Fibonacci numbers (A000045).
  • A082762 (program): Trinomial transform of Lucas numbers (A000032).
  • A082767 (program): Number of edges in the prime graph.
  • A082784 (program): Characteristic function of multiples of 7.
  • A082840 (program): a(n) = 4*a(n-1) - a(n-2) + 3, with a(0) = -1, a(1) = 1.
  • A082841 (program): a(n) = 4*a(n-1) - a(n-2) for n>1, a(0)=3, a(1)=9.
  • A082844 (program): Start with 3,2 and apply the rule a(a(1)+a(2)+…+a(n)) = a(n), fill in any undefined terms with a(t) = 2 if a(t-1) = 3 and a(t) = 3 if a(t-1) = 2.
  • A082845 (program): Partial sums of A082844.
  • A082850 (program): Let S(0) = , S(n) = S(n-1), S(n-1), n ; sequence gives S(infinity).
  • A082851 (program): Partial sums of A082850.
  • A082863 (program): Number of distinct prime factors of n^2-1.
  • A082873 (program): Independence number of king KG_2 on triangle board B_n.
  • A082902 (program): a(n) = gcd(2^n, sigma(2,n)) = gcd(A000079(n), A001157(n)).
  • A082903 (program): a(n) = gcd(2^n, sigma_1(n)) = gcd(A000079(n), A000203(n)) also a(n) = gcd(2^n, sigma_3(n)) = gcd(A000079(n), A001158(n)).
  • A082907 (program): A modified Pascal’s triangle, read by rows, and modified as follows: binomial(n,j) is replaced by gcd(2^n, binomial(n,j)), i.e., the largest power of 2 dividing binomial(n,j).
  • A082908 (program): Largest value of gcd(2^n, binomial(n,j)) with j=0..n-1; maximal value of largest power of 2 dividing binomial(n,j) in the n-th row of Pascal’s triangle.
  • A082909 (program): a(n) = Sum_ d n (d mod 3).
  • A082910 (program): a(n) = prime(prime(n+1)-prime(n)).
  • A082928 (program): If n is prime, a(n) = n+1; if n is even, a(n) = n/2; otherwise a(n) = n.
  • A082934 (program): A082928(1) + A082928(2) + … + A082928(n).
  • A082942 (program): (n^2+1)(4n^2+1)(4n^2+3).
  • A082964 (program): a(n) = m given by arctan(tan(n)) = n - m*Pi.
  • A082969 (program): Numbers n such that (n/4)^2-n/8=sum(k=1,n, k modulo(sum(i=0,k-1,1-t(i))) where t(i)=A010060(i) is the Thue-Morse sequence.
  • A082977 (program): Numbers that are congruent to 0, 1, 3, 5, 6, 8, 10 mod 12.
  • A082981 (program): Start with the sequence S(0)= 1,1 and for k>0 define S(k) to be I(S(k-1)) where I denotes the operation of inserting, for i=1,2,3…, the term a(i)+a(i+1) between any two terms for which 4a(i+1)<=5a(i). The listed terms are the initial terms of the limit of this process as k goes to infinity.
  • A082986 (program): Largest x such that 1/x + 1/y + 1/z = 1/n.
  • A082987 (program): a(n)=sum(k=0,n,3^k*F(k)) where F(k) is the k-th Fibonacci number.
  • A082988 (program): a(n)=sum(k=0,n,4^k*F(k)) where F(k) is the k-th Fibonacci number.
  • A082996 (program): a(n) = card x <= n : bigomega(x) = 4 .
  • A082997 (program): a(n) = card x <= n : omega(x) = 2 .
  • A082999 (program): a(n) = A046195(n) mod 5.
  • A083023 (program): a(n) = number of partitions of n into a pair of parts n=p+q, p>=q>=0, with p-q equal to a square >= 0.
  • A083026 (program): Numbers that are congruent to 0, 2, 4, 5, 7, 9, 11 mod 12.
  • A083028 (program): Numbers that are congruent to 0, 2, 3, 5, 7, 8, 11 mod 12.
  • A083030 (program): Numbers that are congruent to 0, 4, 7 mod 12.
  • A083031 (program): Numbers that are congruent to 0, 3, 7 mod 12.
  • A083032 (program): Numbers that are congruent to 0, 4, 7, 10 mod 12.
  • A083033 (program): Numbers that are congruent to 0, 2, 3, 5, 7, 9, 10 mod 12.
  • A083034 (program): Numbers that are congruent to 0, 1, 3, 5, 7, 8, 10 mod 12.
  • A083035 (program): a(n) = floor(sqrt(2)n)-2floor(n/sqrt(2)).
  • A083036 (program): Partial sums of A083035.
  • A083037 (program): a(n)=2*A083036(n)-n. Also -A123737(n).
  • A083038 (program): A fractal sequence.
  • A083039 (program): Number of divisors of n that are <= 3.
  • A083040 (program): Number of divisors of n that are <= 4
  • A083045 (program): Main diagonal of table A083044.
  • A083051 (program): First column of table A083050.
  • A083054 (program): a(n) = floor(sqrt(3)n) - 3floor(n/sqrt(3)).
  • A083055 (program): a(n) = cardinality k<=n / A083054(k)=1 .
  • A083058 (program): Number of eigenvalues equal to 1 of n X n matrix A(i,j)=1 if j=1 or i divides j.
  • A083062 (program): (n+1)^n/(n+2)-(-1)^n/(n+2).
  • A083065 (program): 4th row of number array A083064.
  • A083066 (program): 5th row of number array A083064.
  • A083067 (program): 6th row of number array A083064.
  • A083068 (program): 7th row of number array A083064.
  • A083069 (program): Main diagonal of number array A083064.
  • A083070 (program): First super-diagonal of number array A083064.
  • A083074 (program): n^3 - n^2 - n - 1.
  • A083076 (program): Third row of number array A083075.
  • A083077 (program): Fifth row of number array A083075.
  • A083078 (program): 6th row of number array A083075.
  • A083079 (program): 4th column of number array A083075.
  • A083085 (program): (2+(-5)^n)/3.
  • A083086 (program): a(n) (2*2^n + (-4)^n)/3.
  • A083088 (program): First column of table A083087.
  • A083089 (program): Numbers that are congruent to 0, 2, 4, 6, 7, 9, 11 mod 12.
  • A083093 (program): Triangle formed by reading Pascal’s triangle (A007318) mod 3.
  • A083094 (program): Numbers k such that Sum_ j=0..k (binomial(k,j) mod 3) is odd.
  • A083095 (program): a(n) = A083094(n)/4.
  • A083096 (program): Numbers n such that 3 divides sum(k=1,n, C(2k,k) ).
  • A083097 (program): a(n) = A083096(n)/6.
  • A083098 (program): a(n) = 2a(n-1) + 6a(n-2).
  • A083099 (program): a(n) = 2a(n-1) + 6a(n-2), a(0) = 0, a(1) = 1.
  • A083101 (program): a(n) = 2a(n-1) + 10a(n-2).
  • A083102 (program): a(n) = 2a(n-1) + 10a(n-2).
  • A083120 (program): Numbers that are congruent to 0, 2, 4, 5, 7, 9, 10 mod 12.
  • A083127 (program): 3n^3+n^2-4n.
  • A083175 (program): Row sums in A083175.
  • A083176 (program): Arithmetic means of rows of A083173.
  • A083196 (program): a(n) = 8n^4 + 9n^2 + 2.
  • A083215 (program): a(n) = 1 + Sum(prime(i)(2i-1): 1<=i<=n).
  • A083217 (program): a(n) = (2*5^n+(-1)^n)/3.
  • A083218 (program): a(n) = n mod (spf(n+1)+1), where spf(n) is the smallest prime factor of n (A020639).
  • A083219 (program): a(n) = n - 2*floor(n/4).
  • A083220 (program): a(n) = n + (n mod 4).
  • A083222 (program): a(n) = (4*5^n + (-5)^n)/5.
  • A083223 (program): a(n) = (5*6^n+(-6)^n)/6.
  • A083224 (program): a(n) = (6*7^n + (-7)^n)/7.
  • A083225 (program): a(n) = (7*8^n + (-8)^n)/8.
  • A083227 (program): a(n) = (9*10^n + (-10)^n)/10.
  • A083228 (program): A Jacobsthal related sequence.
  • A083232 (program): a(n) = (3*7^n+(-1)^n)/4.
  • A083233 (program): a(n) = (3*8^n + 0^n)/4.
  • A083245 (program): Difference between numbers of related and numbers of unrelated numbers belonging to n: a(n) = A073757(n)-A045763(n) = (n-u(n))-u(n) = n-2A045763(n) = 2A073757(n)-n.
  • A083254 (program): a(n) = 2*phi(n) - n.
  • A083266 (program): Sum of related numbers (counted in A073757) belonging to n: a(n) = A000203(n) + A023896(n) - 1; related = divisor-set, RRS .
  • A083271 (program): a(n) = n*tau(n) + 1.
  • A083277 (program): k appears 3k-2 times.
  • A083282 (program): a(n) = n^(3n)
  • A083292 (program): a(n) = n*floor(n/10) + (n mod 10).
  • A083294 (program): a(n) = (4 + (-9)^n)/5.
  • A083302 (program): a(n) = (4*9^n + (-1)^n)/5.
  • A083313 (program): a(0)=1; a(n) = 3^n - 2^(n-1) for n >= 1.
  • A083314 (program): (2*4^n-(3^n-1))/2.
  • A083318 (program): a(0) = 1; for n>0, a(n) = 2^n + 1.
  • A083322 (program): a(n) = 2^n - A081374(n).
  • A083323 (program): a(n) = 3^n - 2^n + 1.
  • A083324 (program): An alternating sum of decreasing powers.
  • A083329 (program): a(0) = 1; for n > 0, a(n) = 3*2^(n-1) - 1.
  • A083330 (program): a(n) = (34^n - 23^n + 2^n)/2.
  • A083337 (program): a(n) = 2a(n-1) + 2a(n-2); a(0)=0, a(1)=3.
  • A083346 (program): Denominator of r(n) = Sum(e/p: n=Product(p^e)).
  • A083356 (program): Total area of all incongruent integer-sided rectangles of area <= n.
  • A083363 (program): Diagonal of table A083362.
  • A083364 (program): Antidiagonal sums of table A083362.
  • A083374 (program): a(n) = n^2 * (n^2 - 1)/2.
  • A083375 (program): n appears prime(n) times.
  • A083392 (program): Alternating partial sums of A000217.
  • A083399 (program): Number of divisors of n that are not divisors of other divisors of n.
  • A083413 (program): a(n) = Sum_ d n d*2^(d-1) for n > 0.
  • A083416 (program): Add 1, double, add 1, double, etc.
  • A083420 (program): a(n) = 2*4^n - 1.
  • A083421 (program): a(n)=2*5^n-2^n.
  • A083423 (program): a(n) = (5*3^n + (-3)^n)/6.
  • A083424 (program): a(n) = (5*4^n + (-2)^n)/6.
  • A083425 (program): a(n) = (5*5^n + (-1)^n)/6.
  • A083426 (program): (4*7^n+2^n)/5.
  • A083445 (program): Largest n-digit number minus the product of its digits; i.e., a(n) = 99999… (n 9’s) - 9^n.
  • A083446 (program): a(n) = ((10^n - 1) - 9^n)/9.
  • A083456 (program): Smallest nontrivial k such that k^n + 1 is a palindrome (k>1 for n>1).
  • A083457 (program): Smallest nontrivial k such that k^n - 1 is a palindrome (k >1 for n>1).
  • A083479 (program): The natural numbers with all terms of A033638 inserted.
  • A083481 (program): Smallest k such that n(n+1)*k is a square.
  • A083511 (program): Members of A000124 which are multiples of 11.
  • A083528 (program): a(n) = 5^n mod 2*n.
  • A083529 (program): a(n) = 5^n mod 3*n.
  • A083530 (program): a(n) = 7^n mod (2*n).
  • A083537 (program): a(0) = a(1) = 0, a(2n) = a(n)+1, a(2n+1) = a(n-1).
  • A083539 (program): a(n) = sigma(n) * sigma(n+1): product of sigma-values for consecutive integers.
  • A083542 (program): a(n) = phi(n+1)*phi(n), product of totients of two consecutive integers.
  • A083553 (program): Product of prime(n+1)-1 and prime(n)-1.
  • A083558 (program): p(p^2-p+1) as p runs through the primes.
  • A083559 (program): Nearest integer to 1/(Sum_ k>=n 1/k^4).
  • A083570 (program): A de Bruijn sequence of length 9 over 0, 1, 2 , repeated.
  • A083575 (program): a(0) = 6; for n>0, a(n) = 2*a(n-1) - 1.
  • A083578 (program): a(n) = (6^n + (-4)^n)/2.
  • A083579 (program): Generalized Jacobsthal numbers.
  • A083581 (program): 8/3-5(-2)^n/3.
  • A083582 (program): a(n) = (82^n-5(-1)^n)/3.
  • A083583 (program): a(n) = (83^n - 50^n)/3.
  • A083584 (program): a(n) = (8*4^n - 5)/3.
  • A083585 (program): (85^n - 52^n)/3.
  • A083589 (program): Expansion of 1/((1-4x)(1-x^4)).
  • A083590 (program): Expansion of 1/((1-5x)(1-x^5)).
  • A083593 (program): Expansion of 1/((1-2x)(1-x^4)).
  • A083594 (program): a(n) = (7 - 4*(-2)^n)/3.
  • A083595 (program): a(n) = (7*2^n - 4(-1)^n)/3.
  • A083597 (program): a(n) = (7*4^n - 4)/3.
  • A083651 (program): Triangular array, read by rows: T(n,k) = k-th bit in binary representation of n (0<=k<=n).
  • A083652 (program): Sum of lengths of binary expansions of 0 through n.
  • A083656 (program): a(n) = Sum_ i=1..n floor(rfloor(ri)), where r=sqrt(2).
  • A083657 (program): a(n)=sum(i=1,n,floor(rfloor(ri))) where r=sqrt(3).
  • A083658 (program): a(n) = a(n-1) + a(n-2) + gcd(a(n-1),a(n-2)) for n>1, with a(0)=1, a(1)=1.
  • A083661 (program): G.f.: 1/(1-x) * sum(k>=0, x^2^(k+2)/(1+x^2^k)).
  • A083662 (program): a(n) = a(floor(n/2)) + a(floor(n/4)), n > 0; a(0)=1.
  • A083667 (program): Number of antisymmetric binary relations on a set of n labeled points.
  • A083669 (program): Number of ordered quintuples (a,b,c,d,e), -n <= a,b,c,d,e <= n, such that a+b+c+d+e = 0.
  • A083679 (program): Decimal expansion of log(4/3).
  • A083680 (program): Decimal expansion of (3/2)*log(3/2).
  • A083683 (program): a(n) = 11*2^n + 1.
  • A083686 (program): a(0) = 8; for n>0, a(n) = 2*a(n-1) - 1.
  • A083704 (program): a(n)=sum(k=1,n,floor(r*floor(k/r))) where r=sqrt(3).
  • A083705 (program): a(n) = 2*a(n-1) - 1 with a(0)=10.
  • A083706 (program): a(n) = 2^(n+1)+n-1.
  • A083707 (program): G.f.: (x+4x^3+x^5)/((1-x)^2(1-x^2)^2*(1-x^3)).
  • A083708 (program): G.f.: (x+4x^3+x^5)/((1-x)^2(1-x^2)^2*(1-x^3)^2).
  • A083713 (program): a(n) = (8^n - 1)*3/7.
  • A083723 (program): a(n) = (prime(n)+1)*n - 1.
  • A083725 (program): a(n) = n * [1 + sum(k=1 to n) prime(k)].
  • A083726 (program): a(n) = (prime(n)+1)*n.
  • A083727 (program): a(n) = n * (2^n - 8).
  • A083729 (program): Decimal expansion of sqrt(2)/(sqrt(2)-1)^2 = 3*sqrt(2)+4.
  • A083730 (program): Greatest prime^2 factor of n, or a(n)=1 for squarefree n.
  • A083741 (program): a(n) = L(n) + a(L(n)), where L(n) = n - 2^floor(log_2(n)) (A053645).
  • A083786 (program): Composite numbers mod 10.
  • A083811 (program): Numbers n such that 2n+1 is the digit reversal of n+1.
  • A083812 (program): 4n-1 is the digit reversal of n-1.
  • A083813 (program): a(n) = 3*(10^n-1).
  • A083818 (program): Numbers n such that 2n-1 is the digit reversal of n.
  • A083822 (program): a(n) = digit reversal of 3*n, divided by 3.
  • A083824 (program): a(n) = digit reversal of 9*n, divided by 9.
  • A083877 (program): Absolute value of determinant of n X n matrix where the element a(i,j) = if i + j > n then 2(i + j -n) - 1, else 2(n + 1 - i - j).
  • A083878 (program): a(0)=1, a(1)=3, a(n)=6a(n-1)-7a(n-2), n>=2.
  • A083879 (program): a(0)=1, a(1)=4, a(n) = 8a(n-1) - 14a(n-2), n >= 2.
  • A083881 (program): a(n) = 6a(n-1) - 6a(n-2), with a(0)=1, a(1)=3.
  • A083884 (program): a(n) = (3^(2*n) + 1) / 2.
  • A083885 (program): (4^n+2^n+0^n+(-2)^n)/4
  • A083904 (program): G.f. 1/(1-x) * Sum_ k>=0 3^k * x^2^(k+1)/(1+x^2^k).
  • A083907 (program): a(1) = 1; for n>1, a(n) = n*a(n-1) if GCD(n,a(n-1)) = 1 else a(n) = a(n-1).
  • A083909 (program): Numbers of the form 10^(m-k)*(10^(m+k+1)-10^k), m, k >= 0.
  • A083911 (program): Number of divisors of n that are congruent to 1 modulo 10.
  • A083912 (program): Number of divisors of n that are congruent to 2 modulo 10.
  • A083919 (program): Number of divisors of n that are congruent to 9 modulo 10.
  • A083920 (program): Number of nontriangular numbers <= n.
  • A083921 (program): Start with (1,2) and then concatenate 2^n+1 previous terms, n>=0 and add 2 if a(2^n+1)=1 or add 1 if a(2^n+1)=2.
  • A083943 (program): A generalized Jacobsthal sequence.
  • A083944 (program): A generalized Jacobsthal sequence.
  • A084008 (program): a(n) = T(n) concatenated with reverse(T(n)) divided by 11, where T(n) is the n-th triangular number.
  • A084009 (program): a(n) = n^2 concatenated with reverse(n^2) divided by 11.
  • A084010 (program): a(n) = (2^n concatenated with Reverse(2^n))) divided by 11.
  • A084011 (program): Digit reversal of 11*n, divided by 11.
  • A084052 (program): 2*n digit-reversed mod 2.
  • A084054 (program): 5*n digit-reversed mod 5.
  • A084055 (program): 6*n digit-reversed mod 6.
  • A084056 (program): a(n) = -a(n-1) + a(n-2) + a(n-3), with a(0)=0, a(1)=1, a(2)=-3.
  • A084057 (program): a(n) = 2a(n-1) + 4a(n-2), a(0)=1, a(1)=1.
  • A084059 (program): a(n) = 4a(n-1) + 2a(n-2) for n>1, a(0)=1, a(1)=2.
  • A084060 (program): a(n) = 1/2 + (1-6n)(-1)^n/2.
  • A084068 (program): a(1) = 1, a(2) = 2; a(2k) = 2a(2k-1) - a(2k-2), a(2k+1) = 4a(2k) - a(2k-1).
  • A084070 (program): a(n) = 38*a(n-1) - a(n-2), with a(0)=0, a(1)=6.
  • A084084 (program): Length of lists created by n substitutions k -> Range[0,1+Mod[k+1,3]] starting with 0 .
  • A084091 (program): Expansion of sum(k>=0, x^2^k/(1+x^2^k+x^2^(k+1))).
  • A084096 (program): Fifth row of number array A084061.
  • A084099 (program): Expansion of (1+x)^2/(1+x^2).
  • A084100 (program): Expansion of (1+x-x^2-x^3)/(1+x^2).
  • A084101 (program): Expansion of (1+x)^2/((1-x)*(1+x^2)).
  • A084103 (program): Expansion of (1+x)^3/(1+x^3).
  • A084104 (program): A period 6 sequence.
  • A084120 (program): a(n)=6a(n-1)-3a(n-2), a(0)=1,a(1)=3.
  • A084128 (program): a(n) = 4a(n-1) + 4a(n-2), a(0)=1, a(1)=2.
  • A084130 (program): a(n) = 8a(n-1)-8a(n-2), a(0)=1, a(1)=4.
  • A084134 (program): a(n)=8a(n-1)-6a(n-2), a(0)=1,a(1)=4.
  • A084152 (program): Exponential self-convolution of Jacobsthal numbers (divided by 2).
  • A084153 (program): Binomial transform of a Jacobsthal convolution.
  • A084158 (program): a(n) = A000129(n)*A000129(n+1)/2.
  • A084159 (program): Pell oblongs.
  • A084170 (program): a(n) = 5*2^n/3 + (-1)^n/3 - 1.
  • A084171 (program): Binomial transform of generalized Jacobsthal numbers A084170.
  • A084172 (program): a(n) = 3a(n-1) - a(n-2) - 3a(n-3) + 2*a(n-4).
  • A084173 (program): a(n) = 3a(n-1) - a(n-2) - 3a(n-3) + 2*a(n-4).
  • A084174 (program): a(n) = 3a(n-1) - a(n-2) - 3a(n-3) + 2*a(n-4).
  • A084175 (program): Jacobsthal oblong numbers.
  • A084177 (program): Binomial transform of Jacobsthal oblongs.
  • A084181 (program): 2^n+(-2)^n-(-1)^n.
  • A084182 (program): 3^n+(-1)^n-[1/(n+1)], where [] represents the floor function.
  • A084183 (program): Jacobsthal reverse-pair sequence.
  • A084184 (program): Partial sums of a Jacobsthal related sequence.
  • A084188 (program): a(0)=1, a(n+1) = 2*a(n) + b(n+2), where b(n)=A004539(n) is the n-th bit in the binary expansion of sqrt(2).
  • A084213 (program): Binomial transform of A081250.
  • A084214 (program): Inverse binomial transform of a math magic problem.
  • A084215 (program): Expansion of g.f.: (1+x^2)/(1-2*x).
  • A084219 (program): Inverse binomial transform of A053088.
  • A084221 (program): a(n+2) = 4*a(n), with a(0)=1, a(1)=3.
  • A084222 (program): a(n) = -2a(n-1) + 3a(n-2), with a(0)=1, a(1)=2.
  • A084231 (program): Numbers k such that the root-mean-square value of 1, 2, …, k, i.e., sqrt((1/k)*Sum_ j=1..k j^2), is an integer.
  • A084232 (program): RMS values associated with A084231.
  • A084240 (program): a(n) = -5a(n-1) - 4a(n-2), a(0)=1, a(1)=0.
  • A084241 (program): a(n) = -5a(n-1)-4a(n-2) with n>1, a(0)=0, a(1)=1.
  • A084244 (program): a(0)=1, a(1)=5, a(n) = -3*a(n-1), n>1.
  • A084245 (program): a(n) = Mod[n+(Mod[Prime[n],7]-3),10]
  • A084247 (program): a(n) = -a(n-1) + 2a(n-2), a(0)=1, a(1)=2.
  • A084253 (program): a(n) is the denominator of the coefficient of z^(2n-1) in the Maclaurin expansion of Sqrt[Pi]Erfi[z].
  • A084262 (program): Binomial transform of double factorials.
  • A084263 (program): Modified triangular numbers.
  • A084264 (program): Binomial transform of A084263.
  • A084265 (program): a(n) = (n^2 + 3*n + 1 + (-1)^n) / 2.
  • A084266 (program): Binomial transform of A084265.
  • A084267 (program): Partial sums of a binomial quotient.
  • A084300 (program): a(n) = phi(n) mod 6.
  • A084301 (program): a(n) = sigma(n) mod 6.
  • A084302 (program): Remainder of tau(n) modulo 6.
  • A084309 (program): a(n) = gcd(prime(n)-1, n).
  • A084310 (program): a(n) = gcd(prime(n)+1, n).
  • A084311 (program): a(n) = gcd(prime(n)-1,n-1).
  • A084326 (program): a(0)=0, a(1)=1; for n>1, a(n) = 6a(n-1)-4a(n-2).
  • A084328 (program): a(0)=0, a(1)=1; a(n) = 13a(n-1) - 11a(n-2).
  • A084329 (program): a(0)=0, a(1)=1, a(n)=20a(n-1)-20a(n-2).
  • A084346 (program): Triangle read by rows in which row n gives decomposition of Fib(n)*Fib(n+1) into non-adjacent Fibonacci numbers (given by their indices).
  • A084351 (program): Length of period of sequences r(k,n)=floor(sin(1)k!)-nfloor(sin(1)*k!/n) when n is fixed.
  • A084359 (program): a(n) = number of partitions of n into pair of parts n=p+q, p>=q>=1, with p-q equal to a square >= 0.
  • A084360 (program): Number of partitions of n into pair of parts whose difference is a prime.
  • A084363 (program): a(n) = n^(n+1) - (n-1)^n.
  • A084364 (program): Define the operations M: multiply by 11, D: divide by 11, R: reverse digits. Sequence gives trajectory of 19 under action of M,R,D,R.
  • A084367 (program): a(n) = n(2n+1)^2.
  • A084377 (program): a(n) = n^3 + 7.
  • A084378 (program): a(n) = n^3 + 3.
  • A084379 (program): a(n) = n^3 + 17.
  • A084380 (program): a(n) = n^3 + 2.
  • A084381 (program): a(n) = n^3 + 5.
  • A084382 (program): a(n) = n^3 + 6.
  • A084421 (program): A005187(A000040(n)).
  • A084431 (program): Expansion of (1 + 6x + 5x^2)/((1-2x)(1+2*x)).
  • A084432 (program): G.f.: 2/(1-x) + sum(k>=0, t^2(3-t)/(1+t)/(1-t)^2, t=x^2^k).
  • A084468 (program): Odd numbers with exactly 3 ones in binary expansion.
  • A084477 (program): Number of fault-free tilings of a 4 X 3n rectangle with right trominoes.
  • A084505 (program): Partial sums of A084506.
  • A084506 (program): The length of each successively larger 3-ball ground-state site swap given in A084501, i.e., the number of digits in each term of A084502.
  • A084508 (program): Partial sums of A084509. Positions of ones in the first differences of A084506.
  • A084509 (program): Number of ground-state 3-ball juggling sequences of period n.
  • A084515 (program): Partial sums of A084516.
  • A084516 (program): The length of each successively larger, indecomposable 3-ball ground-state site swap given in A084511, i.e., the number of digits in each term of A084512.
  • A084525 (program): Partial sums of A084526.
  • A084526 (program): The length of each successively larger, indecomposable, ‘prime’ 3-ball ground-state site swap given in A084521, i.e., the number of digits in each term of A084522.
  • A084535 (program): a(n) = floor(n^2 - n^(3/2)).
  • A084546 (program): Triangle read by rows: T(n,k) = C( C(n,2), k) for n >= 1, 0 <= k <= C(n,2).
  • A084555 (program): Partial sums of A084556.
  • A084556 (program): n occurs n! times.
  • A084557 (program): a(0)=0, after which each n occurs A084556(n) times.
  • A084558 (program): a(0) = 0; for n >= 1: a(n) = largest m such that n >= m!.
  • A084567 (program): Binomial transform of (1,-1,4,-16,64,-256,1024,….)=(3*0^n-(-4)^n)/4.
  • A084568 (program): a(0)=1, a(1)=5, a(n+2)=4a(n), n>0.
  • A084569 (program): Partial sums of A084570.
  • A084570 (program): Partial sums of A084263.
  • A084623 (program): Numerator of 2^(n-1)/n.
  • A084624 (program): floor(C(n+5,5)/C(n+2,2)).
  • A084626 (program): Floor(C(n+6,6)/C(n+2,2)).
  • A084627 (program): Floor(C(n+6,6)/C(n+3,3)).
  • A084628 (program): a(n) = floor(binomial(n+7,7)/binomial(n+3,3)).
  • A084630 (program): Floor(C(n+7,7)/C(n+5,5)).
  • A084631 (program): Floor(C(n+8,8)/C(n+2,2)).
  • A084633 (program): Inverse binomial transform of repeated odd numbers.
  • A084634 (program): Binomial transform of 1,1,1,2,2,2,2,…
  • A084635 (program): Binomial transform of 1,0,1,0,1,1,1,…
  • A084636 (program): Binomial transform of (1,0,1,0,1,0,2,0,2,0,2,0….).
  • A084639 (program): Expansion of x(1+2x)/((1+x)(1-x)(1-2*x)).
  • A084640 (program): Generalized Jacobsthal numbers.
  • A084642 (program): A Jacobsthal ratio.
  • A084643 (program): a(n) = 3^(n-1)(2n-3) + 2^(n+1).
  • A084672 (program): G.f.: (1+x^2+2x^4)/((1-x^3)(1-x)^2).
  • A084678 (program): a(n)=b(n,n) with b(n,1)=n and b(n,k)=binomial(b(n,k-1),d(n,n-k+1)) for 1<k<=n, where d(n,i) are the divisors of n, d(i)<d(j), 1<=i<j<=A000005(n).
  • A084684 (program): Degrees of certain maps.
  • A084703 (program): Squares n such that 2*n+1 is also a square.
  • A084707 (program): a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 27; a(n) = 3a(n-1) - 3a(n-3) + a(n-4) for n > 3.
  • A084737 (program): Beginning with 1, numbers such that a(n+2)-a(n+1) / a(n+1)-a(n) =prime(n).
  • A084747 (program): Leading diagonal of triangle shown below in which the n-th row contains the n smallest numbers > 0 such that when they are incremented by n yield a prime.
  • A084756 (program): For n, k > 0, let T(n, k) be given by T(n, 1) = n and T(n, k+1) = k*T(n, k)+1. Then a(n) = T(n, n).
  • A084792 (program): Primes other than prime(prime(n)+n-1).
  • A084849 (program): a(n) = 1 + n + 2*n^2.
  • A084850 (program): 2^(n-1)*(n^2+2n+2).
  • A084851 (program): Binomial transform of binomial(n+2,2).
  • A084857 (program): Inverse binomial transform of n^2*3^(n-1).
  • A084858 (program): Binomial transform of A001651.
  • A084859 (program): Binomial transform of Cullen numbers A002064.
  • A084860 (program): Expansion of (1-2x+2x^2-x^3)/(1-2x)^2.
  • A084861 (program): Expansion of (1-3x+4x^2-3x^3+x^4)/(1-2x)^2.
  • A084890 (program): Triangular array, read by rows: T(n,k) = arithmetic derivative of n*k, 1<=k<=n.
  • A084899 (program): Binomial transform of heptagonal numbers A000566.
  • A084900 (program): 3^(n-2)n(5n+1)/2.
  • A084901 (program): a(n) = 4^(n-2)n(5*n+3)/2.
  • A084902 (program): a(n) = 5^(n-1)n(n+1)/2.
  • A084903 (program): Binomial transform of positive cubes.
  • A084915 (program): a(n) = (n!)^2*n.
  • A084920 (program): a(n) = (prime(n)-1)*(prime(n)+1).
  • A084921 (program): a(n) = lcm(p-1, p+1) where p is the n-th prime.
  • A084922 (program): a(n) = (prime(n)-1)*(prime(n)+1)/6.
  • A084941 (program): Octagorials: n-th polygorial for k=8.
  • A084943 (program): Decagorials: n-th polygorial for k=10.
  • A084947 (program): a(n) = Product_ i=0..n-1 (7*i+2).
  • A084948 (program): a(n) = Product_ i=0..n-1 (8*i+2).
  • A084949 (program): a(n) = Product_ i=0..n-1 (9*i+2).
  • A084964 (program): Follow n+2 by n. Also solution of a(n+2)=a(n)+1, a(0)=2, a(1)=0.
  • A084967 (program): Multiples of 5 whose GCD with 6 is 1.
  • A084968 (program): Multiples of 7 coprime to 30.
  • A084990 (program): a(n) = n(n^2+3n-1)/3.
  • A085001 (program): a(n) = (3n+1)(3*n+4).
  • A085002 (program): a(n) = floor(phin) - 2floor(phi*n/2) where phi is the golden ratio.
  • A085003 (program): Partial sums of A085002.
  • A085006 (program): Let S(0)= 1,1,2 S(n)= S(n-1), S(n-1)- x , 3-x where x is the last element of S(n-1), then sequence is S(infinity).
  • A085007 (program): Partial sums of A085006.
  • A085025 (program): a(n) = (5n+1)(5*n+6).
  • A085026 (program): a(n) = (6n+1)(6*n+7).
  • A085027 (program): a(n) = (4n+3)(4*n+7).
  • A085036 (program): a(n) = (5n+2)(5*n+7).
  • A085037 (program): Smallest square divisible by the n-th triangular number (n(n+1)/2).
  • A085046 (program): a(n) = n^2 - (1 + (-1)^n)/2.
  • A085058 (program): a(n) = A001511(n+1) + 1.
  • A085059 (program): a(1) = 1, a(n+1) = a(n)-n if a(n) > n else a(n+1) = a(n) + n.
  • A085060 (program): Integer reached in A085058.
  • A085062 (program): A085060(n)/9 - 1/3.
  • A085089 (program): Number of distinct prime signatures arising up to n.
  • A085090 (program): If 2n-1 is prime then a(n) = 2n-1, otherwise a(n) = 0.
  • A085141 (program): Greatest nonnegative integer k such that k(3k+1)/2 <= n.
  • A085151 (program): Numbers generated by the Fibonacci polynomial x^4 + 3x^2 + 1.
  • A085157 (program): Quintuple factorials, 5-factorials, n!!!!!, n!5.
  • A085158 (program): Sextuple factorials, 6-factorials, n!!!!!!, n!6.
  • A085242 (program): a(n) = A085239(n) - 2.
  • A085250 (program): 4 times hexagonal numbers: a(n) = 4n(2*n-1).
  • A085259 (program): Integer part of the conversion from Centigrade to Fahrenheit.
  • A085260 (program): Ratio-determined insertion sequence I(0.0833344) (see the link below).
  • A085265 (program): Numbers that can be written as sum of a positive squarefree number and a positive square.
  • A085268 (program): Integer part of the conversion from Fahrenheit to Centigrade.
  • A085269 (program): Integer part of the conversion from centimeters to inches.
  • A085270 (program): Integer part of the conversion from miles to kilometers.
  • A085271 (program): Difference between n-th composite number and its smallest prime divisor.
  • A085275 (program): Sum of n-th composite number and its largest prime divisor.
  • A085278 (program): Expansion of (1+2x)^2/((1-x^2)(1-2x)).
  • A085279 (program): Expansion of (1 - 2x - 2x^2)/((1 - 2x)(1 - 3*x)).
  • A085280 (program): Expansion of (1-4x+x^2)/((1-x)(1-3x)(1-4x)).
  • A085281 (program): Expansion of (1 - 3x + x^2)/((1-2x)(1-3x)).
  • A085282 (program): Expansion of (1 - 5x + 5x^2)/((1-x)(1-3x)(1-4x)).
  • A085283 (program): a(n) = n*n^n - (n-1)(n-1)^n.
  • A085284 (program): C(n+3,3)n^3/4.
  • A085287 (program): Expansion of (1+4x)/((1-x^2)(1-3x)).
  • A085296 (program): Runs of zeros in Catalan sequence modulo 3: consecutive occurrences of binomial(2*k,k)/(k+1) == 0 (mod 3).
  • A085297 (program): Nonzero residues of Catalan sequence modulo 3; related to the Thue-Morse sequence (A001285).
  • A085339 (program): Modulo 91 remainders of 6th powers.
  • A085340 (program): a(n) is the value of determinant of the following special matrix: diagonal values equal to n-2; upper triangular entries equal to -1; lower triangular values are +1.
  • A085350 (program): Binomial transform of poly-Bernoulli numbers A027649.
  • A085351 (program): Expansion of (1-3x)/((1-4x)(1-5x)).
  • A085354 (program): a(n) = 34^n - (n+4)2^(n-1).
  • A085356 (program): a(n) = polygorial(n,3)/polygorial(3,n), n >= 3.
  • A085357 (program): Common residues of binomial(3n,n)/(2n+1) modulo 2: relates ternary trees (A001764) to the infinite Fibonacci word (A003849).
  • A085369 (program): Cutting sequence for 1/e.
  • A085373 (program): a(n) = binomial(2n+1, n+1)*binomial(n+2, 2).
  • A085374 (program): a(n) = binomial(2n+1, n+1)*binomial(n+3, 3).
  • A085375 (program): a(n) = binomial(2n+1, n+1)binomial(n+4, 4).
  • A085377 (program): a(n) = 15n^2 + 13n^3.
  • A085389 (program): a(n) = (n(n+1)^(n-1)+0^n)/(n+1).
  • A085392 (program): a(n) = largest prime divisor of n, or 1 if n is 1 or a prime.
  • A085405 (program): Common residues of binomial(3n+2,n+1)/(3n+2) modulo 2.
  • A085409 (program): Sum of three solutions of the Diophantine equation x^2 - y^2 = z^3.
  • A085423 (program): a(n) = floor(log_2(3n)).
  • A085424 (program): Number of ones in the symmetric signed digit expansion of n with q=2 (i.e., the representation of n in the (-1,0,1)_2 number system).
  • A085425 (program): Number of minus ones in the symmetric signed digit expansion of n with q=2 (i.e., the representation of n in the (-1,0,1)_2 number system).
  • A085431 (program): a(n) = (2^(n-1) + prime(n+1)-prime(n))/2.
  • A085438 (program): a(n) = Sum_ i=1..n binomial(i+1,2)^3.
  • A085439 (program): a(n) = Sum_ i=1..n binomial(i+1,2)^4.
  • A085440 (program): a(n) = Sum_ i=1..n binomial(i+1,2)^5.
  • A085441 (program): a(n) = Sum_ i=1..n binomial(i+1,2)^6.
  • A085442 (program): a(n) = Sum_ i=1..n binomial(i+1,2)^7.
  • A085447 (program): a(n) = 6*a(n-1) + a(n-2), starting with a(0)=2 and a(1)=6.
  • A085449 (program): Horadam sequence (0,1,4,2).
  • A085461 (program): Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1 <= v5, v2 <= v5, v2 <= v4 and v3 <= v4.
  • A085462 (program): Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1<=v4, v1<=v5, v2<=v4 and v3<=v4.
  • A085463 (program): Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1<=v4, v1<=v5, v2<=v4, v2<=v5 and v3<=v4.
  • A085464 (program): Number of monotone n-weightings of complete bipartite digraph K(4,2).
  • A085465 (program): Number of monotone n-weightings of complete bipartite digraph K(3,3).
  • A085473 (program): a(n) = 6n^2 + 3n + 1.
  • A085474 (program): C(2n+4,4)-C(2n,4).
  • A085479 (program): Product of three solutions of the Diophantine equation x^3 - y^3 = z^2.
  • A085482 (program): Product of three solutions of the Diophantine equation x^2 - y^2 = z^3.
  • A085490 (program): Number of pairs with two different elements which can be obtained by selecting unique elements from two sets with n+1 and n^2 elements respectively and n common elements.
  • A085501 (program): Number of prime powers p^k <= n that are not prime (k = 0 or k > 1).
  • A085504 (program): Horadam sequence (0,1,9,3).
  • A085521 (program): a(n) = Product_ k=0..n (2^(2k+1)+1).
  • A085524 (program): a(0) = 0; a(n) = n^(2*n-1) for n > 0.
  • A085525 (program): a(n) = n^(2*n + 2).
  • A085526 (program): a(n) = n^(2n+1).
  • A085527 (program): a(n) = (2n+1)^n.
  • A085528 (program): a(n) = (2*n+1)^(n+1).
  • A085529 (program): a(n) = (2n+1)^(2n+1).
  • A085530 (program): a(n) = (2n+1)^(2n).
  • A085531 (program): a(n) = (2n+1)^(2n-1).
  • A085532 (program): (2n)^(n+1).
  • A085533 (program): (2n)^(2n+1).
  • A085534 (program): a(n) = (2n)^(2n).
  • A085535 (program): a(n) = (2n)^(2n-1).
  • A085537 (program): a(n) = n^4 - n^3.
  • A085538 (program): a(n) = n^5 - n^4.
  • A085539 (program): a(n) = n^6 - n^5.
  • A085540 (program): a(n) = n*(n+1)^3.
  • A085550 (program): Decimal expansion of (sqrt(13)-3)/2.
  • A085551 (program): Decimal expansion of (sqrt(29)-5)/2.
  • A085552 (program): n-th digit after decimal point of sqrt(n^2+4)-n)/2.
  • A085565 (program): Decimal expansion of lemniscate constant A.
  • A085577 (program): Size of maximal subset of the n^2 cells in an n X n grid such that there are at least 3 edges between any pair of chosen cells.
  • A085583 (program): Number of (3412,1234)-avoiding involutions in S_n.
  • A085599 (program): Number of pairs of coprimes (n-i,n+i), 1<i<n.
  • A085600 (program): Number of simple graphs with 3 edges on n vertices.
  • A085601 (program): a(n) = 2 * (4^n + 2^n) + 1.
  • A085602 (program): Numbers of the form (2n+1)^(2n+1) + 1.
  • A085603 (program): (2n)^(2n) + 1.
  • A085606 (program): (n-1)^n - 1.
  • A085621 (program): Mean prime gaps that do not occur in A049036.
  • A085622 (program): Maximal number of segments (equivalently, corners) in a rook circuit of a 2n X 2n board.
  • A085624 (program): Sum of the entries in the character table of the dihedral group D_ 2n of order 2n.
  • A085641 (program): Smallest prime == 1 mod(pq…k) where p, q, …k are all the distinct prime divisors of n. Or, smallest prime == 1 (mod the largest squarefree divisor of n).
  • A085644 (program): a(1) = 1; a(n+1) = a(n)*2n+2n+1.
  • A085680 (program): Size of largest code of length n and constant weight 2 that can correct a single adjacent transposition.
  • A085683 (program): a(n) = Sum_ k = 1..N-1 floor(N/k) where N is the n-th prime.
  • A085689 (program): a(1) = 4; a(n) = if n == 2 mod 3 then a(n-1)/2, if n == 0 mod 3 then a(n-1)2, if n == 1 mod 3 then a(n-1)3.
  • A085697 (program): a(n) = T(n)^2, where T(n) = A000073(n) is the n-th tribonacci number.
  • A085708 (program): Arithmetic derivative of 10^n.
  • A085717 (program): Consider the square lattice L and the sublattice K of index 5 spanned by (2,-1), (1,2); a(n) = number of points (x,y) in M with x >= 0, y >= 0, x+y <= n.
  • A085731 (program): Greatest common divisor of n and its arithmetic derivative.
  • A085739 (program): Partial sums of A034953(n).
  • A085740 (program): a(n) = T(n)^2 - n^2, where T(n) is a triangular number.
  • A085741 (program): a(n) = T(n)^n, where T() are the triangular numbers (A000217).
  • A085742 (program): a(n) = T(n^3) - T(n), where T() are the triangular numbers (A000217).
  • A085743 (program): a(n) = T(n^3) - T(n^2), where T() are the triangular numbers (A000217).
  • A085744 (program): a(n) = A000217(n^3) - n^3.
  • A085750 (program): Determinant of the symmetric n X n matrix A defined by A[i,j] = i-j for 1 <= i,j <= n.
  • A085781 (program): a(n) = 2binomial(2n+1,n+1) - 2^n.
  • A085786 (program): a(n) = A000217(n) + n^3.
  • A085787 (program): Generalized heptagonal numbers: m(5m - 3)/2, m = 0, +-1, +-2 +-3, …
  • A085788 (program): Partial sums of n 3-spaced triangular numbers beginning with t(3), e.g., a(2)=t(3)+t(6)=6+21=27.
  • A085789 (program): Partial sums of n 3-spaced triangular numbers beginning with t(2), e.g., a(2) = t(2) + t(5) = 3 + 15 = 18.
  • A085801 (program): Maximum number of nonattacking queens on an n X n toroidal board.
  • A085820 (program): Possible two-digit endings of primes (with leading zeros).
  • A085891 (program): Maximal product of three numbers with sum n: a(n) = max(rst), n = r+s+t.
  • A085899 (program): a(n) = floor( 2(1 + n + 2n^2 + 4n^3)/(1 + 2n + n^2)).
  • A085903 (program): G.f.: (1 + 2x^2)/((1 + x)(1 - 2x)(1 - 2*x^2)).
  • A085904 (program): Numbers n such that n, n+1 and n+2 are highly composite numbers (2), i.e., all prime divisors <= 7 (A002473).
  • A085913 (program): Group the natural numbers such that the product of the terms of the n-th group is divisible by n!. (1),(2),(3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16,17,18),(19,20,21,22,23,24),… Sequence contains the first term of every group.
  • A085923 (program): a(0) = 1, a(n+1) = (n+1)*(a(n) + n).
  • A085931 (program): Leading diagonal of A085930.
  • A085952 (program): First n-digit number that occurs in the sequence A085951.
  • A085959 (program): Multiples of 37.
  • A085960 (program): Size of the largest code of length 4 and minimum distance 3 over an alphabet of size n. This is usually denoted by A_ n (4,3).
  • A085970 (program): Number of numbers <= n that are not prime powers.
  • A085972 (program): Number of numbers <= n that are primes or not prime powers.
  • A085975 (program): Number of 1’s in decimal expansion of prime(n).
  • A085977 (program): Number of 3’s in decimal expansion of prime(n).
  • A085979 (program): Number of 5’s in decimal expansion of prime(n).
  • A085980 (program): Number of 6’s in decimal expansion of prime(n).
  • A085981 (program): Number of 7’s in decimal expansion of prime(n).
  • A085983 (program): Number of 9’s in decimal expansion of prime(n).
  • A085990 (program): Number of topological types of polygons with 2n different sides.
  • A086009 (program): Number of 1’s in decimal expansion of n^2.
  • A086010 (program): Number of 2’s in decimal expansion of n^2.
  • A086011 (program): Number of 3’s in decimal expansion of n^2.
  • A086012 (program): Number of 4’s in decimal expansion of n^2.
  • A086013 (program): Number of 5’s in decimal expansion of n^2.
  • A086014 (program): Number of 6’s in decimal expansion of n^2.
  • A086016 (program): Number of 8’s in decimal expansion of n^2.
  • A086017 (program): Number of 9’s in decimal expansion of n^2.
  • A086020 (program): a(n) = Sum_(i=1..n) C(i+2,3)^2 [ Sequential sums of the tetragonal numbers or “tetras” (pyramidal, square) raised to power 2 (drawn from the 4th diagonal - left or right - of Pascal’s Triangle) ].
  • A086021 (program): a(n) = Sum_ i=1..n C(i+2,3)^3.
  • A086023 (program): a(n) = Sum_ i=1..n C(i+3,4)^2.
  • A086025 (program): a(n) = Sum_ i=1..n C(i+4,5)^2.
  • A086027 (program): a(n) = Sum_ i=1..n binomial(i+5,6)^2.
  • A086029 (program): a(n) = Sum_ i=1..n C(i+6,7)^2.
  • A086070 (program): Where records in A086068 occur.
  • A086072 (program): Number of 1’s in decimal expansion of triangular number n(n+1)/2.
  • A086090 (program): 2^n+n3^n.
  • A086093 (program): 3^n+2n*4^(n-1).
  • A086099 (program): a(n) = OR(k AND (n-k): 0<=k<=n), AND and OR bitwise.
  • A086111 (program): Numerator of the mean deviation of a discrete uniform distribution on n elements.
  • A086112 (program): Denominator of the mean deviation of a discrete uniform distribution on n elements.
  • A086113 (program): Number of 3 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.
  • A086114 (program): Number of 4 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.
  • A086115 (program): Number of 5 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.
  • A086116 (program): Numerator of mean deviation of a symmetrical binomial distribution on n elements.
  • A086117 (program): Denominator of mean deviation of a symmetrical binomial distribution on n elements.
  • A086130 (program): a(n) = lcm(n, A003415(n)).
  • A086148 (program): Sum of the orders of the elements in the dihedral group D_2n.
  • A086159 (program): Number of partitions of n into the first three triangular numbers, 1, 3 and 6.
  • A086161 (program): Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^2.
  • A086162 (program): Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^3.
  • A086178 (program): Decimal expansion of 1 + 2*sqrt(2).
  • A086206 (program): Number of n X n matrices with entries in 0,1 with no zero row and with zero main diagonal.
  • A086221 (program): Bisection of A086652.
  • A086223 (program): Every integer can be represented uniquely as m = k*2^(j+1)+2^j-1. Sequence gives values of k for m = repunit(n).
  • A086224 (program): a(n) = 7*2^n-1.
  • A086225 (program): a(n) = 11*2^n - 1.
  • A086274 (program): Antidiagonal sums of A086272 (and of A086273).
  • A086299 (program): a(n) = if n is 7-smooth then 1 else 0: characteristic function of 7-smooth numbers.
  • A086302 (program): a(n) = 4n^4 + 24n^3 + 48n^2 + 36n + 8.
  • A086303 (program): Numbers n such that n+15 is prime.
  • A086304 (program): Numbers n such that n+6 is prime.
  • A086325 (program): Let u(1)=0, u(2)=1, u(k)=u(k-1)+u(k-2)/(k-2); then a(n)=n!*u(n).
  • A086327 (program): Number of factors over Q in the factorization of the Chebyshev polynomial of the second kind U_n(x).
  • A086330 (program): a(n) = sum_ m >= 2 m! mod n.
  • A086341 (program): a(n) = 2*2^floor(n/2) - (-1)^n.
  • A086343 (program): a(n) starts new run of consecutive values in A055938.
  • A086344 (program): a(n) = -2a(n-1) + 4a(n-2), a(0) = 1, a(1) = 0.
  • A086347 (program): On a 3 X 3 board, number of n-move routes of chess king ending in a given side square.
  • A086351 (program): T(n,3) of A086350.
  • A086358 (program): Digital root of n!.
  • A086359 (program): Fixed point if [decimal-digit-sum]-function at initial-value=A000984(n)=C[2n,n] is iterated.
  • A086360 (program): Fixed point if (decimal-digit-sum)-function at initial value = n-th primorial = A002110(n) is iterated.
  • A086369 (program): Number of factors over Q in the factorization of T_n(x) - 1 where T_n(x) is the Chebyshev polynomial of the first kind.
  • A086374 (program): Number of factors over Q in the factorization of T_n(x) + 1 where T_n(x) is the Chebyshev polynomial of the first kind.
  • A086377 (program): a(1)=1; a(n)=a(n-1)+2 if n is in the sequence; a(n)=a(n-1)+2 if n and (n-1) are not in the sequence; a(n)=a(n-1)+3 if n is not in the sequence but (n-1) is in the sequence.
  • A086405 (program): Row T(n,3) of number array A086404.
  • A086435 (program): Maximum number of parts possible in a factorization of n into a product of distinct numbers > 1.
  • A086436 (program): Maximum number of parts possible in a factorization of n; a(1) = 1, and for n > 1, a(n) = A001222(n) = bigomega(n).
  • A086445 (program): Partial sums of A005578.
  • A086459 (program): Determinant of the circulant matrix whose rows are formed by successively rotating the vector (1, 2, 4, 8, …, 2^(n-1)) right.
  • A086461 (program): Symmetric version of square array A086460.
  • A086462 (program): Expansion of (1+x)(1+4x)/((1-x)(1-4x)).
  • A086465 (program): Decimal expansion of (5 + 4sqrt(5)arcsch(2))/25.
  • A086482 (program): Beginning with 1, the smallest number not included earlier such that the n-th partial product is an n-th power; or the geometric mean of the first n terms is an integer.
  • A086483 (program): Bit that is two places to left of least significant bit in binary expansion of n.
  • A086500 (program): Group the natural numbers such that the n-th group sum is divisible by the n-th triangular number: (1), (2, 3, 4), (5, 6, 7), (8, 9, 10, 11, 12), (13, 14, 15, 16, 17), (18, 19, 20, 21, 22, 23, 24), … Sequence contains the group sum.
  • A086514 (program): Difference between the arithmetic mean of the neighbors of the terms and the term itself follows the pattern 0,1,2,3,4,5,…
  • A086520 (program): Number of integers strictly greater than (n-sqrt(n))/2 and strictly less than (n+sqrt(n))/2.
  • A086529 (program): Beginning with 2, distinct even numbers such that the arithmetic mean of successive pairs of terms gives odd primes in their natural order. a(n) + a(n+1) /2 = prime(n+1).
  • A086568 (program): Smallest number having as many distinct prime factors as n has prime factors, when counted with multiplicity.
  • A086570 (program): Expansion of (1 + 3x + 5x^2 + 7x^3…) / (1 - 2x + 3x^2 - 4x^3…).
  • A086573 (program): a(n) = 2*(10^n - 1).
  • A086574 (program): a(n) = 3*(10^n-1).
  • A086575 (program): a(n) = 4*(10^n - 1).
  • A086576 (program): a(n) = 5*(10^n - 1).
  • A086577 (program): a(n) = 6*(10^n - 1).
  • A086578 (program): a(n) = 7*(10^n - 1).
  • A086579 (program): a(n) = 8*(10^n - 1).
  • A086580 (program): a(n) = 9*(10^n - 1).
  • A086601 (program): Triangular numbers + 1 squared.
  • A086602 (program): a(n) = A000217(A000217(n))-n^2.
  • A086603 (program): a(n) = n^3*3^(n-1).
  • A086605 (program): a(n) = 9n^3 - 18n^2 + 10*n.
  • A086640 (program): Arrange n^2 octagons that each have area 7 so that they leave (n-1)^2 square gaps each with area 2; a(n) is the total area of these polygons.
  • A086645 (program): Triangle read by rows: T(n, k) = binomial(2n, 2k).
  • A086652 (program): a(n) = A000225(n+3)-A052955(n).
  • A086653 (program): 2^n + 3*n.
  • A086655 (program): (C(2p,p)-2)/(2p) where p runs through the primes.
  • A086663 (program): Number of non-attacking knights on a n*n board with all non-perimeteral squares removed.
  • A086664 (program): n - sum of prime power components of n .
  • A086666 (program): a(n) = sigma_2(n) - sigma_1(n).
  • A086670 (program): Sum of floor(d/2) where d is a divisor of n.
  • A086689 (program): a(n) = Sum_ i=1..n i^2*t(i), where t = A000217.
  • A086694 (program): A run of 2^n 1’s followed by a run of 2^n 0’s, for n=0, 1, 2, …
  • A086695 (program): a(n) = 100^n - 10^n - 1.
  • A086700 (program): Euler phi function applied to the triangular numbers.
  • A086746 (program): Multiples of 3018.
  • A086747 (program): Baum-Sweet sequence: a(n) = 1 if binary representation of n contains no block of consecutive zeros of odd length; otherwise a(n) = 0.
  • A086748 (program): Numbers m such that when C(2k, k) == 1 (mod m) then k is necessarily even.
  • A086755 (program): Sum_ k=1..n (k(k+1))^2/2.
  • A086756 (program): a(n) = n^n mod 10^n.
  • A086760 (program): a(n) = 8n^2 + 88n + 43.
  • A086767 (program): Last coefficient of the last term in the numerator of the simplified expansion of the solutions of FLT for n=2 for FLT n=1,2,3,..
  • A086769 (program): a(n) = sum 2^(b(i)-1): 1<=i<=n , where b(n) is the differences between consecutive primes.
  • A086784 (program): Number of non-trailing zeros in binary representation of n.
  • A086790 (program): a(n) = floor((1+n+2n^2+4n^3)/(1+2*n+n^2))
  • A086799 (program): Replace all trailing 0’s with 1’s in binary representation of n.
  • A086801 (program): a(n) = prime(n) - 3.
  • A086813 (program): a(1)=1 then a(n)= (1/2) (5a(n-1)+1) if a(n-1) is odd, a(n)=3/2*a(n-1) otherwise.
  • A086814 (program): a(n) = ceiling( (1 + n + 2n^2 + 4n^3)/(1 + 2*n + n^2) ).
  • A086815 (program): a(n)=(n-1)n^(2n)
  • A086822 (program): a(n) = floor((6n^0+5n^1+4n^2+3n^3) / (1n^0+1n^1+1*n^2)).
  • A086824 (program): Least k such that k!>=n^k.
  • A086845 (program): a(1) = 0, a(n) = a(floor(n/2)) + 2*a(ceiling(n/2)) + floor(n/2).
  • A086849 (program): Sum of first n nonsquares.
  • A086851 (program): a(0) = 1, a(n+1) = a(n)^2 - n.
  • A086858 (program): Let f(n) be the inverse of the function g(x) = x^x. Then a(n) = floor(f(n)).
  • A086874 (program): Seventh power of odd primes.
  • A086876 (program): Run lengths in A071542.
  • A086893 (program): a(n) is the index of F(n+1) at the unique occurrence of the ordered pair of reversed consecutive terms (F(n+1),F(n)) in Stern’s diatomic sequence A002487, where F(k) denotes the k-th term of the Fibonacci sequence A000045.
  • A086894 (program): a(n) = (A000522(2*n) + 1)/2.
  • A086901 (program): a(1) = a(2) = 1; for n>2, a(n) = 4a(n-1) + 3a(n-2).
  • A086903 (program): a(n) = 8*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 8, a(n) = (4+sqrt(15))^n + (4-sqrt(15))^n.
  • A086905 (program): a(n) = Sum_ k=0..n (-1)^(n-k)*binomial(k,floor(k/2)).
  • A086910 (program): a[1]=1; a[n] =1+Abs[Prime[n]-a[n-1]]
  • A086926 (program): Product of Fibonacci and (shifted) triangular numbers.
  • A086931 (program): a(0) = 1, a(n) = spf(n)*a(n-spf(n)), where spf=A020639 (smallest prime factor).
  • A086936 (program): Number of primes between n and p(n) inclusive.
  • A086937 (program): Number of distinct zeros of x^2-x-1 mod prime(n).
  • A086940 (program): a(n) = k where R(k+4) = 2.
  • A086941 (program): a(n) = k where R(k+6) = 3.
  • A086942 (program): Integers k such that R(k+8) = 4.
  • A086943 (program): Integers k such that R(k+7) = 3.
  • A086944 (program): a(n) = k where R(k+8) = 5.
  • A086945 (program): a(n) = 7*10^n - 9.
  • A086946 (program): a(n) = k where R(k+6) = 2.
  • A086947 (program): Numbers k such that Reverse(k+9) = 3.
  • A086948 (program): a(n) = k where R(k+8) = 2.
  • A086949 (program): a(n) = k where R(k+9) = 5.
  • A086950 (program): Binomial transform of decagonal numbers A001107.
  • A086951 (program): n3^n(4n-1)/9.
  • A086952 (program): n^2*4^n/4.
  • A086953 (program): Binomial transform of (-1)^mod(n,3) (A257075).
  • A086955 (program): a(n) = n^2 + 2*n + 2 - (-1)^n.
  • A086970 (program): Fix 1, then exchange the subsequent odd numbers in pairs.
  • A086972 (program): a(n) = n*3^(n-1) + (3^n+1)/2.
  • A086994 (program): Decimal expansion of Pi written in base 2.
  • A086996 (program): Decimal expansion of e (A001113) written in base 2.
  • A087003 (program): a(2n) = 0 and a(2n+1) = mu(2n+1); also the sum of Mobius function values computed for terms of 3x+1 trajectory started at n, provided that Collatz conjecture is true.
  • A087009 (program): Least m such that omega(m) + Omega(m) = n, or 0 if no such m exists.
  • A087030 (program): n “reflected” in the next prime: a(n)=2p-n, p is smallest prime > n.
  • A087035 (program): Maximum value taken on by f(P)=sum(i=1..n, p(i)*p(n+1-i) ) as p(1),p(2),…,p(n) ranges over all permutations P of 1,2,3,…n .
  • A087039 (program): If n is prime then 1 else 2nd largest prime factor of n.
  • A087047 (program): a(n) = n(n+1)(n+2)*a(n-1)/6 for n >= 2; a(1) = 1.
  • A087049 (program): Characteristic sequence for numbers n>=0 that are either squares or have a square > 1 as factor.
  • A087055 (program): Largest square number less than 2*n^2.
  • A087056 (program): Difference between 2 * n^2 and the next smaller square number.
  • A087057 (program): Smallest number whose square is larger than 2*n^2.
  • A087058 (program): Smallest square number greater than 2*n^2.
  • A087059 (program): Difference between 2*n^2 and the next greater square number.
  • A087060 (program): Difference between 2n^2 and the nearest square number.
  • A087069 (program): a(n) = Sum_ k >= 0 floor(n/(4^k)).
  • A087076 (program): Sums of the squares of the elements in the subsets of the integers 1 to n.
  • A087088 (program): Positive ruler-type fractal sequence with 1’s in every third position.
  • A087099 (program): Partial sums of A063914.
  • A087116 (program): Number of maximal groups of consecutive zeros in binary representation of n.
  • A087120 (program): Smallest numbers having in binary representation exactly n maximal groups of consecutive zeros.
  • A087125 (program): Indices n of hex numbers H(n) that are also triangular.
  • A087131 (program): a(n) = 2^n*Lucas(n), where Lucas = A000032.
  • A087136 (program): Smallest positive number m such that A073642(m)=n.
  • A087156 (program): Nonnegative numbers excluding 1.
  • A087161 (program): Records in A087159, i.e., A087159(a(n)) = n, and satisfies the recurrence a(n+3) = 5a(n+2) - 6 a(n+1) + 2*a(n) with a(1) = 1, a(2) = 2, and a(3) = 4.
  • A087165 (program): a(n)=1 when n == 1 (mod 4), otherwise a(n) = a(n - ceiling(n/4)) + 1. Removing all the 1’s results in the original sequence with every term incremented by 1.
  • A087168 (program): Expansion of (1 + 2x)/(1 + 3x + 4*x^2).
  • A087169 (program): Expansion of (1 + 3x)/(1 + 5x + 9*x^2).
  • A087170 (program): Expansion of (1 + 4x)/(1 + 7x + 16*x^2).
  • A087171 (program): Expansion of (1 + 5x)/(1 + 9x + 25*x^2).
  • A087172 (program): Greatest Fibonacci number that does not exceed n.
  • A087192 (program): a(n) = ceiling(a(n-1)*4/3), with a(1) = 1.
  • A087204 (program): Period 6: repeat [2, 1, -1, -2, -1, 1].
  • A087205 (program): a(n) = -2a(n-1) + 4a(n-2), a(0)=1, a(1)=2.
  • A087206 (program): a(n) = 2a(n-1) + 4a(n-2); with a(0)=1, a(1)=4.
  • A087208 (program): Expansion of e.g.f.: exp(x)/(1-x^2).
  • A087211 (program): Floor((1+2^n+3^n)/3).
  • A087215 (program): Lucas(6n): a(n) = 18a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 18.
  • A087229 (program): Exponent of p=2 in 12n+4 = 3(4n+1)+1.
  • A087230 (program): Exponent of p=2 in 6n + 4 = 3(2n+1) + 1 (2-adic valuation of 6n + 4).
  • A087231 (program): a(n) is the smallest number such that the exponent of p=2 factor in 6*a(n)+4 equals n.
  • A087233 (program): a(n)=floor[sigma[A002110(n)]/A002110(n)]; integer quotient of divisor-sum of primorial numbers and primorials.
  • A087265 (program): Lucas numbers L(8*n).
  • A087267 (program): a(n) = gcd(n, pi(n)) where pi is A000720.
  • A087273 (program): Largest prime factor of 3*prime(n) + 1.
  • A087274 (program): Prime index of largest prime factor of 3*prime(n)+1.
  • A087278 (program): Distance to nearest square is not greater than 1.
  • A087279 (program): Nonnegative numbers such that distance to nearest positive square equals exactly 1.
  • A087281 (program): a(n) = Lucas(7*n).
  • A087287 (program): a(n) = Lucas(9*n).
  • A087288 (program): a(n)=2a(n-1)+a(n-2)-2a(n-3).
  • A087289 (program): a(n) = 2^(2*n+1) + 1.
  • A087290 (program): Number of pairs of polynomials (f,g) in GF(3)[x] satisfying deg(f) <= n, deg(g) <= n and gcd(f,g) = 1.
  • A087291 (program): Number of pairs of polynomials (f,g) in GF(2)[x] satisfying 1 <= deg(f) <= n, 1 <= deg(g) <= n and gcd(f,g) = 1.
  • A087292 (program): Number of pairs of polynomials (f,g) in GF(3)[x] satisfying 1 <= deg(f) < =n, 1 <= deg(g) <= n and gcd(f,g) = 1.
  • A087298 (program): Exponent of 2 in factorization of (3n)!.
  • A087299 (program): Ratio of volume of n-dimensional ball to circumscribing n-cube is Pi^floor(n/2) divided by a(n).
  • A087322 (program): Triangle T read by rows: T(n, 1) = 2n + 1. For 1 < k <= n, T(n, k) = 2T(n,k-1) + 1.
  • A087323 (program): a(n) = (n+1) * 2^n - 1.
  • A087327 (program): Independence numbers for KT_2 knight on triangular board.
  • A087348 (program): a(n) = 10n^2 - 6n + 1.
  • A087349 (program): n + (smallest prime-factor of n+1).
  • A087355 (program): n^10 mod 10^n.
  • A087370 (program): Numbers n such that 3n - 1 is a prime.
  • A087385 (program): a(n) = smallest prime == 1 (mod T(n)) where T(n) is the n-th triangular number (A000217).
  • A087404 (program): a(n) = 4a(n-1) + 5a(n-2).
  • A087405 (program): First differences of A087404: a(n)=A087404(n)-A087404(n-1), a(0)=A087404(0).
  • A087413 (program): a(n) = Sum_ k=1..n C(3*k,k)/3.
  • A087420 (program): a(n) is the sum of the squares of the sizes of the conjugacy classes in the dihedral group D_2n.
  • A087426 (program): a(n) = S(n,4) where S(n,m) = sum(k=0,n,binomial(n,k)Fibonacci(mk)).
  • A087427 (program): Number of lattice points on or inside the rectangle formed by [1 <= x <= (q-1)/2] and [1 <= y <= (p-1)/2], where p = n-th prime, q = (n-1)-st prime.
  • A087431 (program): a(n) = 0^n/2 + 2^n*(n^2+n+2)/4.
  • A087432 (program): Expansion of 1+x(1-x-4x^2)/((1+x)(1-2x)(1-3x)).
  • A087433 (program): Expansion of (1-2x)(1-4x+x^2)/((1-x)(1-3x)(1-4*x)).
  • A087436 (program): Number of odd prime factors of n, counted with repetitions.
  • A087438 (program): a(n) = 32^(2(n-1)) + 2^(n-2)*(n+1).
  • A087439 (program): Expansion of (1-4x)/((1-x)(1-3x)(1-5x)).
  • A087440 (program): Expansion of (1-2x-3x^2)/((1-2x)(1-4x)).
  • A087444 (program): Numbers that are congruent to 1, 4 mod 9.
  • A087445 (program): Numbers that are congruent to 1 or 5 mod 12.
  • A087446 (program): Numbers that are congruent to 1, 6 mod 15.
  • A087447 (program): a(0) = a(1) = 1; for n>1, a(n) = (n+2)*2^(n-2).
  • A087448 (program): 3^(n-1)(n+3)/2-(n-1)/2.
  • A087449 (program): a(n) = n * 4^(n-1) + (2*4^n + 1) / 3.
  • A087451 (program): G.f.: (2-x)/((1+2x)(1-3x)); e.g.f.: exp(3x)+exp(-2x); a(n)=3^n+(-2)^n.
  • A087452 (program): G.f.: (2-x)/((1+3x)(1-4x)); e.g.f.: exp(4x) + exp(-3x); a(n) = 4^n + (-3)^n.
  • A087453 (program): a(n) = S(n,5), where S(n,m) = Sum_ k=0..n binomial(n,k)Fibonacci(mk).
  • A087455 (program): Expansion of (1 - x)/(1 - 2x + 3x^2) in powers of x.
  • A087458 (program): Greatest prime p such that prime(n)+p <= prime(n+1); a(1)=1.
  • A087461 (program): Arithmetic mean of n-th and 2n-th primes.
  • A087475 (program): a(n) = n^2 + 4.
  • A087477 (program): Decimal expansion of sqrt(51)-4.
  • A087480 (program): Sum of all the primes raised to their corresponding powers.
  • A087483 (program): Row 0 of the order array of 3/2, i.e., row 0 of the transposable dispersion in A087465.
  • A087503 (program): a(n) = 3(a(n-2) + 1), with a(0) = 1, a(1) = 3.
  • A087505 (program): Numbers k such that 5*k+3 is a prime.
  • A087507 (program): # 0<=k<=n: k*n is divisible by 3 .
  • A087508 (program): Number of k such that mod(k*n,3) = 1 for 0 <= k <= n.
  • A087509 (program): Number of k such that (k*n) == 2 (mod 3) for 0 <= k <= n.
  • A087539 (program): First differences of A011849.
  • A087560 (program): Smallest m > n such that gcd(m, n^2) = n.
  • A087572 (program): Smallest prime of the form n + (n-1) + (n-2) + …(n-k), k < n, or 0 if no such prime exists.
  • A087611 (program): a(n) = (prime(n) - 1) mod n.
  • A087620 (program): # 0<=k<=n: k*n is divisible by 4 .
  • A087624 (program): a(n)=0 if n is prime, A001221(n) otherwise.
  • A087627 (program): Count …n,2n,2n…
  • A087635 (program): a(n) = S(n,3) where S(n,m) = Sum_ k=0..n binomial(n,k)fibonacci(mk).
  • A087645 (program): Third column of A071223.
  • A087656 (program): Let f be defined on the rationals by f(p/q) =(p+1)/(q+1)=p_ 1 /q_ 1 where (p_ 1 ,q_ 1 )=1. Let f^k(p/q)=p_ k /q_ k where (p_ k ,q_ k )=1. Sequence gives least k such that p_ k -q_ k = 1 starting at n.
  • A087691 (program): Squares of primes of the form 4n+3.
  • A087719 (program): Least number m such that the number of numbers k <= m with k > spf(k)^n exceeds the number of numbers with k <= spf(k)^n.
  • A087733 (program): Partial sums of A068639.
  • A087734 (program): a(n) = f(f(n)), where f() = A035327().
  • A087737 (program): Value of (n,n+1) concatenated in binary representation.
  • A087743 (program): Numbers n >= 3 with property that the remainder when n is divided by k (for 3 <= k <= n-2) is not 1.
  • A087745 (program): Numbers A001317 repeated.
  • A087752 (program): Powers of 49.
  • A087755 (program): Triangle read by rows: Stirling numbers of the first kind (A008275) mod 2.
  • A087756 (program): a(n) = A087745(n+1).
  • A087775 (program): a[1] = 1, a[2] = 2, a[3] = 2; a[n] = 3a[abs[a[n-2]]] - 3a[n-abs[a[n-2]]] + a[n-3].
  • A087799 (program): a(n) = 10*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 10.
  • A087800 (program): a(n) = 12*a(n-1) - a(n-2), with a(0) = 2 and a(1) = 12.
  • A087802 (program): Sum(mu(d): d nonprime divisor of n), mu=A008683.
  • A087805 (program): Partial sums of b(k) where b(k) _ k>=0 = limit n ->infty A080578(k)-2k : k=2^n,2^n+1,2^n+2,…… .
  • A087808 (program): a(0) = 0; a(2n) = 2a(n), a(2n+1) = a(n) + 1.
  • A087810 (program): First differences of A029931.
  • A087811 (program): Numbers n such that ceiling(sqrt(n)) divides n.
  • A087839 (program): a[n] =a[a[a[a[a[n-2]]]]]+ a[n - a[n-2]].
  • A087847 (program): a(n) = a( n - a(n-1) ) + a(a(a( n - a(n-4) ))).
  • A087863 (program): (n^3+24n^2+65n+36)/6.
  • A087887 (program): a(n) = 18n^3 + 6n^2.
  • A087893 (program): Number of numbers m satisfying 1 < m < n such that m^2 == m (mod n).
  • A087895 (program): Primes p such that 10^p - 9^p is composite.
  • A087908 (program): Largest integer not expressible as a nonnegative linear combination of n and n^2 + 1.
  • A087915 (program): Even numbers n such that 2*n+3 is a prime.
  • A087940 (program): a(n) = Sum_ k=0..n binomial(n+(-1)^k, k).
  • A087946 (program): Expansion of (1-3x+x^2)/((1-2x)(1-4x+x^2)).
  • A087953 (program): a(n) = floor((Fibonacci(2*n+1)+1)/2).
  • A087960 (program): a(n) = (-1)^binomial(n+1,2).
  • A087963 (program): Exponent of highest power of 2 dividing 3*prime(n)+1.
  • A087968 (program): a(n) = gcd(1 + 2^n, n^2).
  • A088003 (program): Take the list t(n,0) = 1,…,n ; denote by t(n,j) this list after rotating to left (or right) by j positions. Calculate inner product of t(n,0) and t(n,j) and denote the value by s(n,j). Compute this inner product for all j = 1..n and choose the smallest. This is a(n).
  • A088023 (program): Set a(1) = 1. Then take the list of defined initial terms, reverse their order, add 1, 2, 3…to the reversed list in succession and append this new list to the right of the previously defined terms. Repeat this process indefinitely.
  • A088037 (program): Smallest square k == 1 (mod some n-th power), k > 1.
  • A088038 (program): Smallest cube k == 1 (mod some n-th power), k > 1.
  • A088039 (program): Smallest k such that k^3 == 1 (mod some n-th power), k > 1.
  • A088040 (program): Smallest fourth power k such that k-1 is divisible by an n-th power, k > 1.
  • A088041 (program): Smallest k such that k^4 - 1 is divisible by an n-th power, k > 1.
  • A088129 (program): Expansion of sinh(x)/(1-x)^2.
  • A088133 (program): Sum of first and last digits of n. Different from A115299.
  • A088137 (program): Generalized Gaussian Fibonacci integers.
  • A088138 (program): Generalized Gaussian Fibonacci integers.
  • A088139 (program): a(n) = 2a(n-1) - 6a(n-2), a(0)=0, a(1)=1.
  • A088140 (program): a(n) = 1 if n is an odd prime otherwise a(n) = n.
  • A088146 (program): n-th prime rotated one binary place to the right.
  • A088147 (program): n-th prime rotated one binary place to the left.
  • A088150 (program): Value of n-th digit in binary representation of n^n.
  • A088162 (program): n-th prime rotated one binary place to the right less the n-th prime rotated one binary place to the left.
  • A088163 (program): Numbers for which rotating one binary place to the right less rotating one binary place to the left is equal to zero.
  • A088202 (program): Chromatic number of the n X n queen graph.
  • A088207 (program): a(n) = Sum_ k=0..n floor(k*phi^2)) where phi=(1+sqrt(5))/2.
  • A088209 (program): Numerators of convergents of the continued fraction with the n+1 partial quotients: [1;1,1,…(n 1’s)…,1,n+1], starting with [1], [1;2], [1;1,3], [1;1,1,4], …
  • A088210 (program): Numerators of convergents of the continued fraction with the n+1 partial quotients: [2;2,2,…(n 2’s)…,2,n+1], starting with [1], [2;2], [2;2,3], [2;2,2,4], …
  • A088211 (program): Denominators of convergents of the continued fraction with the n+1 partial quotients: [2;2,2,…(n 2’s)…,2,n+1], starting with [1], [2;2], [2;2,3], [2;2,2,4], …
  • A088218 (program): Total number of leaves in all rooted ordered trees with n edges.
  • A088225 (program): Solutions to x^n == 7 (mod 11).
  • A088226 (program): a(1)=0, a(2)=0, a(3)=1; for n>3, a(n)=abs(a(n-1)-a(n-2)-a(n-3)).
  • A088227 (program): Solutions x to x^n == 7 mod 13.
  • A088305 (program): a(0) = 1, a(n) = Fibonacci(2n). It has the property: a(n) = 1a(n-1) + 2a(n-2) + 3a(n-3) + 4*a(n-4) + …
  • A088308 (program): 2 followed by list of composite numbers mod 10.
  • A088333 (program): A version of Josephus problem: a(n) is the surviving integer under the following elimination process. Arrange 1,2,3,…,n in a circle, increasing clockwise. Starting with i=1, delete the integer 3 places clockwise from i. Repeat, counting 3 places from the next undeleted integer, until only one integer remains.
  • A088347 (program): This sequence needs a definition.
  • A088371 (program): Position where n is inserted into the n-th row of triangle A088370, where the n-th row differs from the prior row only by the presence of n.
  • A088377 (program): (Smallest prime-factor of n)^2.
  • A088378 (program): (Smallest prime-factor of n)^3.
  • A088379 (program): (Smallest prime-factor of n)^4.
  • A088386 (program): a(n) = 2^n*(n!)^3.
  • A088439 (program): a(3n) = 3n, otherwise a(n) = 1.
  • A088440 (program): a(4n) = 4n, otherwise a(n) = 1.
  • A088441 (program): A one third Cantor set as a factorial product function.
  • A088462 (program): a(1)=1, a(n) = ceiling((n - a(a(n-1)))/2).
  • A088472 (program): Numbers n such that the lunar sum of the distinct lunar prime divisors of n is < n.
  • A088475 (program): Numbers n such that the lunar sum of the distinct lunar prime divisors of n is >= n.
  • A088476 (program): Numbers n such that the lunar sum of the distinct lunar prime divisors of n is > n.
  • A088480 (program): Numbers n such that the lunar product of the distinct lunar prime divisors of n is >= n.
  • A088481 (program): Numbers n such that the lunar product of the distinct lunar prime divisors of n is > n.
  • A088487 (program): a(n) = Sum_ k=1..8 floor(A254864(n,k)/A254864(n-1,k)), where A254864(n,k) = n! / (n-floor(n/3^k))!.
  • A088491 (program): A factorial subtraction sequence based on Conway’s A004001.
  • A088499 (program): Doubly (3)-perfect numbers.
  • A088502 (program): Numbers n such that (n^2 - 5)/4 is prime.
  • A088512 (program): Number of partitions of n into two parts whose xor-sum is n.
  • A088520 (program): Permutation of natural numbers generated by 3-rowed array shown below.
  • A088534 (program): Number of representations of n by the quadratic form x^2 + xy + y^2 with 0 <= x <= y.
  • A088545 (program): Quotient Fib(5n)/(5*Fib(n)), where Fib(n)=A000045(n).
  • A088556 (program): Numbers of the form (4^n + 4^(n-1) + … + 1) + (n mod 2).
  • A088564 (program): a(n)=sum(i=0,n,binomial(2*i,i) (mod 3)).
  • A088578 (program): a(n) = nx^n + (n-1)x^(n-1) + . . . + x + 1 for x=2.
  • A088580 (program): a(n) = 1 + sigma(n).
  • A088581 (program): a(n) = nx^n + (n-1)x^(n-1) + . . . + x + 1 for x=3.
  • A088582 (program): a(n) = nx^n + (n-1)x^(n-1) + . . . + x + 1 for x=4.
  • A088625 (program): 14*C(n,8).
  • A088626 (program): 42*C(n,10).
  • A088631 (program): Largest number m < n such that m+n is a prime.
  • A088633 (program): P-n where P = smallest prime > 2n.
  • A088648 (program): a(1) = 1, then the smallest odd number not occurring earlier such that the concatenation a(r), a(s) is composite for all s > r.
  • A088650 (program): a(n) = smallest value of x pertaining to A020498, or the smallest x such that A020498(k) + x is prime for all k = 1 to n.
  • A088659 (program): a(n) = n*(p-1) where p is the largest prime factor of n.
  • A088666 (program): a(n) = (n^4 + 1) mod 10.
  • A088667 (program): n^4 + 6 mod 10.
  • A088673 (program): n mod A002024(n), where A002024 is “n appears n times”: 1, 2, 2, 3, 3, 3, …
  • A088680 (program): a(n) = prime(2n+1) - prime(2n).
  • A088682 (program): a(n) = prime(3n+1) - prime(3n-1).
  • A088683 (program): a(n) = prime(3n+2) - prime(3n).
  • A088689 (program): Jacobsthal numbers modulo 3.
  • A088696 (program): Triangle read by rows, giving number of partial quotients in continued fraction representation of terms in the left branch of the infinite Stern-Brocot tree.
  • A088705 (program): First differences of A000120. One minus exponent of 2 in n.
  • A088720 (program): Unique monotone sequence satisfying a(a(a(n))) = 2n.
  • A088721 (program): Unique monotone sequence satisfying a(a(a(a(n)))) = 2n.
  • A088722 (program): Number of divisors d>1 of n such that also d+1 divides n.
  • A088736 (program): 10^p - p for prime p.
  • A088741 (program): Number of connected strongly regular simple graphs on n nodes.
  • A088743 (program): a(n) = 2*A088023(n) - 1.
  • A088744 (program): a(n) = 3*A088023(n) - 2.
  • A088748 (program): a(n) = 1 + Sum_ k=0..n-1 2 * A014577(k) - 1.
  • A088795 (program): Fibonacci(n) as n runs through the quarter-squares.
  • A088802 (program): Denominators of the coefficients of powers of n^(-1) in the Romanovsky series expansion of the mean of the standard deviation from a normal population.
  • A088805 (program): 10^p + p for prime p.
  • A088821 (program): a(n) is the sum of smallest prime factors of numbers from 1 to n.
  • A088822 (program): a(n) is the sum of largest prime factors of numbers from 1 to n.
  • A088828 (program): Nonsquare positive odd numbers.
  • A088837 (program): Numerator of sigma(2*n)/sigma(n). Denominator see in A038712.
  • A088838 (program): Numerator of the quotient sigma(3n)/sigma(n).
  • A088839 (program): Numerator of sigma(4n)/sigma(n).
  • A088840 (program): Denominator of sigma(4n)/sigma(n).
  • A088841 (program): Numerator of quotient=sigma[7n]/sigma[n].
  • A088842 (program): Denominator of quotient=sigma(7n)/sigma(n).
  • A088859 (program): a(n) = L(n) + 2^n where L(n) = A000032(n) (the Lucas numbers).
  • A088860 (program): Twice the primorials (first definition), 2*A002110(n).
  • A088879 (program): Numbers n such that 3n + 5 is a prime.
  • A088891 (program): Polynexus numbers of order 9.
  • A088892 (program): Polynexus numbers of order 14.
  • A088911 (program): Period 6: repeat [1, 1, 1, 0, 0, 0].
  • A088917 (program): Central Delannoy numbers (mod 3); Characteristic function for Cantor set.
  • A088920 (program): Solutions k to the Diophantine equation k = 2n^2 = m^2+1.
  • A088921 (program): The number of 321- and 2143-avoiding permutations of length n.
  • A088922 (program): Consider the n X n matrix with entries (i*j mod n), where i,j=0..n-1; a(n) = rank of this matrix over the real numbers.
  • A088932 (program): G.f.: 1/((1-x)^2(1-x^2)(1-x^4)*(1-x^8)).
  • A088938 (program): Occurrences of 2’s in A088936.
  • A088941 (program): a(n)=12sum(1<=i<=j<=k<=n,ij/k).
  • A088954 (program): G.f.: 1/((1-x)^2(1-x^2)(1-x^4)(1-x^8)(1-x^16)).
  • A088955 (program): Primes of the form 60*n + 1.
  • A088958 (program): Numbers n such that 60*n+1 is prime.
  • A088967 (program): Numbers n such that n+9 is a prime.
  • A088978 (program): Number of Pythagorean triangles having the n-th prime prime(n) as one of their sides.
  • A088981 (program): a(n+2) = a(n+1) + a(n) - [(2*n)+1] where a(0)=7, a(1)=11.
  • A088982 (program): Primes that are between consecutive prime-indexed primes.
  • A089010 (program): a(n) = 1 if n is an exponent of the Weyl group W(E_8), 0 otherwise.
  • A089011 (program): a(n) = 1 if n is an exponent of the Weyl group W(E_7), 0 otherwise.
  • A089012 (program): a(n) = 1 if n is an exponent of the Weyl group W(E_6), 0 otherwise.
  • A089013 (program): a(n) = (A088567(8n) mod 2).
  • A089026 (program): a(n) = n if n is a prime, otherwise a(n) = 1.
  • A089027 (program): a(n) =1 if the prime gap A001223(n) is <=2, otherwise a(n)=n+1.
  • A089033 (program): Numbers n such that 7*n+3 is prime.
  • A089034 (program): a(n) = (prime(n)^4 - 1) / 240.
  • A089038 (program): Nonnegative numbers k such that 2k+5 is prime.
  • A089061 (program): a(0) = 5, a(1) = 7; for n>1, a(n) = a(n-1)+a(n-2)-(2n-2).
  • A089068 (program): a(n) = a(n-1)+a(n-2)+a(n-3)+2 with a(0)=0, a(1)=0 and a(2)=1.
  • A089071 (program): Number of liberties a big eye of size n gives in the game of Go.
  • A089072 (program): Triangle read by rows: T(n,k) = k^n, n>=1, 1<=k<=n.
  • A089079 (program): Numbers n such that 7*n - 23 is prime.
  • A089080 (program): Sequence is S(infinity) where S(1)= 1,2 and S(n)=S(n-1)S’(n-1), where S’(k) is obtained from S(k) by replacing the single 1 with the least integer not occurring in S(k).
  • A089081 (program): 26th powers: a(n) = n^26.
  • A089083 (program): T(n,k) = floor(kn/2) * ceiling(kn/2), triangular array read by rows, 1 <= k <= n.
  • A089086 (program): Greatest common divisor of n^2-5 and n^2+5.
  • A089090 (program): a(n) is the smallest composite number coprime to n.
  • A089101 (program): a(n) = (n - 4 + prime(n) mod 9) mod 10.
  • A089103 (program): a(n) = Mod[n+Prime[n],10]
  • A089105 (program): Values taken by least witness function W(n).
  • A089108 (program): Convoluted convolved Fibonacci numbers G_4^(r).
  • A089109 (program): Convoluted convolved Fibonacci numbers G_5^(r).
  • A089111 (program): Convoluted convolved Fibonacci numbers G_6^(r).
  • A089118 (program): Nonnegative numbers in (3*A005836 - 1) [A005836 are the numbers with base representation containing no 2].
  • A089120 (program): Smallest prime factor of n^2 + 1.
  • A089123 (program): Smallest prime factor of numbers of the form A^2 + 3.
  • A089124 (program): Largest prime factor of numbers of the form A^2 + 3.
  • A089128 (program): a(n) = gcd(6,n).
  • A089129 (program): Greatest common divisor of n^2 - 7 and n^2 + 7.
  • A089143 (program): a(n) = 9*2^n - 6.
  • A089145 (program): Greatest common divisor of n^2-3 and n^2+3.
  • A089146 (program): Greatest common divisor of n^2 - 4 and n^2 + 4.
  • A089156 (program): a(n) = A069722(n+1)^2.
  • A089186 (program): Decreases from 9 * 10^k down to 1, restarting at 9 * 10^(k+1).
  • A089192 (program): Numbers n such that 2n - 7 is a prime.
  • A089193 (program): Odd numbers n such that 2n-7 is a prime of the form 4k+3.
  • A089196 (program): Floor(n / (smallest prime factor of n+1)).
  • A089205 (program): a(n) = n^n * (n-1).
  • A089207 (program): a(n) = 4n^3 + 2n^2.
  • A089211 (program): 10*n^n+(n-1).
  • A089214 (program): Let u(1)=0, u(2)=1; for k>2, u(k)= A010060(k)*u(k-1) + u(k-2) (mod 2); then a(n)=4n-b(n) where sequence (b(k)) gives values such that u(b(k))=0.
  • A089215 (program): Thue-Morse sequence on the integers.
  • A089217 (program): n-2 is a prime of the form 4*k+3.
  • A089241 (program): Even numbers k such that k/2 - 1 is prime.
  • A089242 (program): Sequence is S(infinity), where S(1) = 1, S(m+1) = concatenation S(m), a(m)+1, S(m) and a(m) is the m-th term of S(m). a(m) is also the m-th term of the sequence.
  • A089250 (program): Add 2 (mod 10) to each decimal digit of Pi.
  • A089253 (program): Numbers n such that 2n - 5 is a prime.
  • A089255 (program): Odd numbers n such that 2*n-5 is a prime.
  • A089257 (program): Even numbers n such that 2n-5 is a prime of the form 4k+3.
  • A089262 (program): a(n) = 2^floor(log_2(n)) - 2^floor(log_2(n*2/3)).
  • A089263 (program): First differences of A080791.
  • A089265 (program): a(1) = 0; thereafter a(2n) = a(n) + 1, a(2n+1) = 2*n.
  • A089271 (program): Third column (k=4) of array A078739(n,k) ((2,2)-generalized Stirling2).
  • A089279 (program): a(n) = 2 + sum(k=1 to n) [(-1)^k A001511(k)].
  • A089293 (program): Sum of digits in the mixed-base enumeration system n=…d(4)d(3)d(2)d(1), where the digits satisfy 0<=d(i)<=1 if i is odd, 0<=d(i)<=2 if i is even.
  • A089303 (program): a(n) = floor( (10^n - 1) / (9*n) ).
  • A089309 (program): Write n in binary; a(n) = length of the rightmost run of 1’s.
  • A089311 (program): Write n in binary; a(n) = number of 0’s in rightmost block of zeros, after dropping any trailing 0’s.
  • A089312 (program): Write n in binary; a(n) = number represented by rightmost block of 1’s.
  • A089348 (program): Primes of the form smallest multiple of n followed by a 1.
  • A089357 (program): a(n) = 2^(6*n).
  • A089361 (program): Numbers of pairs (i, j), i, j > 1, such that i^j <= n.
  • A089362 (program): Numbers n such that n^2 - 5n + 5 is prime.
  • A089368 (program): Least k such that 2*pi(n) = pi(n+k), where pi(n) = number of primes up to n. (The number of primes between 1 to n is the same as the number of primes between n+1 and n+k.
  • A089389 (program): Sum of the smallest and the largest nontrivial divisor of n or 0 if n is 1 or a prime.
  • A089410 (program): Least common multiple of all cycle sizes (also the maximum cycle size) in range [A014137(n-1)..A014138(n-1)] of permutation A074679/A074680.
  • A089418 (program): Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A082333/A082334.
  • A089422 (program): Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A082335/A082336 (and also of A082349/A082350, to be proved).
  • A089425 (program): Least common multiple of all cycle sizes (and also the maximum cycle size) in range [A014137(n-1)..A014138(n-1)] of permutation A082351/A082352.
  • A089451 (program): a(n) = mu(prime(n)-1), where mu is the Moebius function (A008683).
  • A089495 (program): a(n) = mu(prime(n)+1), where mu is the Moebius function.
  • A089499 (program): a(0)=0; a(1)=1; a(2n)=4*Sum_ k=0…n a(2k-1); a(2n+1)=a(2n)+a(2n-1).
  • A089508 (program): Solution to a binomial problem together with companion sequence A081016(n-1).
  • A089533 (program): a(n)=(A089348(n)-1)/10n.
  • A089559 (program): Nonnegative numbers n such that 2*n + 15 is prime.
  • A089574 (program): Column 4 of an array closely related to A083480. (Both arrays have shape sequence A083479).
  • A089581 (program): a(n) = prime(2n-1)prime(2*n).
  • A089594 (program): Alternating sum of squares to n.
  • A089598 (program): G.f.: (1+x^2+x^3)/(1-x^3)^2.
  • A089607 (program): a(n)=((-1)^(n+1)*A002425(n)) modulo 4.
  • A089608 (program): a(n) = ((-1)^(n+1)*A002425(n)) modulo 6.
  • A089612 (program): a(n) = ((-1)^(n+1)*A002425(n)) modulo 5.
  • A089619 (program): Greatest prime factor of n^2 + (n+1)^2.
  • A089620 (program): n^3 + n-th prime.
  • A089621 (program): n^4 + n-th prime.
  • A089622 (program): a(n) = n^n + n-th prime.
  • A089633 (program): Numbers having no more than one 0 in their binary representation.
  • A089643 (program): 3^a(n) divides C(3n,n); 3-adic valuation of A005809.
  • A089644 (program): Numbers k such that 7 divides the numerator of B(2*k) where B(k) = the k-th Bernoulli number.
  • A089650 (program): a(n) = A089649(n) mod 3.
  • A089655 (program): a(1)=1 and for n>=2 a(n) is the denominator of A(n) (see comment for A(n) definition).
  • A089658 (program): Let S1 := (n,t)->add( k^t * add( binomial(n,j), j=0..k), k=0..n); a(n) = S1(n,1).
  • A089676 (program): a(n) is the maximal size of a set S of points in 0,1 ^n in real n-dimensional Euclidean space such that every angle determined by three points in S is acute.
  • A089683 (program): a(n) = 3^(4n).
  • A089709 (program): a(1) = 1, a(2) = 2; for n>2, a(n) = sum_ r=1..n sum of all previous terms taken r at a time .
  • A089723 (program): a(1)=1; for n>1, a(n) gives number of ways to write n as n = x^y, 2 <= x, 1 <= y.
  • A089727 (program): Largest prime of the form n*k+1, k <= n.
  • A089756 (program): a(1)=1 and a(i+1)=a(i)+9 if a(i)<=35, and a(i+1)=a(i)-35 if a(i)>35.
  • A089772 (program): a(n) = Lucas(11*n).
  • A089775 (program): Lucas numbers L(12n).
  • A089781 (program): Successive coprime numbers with distinct successive differences: gcd(a(k+1),a(k)) = gcd(a(m+1),a(m)) = 1 and a(k+1)-a(k) = a(m+1)-a(m) <==> m=k.
  • A089792 (program): a(n) = n-(exponent of highest power of 3 dividing n!).
  • A089799 (program): Expansion of Jacobi theta function theta_2(q^(1/2))/q^(1/8).
  • A089800 (program): Expansion of Jacobi theta function theta_2(q)/q^(1/4).
  • A089801 (program): a(n) = 0 unless n = 3j^2+2j or 3j^2+4j+1 for some j>=0, in which case a(n) = 1.
  • A089806 (program): Expansion of Jacobi theta function (theta_3(q^(1/3))-theta_2(q^3))/2/q^(1/12).
  • A089809 (program): Complement of A078588.
  • A089815 (program): a(n) = floor((n+2)^(n+2)/((n+2)^2-1)).
  • A089816 (program): a(n) = floor((n+3)^(n+2)/((n+3)^2-1)).
  • A089817 (program): a(n) = 5*a(n-1) - a(n-2) + 1 with a(0)=1, a(1)=6.
  • A089819 (program): Number of subsets of 1,2,…,n containing no primes.
  • A089821 (program): Number of subsets of 1,.., n containing exactly one prime.
  • A089830 (program): Expansion of (1-3x+6x^2-5x^3+3x^4-x^5)/(1-x)^6.
  • A089849 (program): Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A069772.
  • A089885 (program): Triangle A046899 read mod 2.
  • A089887 (program): Number of subsets of 1,.., n containing no squares.
  • A089893 (program): a(n) = (A001317(2n)-1)/4.
  • A089898 (program): Product of (digits of n each incremented by 1).
  • A089910 (program): Indices n at which blocks (1;1) occur in infinite Fibonacci word, i.e., such that A005614(n) = A005614(n+1) = 1.
  • A089911 (program): a(n) = Fibonacci(n) mod 12.
  • A089927 (program): Expansion of 1/((1-x^2)(1-5x+x^2)).
  • A089928 (program): a(n) = 2a(n-1) + 2a(n-3) + a(n-4).
  • A089929 (program): Algebraic degree of cot(Pi/n).
  • A089945 (program): Main diagonal of array A089944, in which the n-th row is the n-th binomial transform of the natural numbers.
  • A089946 (program): Secondary diagonal of array A089944, in which the n-th row is the n-th binomial transform of the natural numbers.
  • A089950 (program): Partial sums of A001652.
  • A089953 (program): Numbers n such that 3*n+7 is prime.
  • A089985 (program): a(n)=A089709(n+1)/A089709(n).
  • A089986 (program): Numbers n such that 4n + 7 is prime.
  • A090001 (program): Length of longest contiguous block of 1’s in binary expansion of n^2.
  • A090017 (program): a(n) = 4a(n-1) + 2a(n-2) for n>1, a(0)=0, a(1)=1.
  • A090019 (program): a(n) = (310^n + 20^n)/5.
  • A090040 (program): (3*6^n + 2^n)/4.
  • A090044 (program): Triangle read by rows: T(n,k) = A083093 with 1’s and 2’s interchanged.
  • A090075 (program): (Presumed) number of palindromes in the Reverse and Add! trajectory of 10^n.
  • A090076 (program): a(n) = prime(n)*prime(n+2).
  • A090079 (program): In binary expansion of n: reduce contiguous blocks of 0’s to 0 and contiguous blocks of 1’s to 1.
  • A090090 (program): a(n) = prime(n)*prime(n+3).
  • A090115 (program): a(n)=Product[p(n)-j, j=1..n]/n!=A090114(n)/n!.
  • A090129 (program): Smallest exponent such that -1 + 3^a(n) is divisible by 2^n.
  • A090131 (program): Expansion of (1+x)/(1 - 2x + 2x^2).
  • A090168 (program): Floor( 3n/2 ) - floor( 2n/3 ).
  • A090169 (program): a(n) = floor( 3n/2 ) + floor( 2n/3 ).
  • A090176 (program): G.f.: (1+x^9)/((1-x^4)(1-x^6)(1-x^12)).
  • A090178 (program): a(1) = 2; for n > 1, a(n) = n + prime(n-1).
  • A090187 (program): Primes of the form 11*n+2.
  • A090193 (program): a(n) = A053838(n) + 1 modulo 3.
  • A090197 (program): a(n) = n^3 + 6n^2 + 6n + 1.
  • A090198 (program): a(n) = N(5,n), where N(5,x) is the 5th Narayana polynomial.
  • A090199 (program): a(n) = N(6,n), where N(6,x) is the 6th Narayana polynomial.
  • A090205 (program): n^n * (n+1)^(n+1).
  • A090223 (program): Nonnegative integers with doubled multiples of 4.
  • A090239 (program): a(n) = A053838(n) + 2 modulo 3.
  • A090281 (program): “Plain Bob Minimus” in bell-ringing is a sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), … which runs through all permutations of 1,2,3,4 with period 24; sequence gives position of bell 1 (the treble bell) in n-th permutation.
  • A090288 (program): a(n) = 2n^2 + 6n + 2.
  • A090294 (program): a(n) = K_3(n) = Sum_ k>=0 A090285(3,k)2^kbinomial(n,k). a(n) = (4n^3+30n^2+56*n+15)/3.
  • A090296 (program): a(n) = K_4(n) = Sum_ k>=0 A090285(4,k)2^kbinomial(n,k). a(n) = 2(n^4+14n^3+62n^2+91n+21)/3.
  • A090300 (program): a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.
  • A090326 (program): Number of rules of a context-free grammar in Chomsky normal form that generates all permutations of n symbols.
  • A090327 (program): Number of rules of a context-free grammar in Chomsky normal form that generates all permutations of n symbols.
  • A090328 (program): Number of rules of a context-free grammar in Chomsky normal form that generates all permutations of n symbols.
  • A090346 (program): Number of divisors of prime(n) + prime(n+1).
  • A090368 (program): a(1) = 1; for n>1, smallest divisor > 1 of 2n-1.
  • A090369 (program): Smallest divisor of 2n that is > 2, or 0 if no such divisor exists.
  • A090370 (program): Least m > 3 such that gcd(n-1, m*n - 1) = m-1.
  • A090381 (program): Expansion of (1+4x+7x^2)/((1-x)^2*(1-x^2)).
  • A090384 (program): Maximal number of vertices of polytope P_T associated with any binary tree having 2n+1 nodes.
  • A090386 (program): Fifth diagonal (m=4) of triangle A084938; a(n) = A084938(n+4,n) = (n^4 + 18n^3 + 131n^2 + 426*n)/24.
  • A090387 (program): Numerator of d(n)/n, where d(n) (A000005) is the number of divisors of n.
  • A090388 (program): Decimal expansion of 1 + sqrt(3).
  • A090390 (program): Repeatedly multiply (1,0,0) by ([1,2,2],[2,1,2],[2,2,3]); sequence gives leading entry.
  • A090395 (program): Denominator of d(n)/n, where d(n) (A000005) is the number of divisors of n.
  • A090405 (program): a(n) = PrimePi(n+2) - PrimePi(n).
  • A090407 (program): a(n) = Sum_ k = 0..n C(4n + 1, 4k).
  • A090408 (program): a(n) = Sum_ k=0..n binomial(4n+3,4k).
  • A090409 (program): 7*8^n/9+2(-1)^n/9.
  • A090411 (program): G.f.: (1-x)/(1-16x).
  • A090448 (program): Fourth column (m=3) of triangle A090447.
  • A090450 (program): Row sums of triangle A090447.
  • A090453 (program): Third column (m=4) of array A090452.
  • A090458 (program): Decimal expansion of (3 + sqrt(21))/2.
  • A090461 (program): Numbers n such that there is a permutation of the numbers 1 to n such that the sum of adjacent numbers is a square.
  • A090488 (program): Decimal expansion of 2 + 2*sqrt(2).
  • A090529 (program): a(n) is the smallest m such that n <= m!.
  • A090532 (program): Let f(n) = n - pi(n). Then a(n) = least number of steps such that f(f(…(n)))=1.
  • A090550 (program): Decimal expansion of solution to n/x = x - n for n = 5.
  • A090568 (program): Least m such that m^n begins with k^(n-1) for some k > 1.
  • A090570 (program): Numbers that are congruent to 0, 1 mod 9.
  • A090585 (program): Numerator of (Sum_ k=1..n k) / (Product_ k=1..n k).
  • A090590 (program): (1,1) entry of powers of the orthogonal design shown below.
  • A090591 (program): Expansion of g.f.: 1/(1 - 2x + 8x^2).
  • A090614 (program): Numbers n such that 14n+3 is prime.
  • A090616 (program): Highest power of 4 dividing n!.
  • A090617 (program): Highest power of 8 dividing n!.
  • A090618 (program): Highest power of 9 dividing n!.
  • A090620 (program): Highest power of 13 dividing n!.
  • A090621 (program): Highest power of 16 dividing n!.
  • A090633 (program): Start with the sequence [1, 1/2, 1/3, …, 1/n]; form new sequence of n-1 terms by taking averages of successive terms; repeat until reach a single number F(n); a(n) = numerator of F(n).
  • A090642 (program): Triangle read by rows: T(n,k) = binomial(n^2, k), 0 <= k <= n.
  • A090650 (program): n^(n+6).
  • A090654 (program): Decimal expansion of 4 + 2*sqrt(6).
  • A090658 (program): Numbers n such that n-1 is a prime of the form 4k+3.
  • A090670 (program): Odd numbers k such that 2k-3 is a prime of the form 4j+3.
  • A090671 (program): Decreases from 10^k - 1 down to 1, restarting at 10^(k+1) - 1, for k >= 1.
  • A090672 (program): a(n) = (n^2-1)*n!/3.
  • A090678 (program): a(n) = A088567(n) mod 2.
  • A090702 (program): a(n) is the minimal number k such that every binary word of length n can be transformed into a palindrome or an antipalindrome by deleting at most k letters.
  • A090731 (program): a(n) = 23a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 23.
  • A090739 (program): Exponent of 2 in 9^n - 1.
  • A090740 (program): Exponent of 2 in 3^n - 1.
  • A090763 (program): a(n) = (3n+3)!/(3n!(2n+2)!).
  • A090771 (program): Numbers that are congruent to 1, 9 mod 10.
  • A090772 (program): Numbers that are congruent to 2, 8 mod 10.
  • A090773 (program): Numbers that are congruent to 4, 6 mod 10.
  • A090792 (program): a(0)=1; for n>0, a(n)=a([n/2])+a([n/4])+a([n/8]).
  • A090809 (program): Coefficient of the irreducible character of S_m indexed by (m-2n+2,2n-2) in the n-th Kronecker power of the representation indexed by (m-2,2).
  • A090815 (program): a(n)=denominator(B(2*prime(n))) where prime(n)=n-th prime and B(k) denotes the k-th Bernoulli number.
  • A090816 (program): a(n) = (3n+1)!/((2n)! * n!).
  • A090843 (program): Number of nodes on a tree with degree 11 interior nodes and degree 1 boundary nodes.
  • A090848 (program): Positions of the terms of A090847^4 in A090847, where A090847 is equal to the union of the self-convolutions A090847^2 and A090847^4 when ordered by size.
  • A090860 (program): Number of ways of 4-coloring a map in which there is a central circle surrounded by an annulus divided into n-1 regions. There are n regions in all.
  • A090879 (program): a(n) = Sum_ d n d*2^(n-d).
  • A090885 (program): Sum of the squares of the exponents in the prime factorization of n.
  • A090889 (program): Double partial sums of (n * its dyadic valuation).
  • A090908 (program): Terms a(k) of A073869 for which a(k)=a(k+1).
  • A090909 (program): Terms a(k) of A073869 for which a(k-1), a(k) and a(k+1) are distinct.
  • A090932 (program): a(n) = n! / 2^floor(n/2).
  • A090942 (program): n-th arithmetic mean = prime(n).
  • A090949 (program): a(n) = (1/24)(n+1)(3n^3+59n^2+358*n+648).
  • A090950 (program): a(n) = (1/24)(n+1)(n+3)(n^2+22n+88).
  • A090957 (program): a(n) = 1/(Integral_ x=0..1 (x^4 - x^5)^n dx).
  • A090964 (program): Permutation of natural numbers generated by 2-rowed array shown below.
  • A090965 (program): a(n) = 8a(n-1) - 4a(n-2), where a(0) = 1, a(1) = 4.
  • A090969 (program): a(n) = 1/Integral_ x=0..1 (x^5 - x^6)^n.
  • A090971 (program): Sierpiński’s triangle, read by rows, starting from 1: T(n,k) = (T(n-1,k) + T(n-1,k-1)) mod 2.
  • A090973 (program): a(n) = ceiling((prime(n)/n).
  • A090976 (program): a(n) = 100 reduced mod n.
  • A090988 (program): a(n) = 2^A004736(n).
  • A090989 (program): Number of meaningful differential operations of the n-th order on the space R^4.
  • A090990 (program): Number of meaningful differential operations of the n-th order on the space R^5.
  • A090991 (program): Number of meaningful differential operations of the n-th order on the space R^6.
  • A090993 (program): Number of meaningful differential operations of the n-th order on the space R^8.
  • A090995 (program): Number of meaningful differential operations of the n-th order on the space R^10.
  • A090996 (program): Number of leading 1’s in binary expansion of n.
  • A091000 (program): Number of closed walks of length n on the Petersen graph.
  • A091001 (program): Number of walks of length n between adjacent nodes on the Petersen graph.
  • A091002 (program): Number of walks of length n between non-adjacent nodes on the Petersen graph.
  • A091005 (program): Expansion of x^2/((1-2x)(1+3*x)).
  • A091024 (program): Let v(0) be the column vector (1,0,0,0)’; for n>0, let v(n) = [1 1 1 1 / 1 1 1 0 / 1 1 0 0/ 1 0 0 0] v(n-1). Sequence gives third entry of v(n).
  • A091030 (program): Partial sums of powers of 13 (A001022).
  • A091032 (program): Second column (k=3) of array A090438 ((4,2)-Stirling2) divided by 8.
  • A091033 (program): Third column (k=4) of array A090438 ((4,2)-Stirling2).
  • A091042 (program): Triangle of even numbered entries of odd numbered rows of Pascal’s triangle A007318.
  • A091044 (program): One half of odd-numbered entries of even-numbered rows of Pascal’s triangle A007318.
  • A091045 (program): Partial sums of powers of 17 (A001026).
  • A091052 (program): Record values in A091023.
  • A091055 (program): Expansion of x(1-2x)/((1-x)(1+2x)(1-6x)).
  • A091056 (program): Expansion of x^2/((1-x)(1+2x)(1-6x)).
  • A091074 (program): Fibonacci sequence beginning 12, 67.
  • A091084 (program): a(n) = A001045(n) mod 10.
  • A091085 (program): a(n) = mod(A078008(n),10).
  • A091086 (program): a(n) = A000975(n) mod 10.
  • A091087 (program): a(n) = floor(r*n) + floor(n/r), where r=sqrt(2).
  • A091090 (program): In binary representation: number of editing steps (delete, insert, or substitute) to transform n into n + 1.
  • A091095 (program): Expansion of (1+4x-24x^2)/((1-4x)(1+4x)).
  • A091131 (program): Decimal expansion of e - 1.
  • A091135 (program): Number of Dyck paths of semilength n+4, having exactly two long ascents (i.e., ascents of length at least two).
  • A091144 (program): a(n) = binomial(n^2, n)/(1+(n-1)*n).
  • A091177 (program): Numbers m such that the m-th prime is of the form 3*k-1.
  • A091178 (program): Numbers k such that k-th prime is of the form 6*m+1.
  • A091194 (program): Number of abundant numbers <= n.
  • A091265 (program): Take sequence of prime numbers (A000040) and reverse successive subsequences of lengths 1,2,3,4,…
  • A091270 (program): Smallest number having in binary representation a prefix of length n that is also a suffix of its successor.
  • A091282 (program): Exponent of 2 in prime(n)^2 - 1.
  • A091283 (program): Exponent of 2 in -1+prime[n]^s, if s is an exponent of the form s=8k-4.
  • A091284 (program): Exponent of 2 in -1+prime[n]^s, if s is an exponent of form 16k-8. Except a(1)=0, a(n)=1+A091283(n).
  • A091297 (program): A fixed point of the morphism 0 -> 02, 1 -> 02, 2 -> 11, starting from 0.
  • A091304 (program): a(n) = Omega(2n-1) (number of prime factors of the n-th odd number, counted with multiplicity).
  • A091307 (program): a(n)=6*2^n+4 (Bode Number A003461(n+2)) except for a(1)=6.
  • A091311 (program): Partial sums of 3^A007814(n).
  • A091335 (program): Number of prime divisors of n-th term of Sylvester’s sequence A000058.
  • A091336 (program): Number of prime divisors of A000058(n)-1 = A000058(0)A000058(n-1).
  • A091337 (program): a(n) = (2/n), where (k/n) is the Kronecker symbol.
  • A091344 (program): a(n) = 23^n - 32^n + 1.
  • A091361 (program): Numbers n such that A001840(n) == 0 (mod n).
  • A091363 (program): a(n) = n!*n^3.
  • A091364 (program): a(n) = n! * n^4.
  • A091369 (program): a(n) = Sum_ i=1..n phi(i)*ceiling(n/i).
  • A091393 (program): a(n) = Product_ p n (1 + Legendre(-3,p) ).
  • A091398 (program): a(n) = Product_ p n (1 + Legendre(5,p) ).
  • A091435 (program): Array T(n,k) = n*(n+k), read by antidiagonals.
  • A091453 (program): Triangular array T(n,k) read by rows in which row n consists of the numbers floor(2n/k), k=1,2,…,2n+1.
  • A091482 (program): a(n) = (3*n)^n.
  • A091483 (program): a(n) = (4*n)^n.
  • A091512 (program): a(n) is the largest integer m such that 2^m divides (2n)^n, i.e., the exponent of 2 in (2n)^n.
  • A091519 (program): G.f.: sum(k>=0, 2^kt(1+t)/(1-t)^3, t=x^2^k).
  • A091535 (program): First column (k=2) of array A091534 ((5,2)-Stirling2).
  • A091544 (program): First column sequence of array A091746 ((6,2)-Stirling2).
  • A091545 (program): First column sequence of the array (7,2)-Stirling2 A091747.
  • A091546 (program): First column of the array A092077 ((8,2)-Stirling2).
  • A091570 (program): Sum of odd proper divisors of n. Sum of the odd divisors of n that are less than n.
  • A091573 (program): Poincaré series [or Poincare series] of the preprojective algebra of an extended Dynkin diagram of type E_6.
  • A091574 (program): Poincaré series [or Poincare series] of the preprojective algebra of an extended Dynkin diagram of type D_4.
  • A091577 (program): Poincaré series [or Poincare series] of the preprojective algebra of a Dynkin diagram of type E_6.
  • A091596 (program): Expansion of x(1-2x^2)/(1-x-2x^2)^2.
  • A091626 (program): Number of ordered integer pairs (b,c) with 0 <= b, c <= n such that both roots of x^2+bx+c=0 are integers.
  • A091627 (program): Number of ordered integer pairs (b,c) with 1 <= b,c <= n such that both roots of x^2+bx+c=0 are integers.
  • A091628 (program): Concatenation of n 2’s followed by 3.
  • A091629 (program): Product of digits associated with A091628(n). Essentially the same as A007283.
  • A091650 (program): Let M = the 4 X 4 matrix [0 1 0 0 / 0 0 1 0 / 0 0 0 1 / -1 -1 3 2]. Set seed vector = [1 1 1 1] = first row, then take M*[1 1 1 1] = [1 1 1 3] then M * [1 1 1 3], etc. Sequence gives terms in rightmost column.
  • A091682 (program): Decimal expansion of 2(18 + sqrt(3)Pi)/27.
  • A091684 (program): a(n) = 0 if n is divisible by 3, otherwise a(n) = n.
  • A091685 (program): Sieve out 6n+1 and 6n-1.
  • A091692 (program): (10^n-1) * (n+9) / 9.
  • A091693 (program): (n*10^n - n + 9)/9.
  • A091703 (program): Count, setting 5n to zero.
  • A091711 (program): Exponent of 2 in (n^2)!.
  • A091720 (program): Babylonian sexagesimal (base 60) expansion of 1/7.
  • A091721 (program): Babylonian sexagesimal (base 60) expansion of 1/11.
  • A091735 (program): Primes arising in the first row of array in A091734.
  • A091738 (program): Primes arising in the second row of array in A091734.
  • A091761 (program): a(n) = Pell(4n) / Pell(4).
  • A091775 (program): 1 + 4^n + 9^n + 16^n.
  • A091818 (program): Sum of even proper divisors of 2n. Sum of the even divisors of 2n that are less than 2n.
  • A091823 (program): a(n) = 2n^2 + 3n - 1.
  • A091835 (program): Double factorial of primes.
  • A091848 (program): Johnson bound J(n,4,2).
  • A091870 (program): A trinomial transform of Fibonacci(3n).
  • A091881 (program): Expansion of (1-11x)/((1-x)(1-16x)).
  • A091882 (program): Expansion of (1-10x)/(1-15x).
  • A091904 (program): Expansion of x/((1+4x)(1-8x)).
  • A091914 (program): a(n) = 2a(n-1) + 12a(n-2).
  • A091915 (program): Maximum of even products of partitions of n.
  • A091916 (program): Maximum of odd products of partitions of n.
  • A091919 (program): Expansion of 1/((1-2x)(1-x^2)^2).
  • A091921 (program): Sum of odd proper distinct prime divisors of n. That is, the sum of odd distinct prime divisors of n that are less than n.
  • A091931 (program): Change the first bit to 0 in binary notation for the n-th prime.
  • A091940 (program): Given n colors, sequence gives number of ways to color the vertices of a square such that no edge has the same color on both of its vertices.
  • A091947 (program): (Fractional part of 1.1^n) * 10^n.
  • A091954 (program): Number of odd proper divisors of n. That is, the number of odd divisors of n that are less than n.
  • A091960 (program): a(1)=1, a(2n)=a(2n-1)+(a(n)mod 2), a(2n+1)=a(2n)+1.
  • A091972 (program): G.f.: (1 + x^5 ) / ( (1-x^3)*(1-x^4)).
  • A091983 (program): a(0) = 1, a(n) = 20*sigma3.
  • A091985 (program): Number of steps required for the initial value p = 10^n to reach 0 in the recurrence p = pi(p).
  • A091986 (program): a(0)=1, a(n) = sigma_3(2n).
  • A091998 (program): Numbers that are congruent to 1, 11 mod 12.
  • A091999 (program): Numbers that are congruent to 2, 10 mod 12.
  • A092028 (program): a(n) is the smallest m > 1 such that m divides n^m-1.
  • A092038 (program): a(n+1) = a(n) + (a(n) mod 2)^(n mod a(n)), a(1) = 1.
  • A092041 (program): Decimal expansion of cube root of e.
  • A092042 (program): Decimal expansion of e^(1/4).
  • A092043 (program): Numerator of n!/n^2.
  • A092054 (program): Base-2 logarithm of the sum of numerator and denominator of the convergents of the continued fraction expansion [1; 1/2, 1/3, 1/4, …, 1/n, …].
  • A092055 (program): C(2+2^n,3).
  • A092067 (program): a(n) is the smallest number m such that m > 1 and m divides n^m + 1.
  • A092076 (program): Expansion of (1+4x^3+x^6)/((1-x)(1-x^3)^2).
  • A092092 (program): Back and Forth Summant S(n, 3): a(n) = Sum i=0..floor(2n/3) (n-3i).
  • A092093 (program): Back and Forth Summant S(n, 5): a(n) = sum i = 0..floor(2n/5) n-5i.
  • A092094 (program): a(n) = Sum_ i=0,1,2,..; n-k*i >= -n n-k*i for k=3.
  • A092137 (program): Lower bound for A005842(n).
  • A092163 (program): a(n) = Prime(2n) + prime(2n+1).
  • A092164 (program): Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,1) entry of M^n.
  • A092165 (program): Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,2) entry of M^n.
  • A092166 (program): Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,1) entry of M^n.
  • A092167 (program): Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,2) entry of M^n.
  • A092168 (program): Primes congruent to 3 (modulo 19).
  • A092176 (program): A067076 + A000079/2.
  • A092178 (program): Primes congruent to 8 mod 13.
  • A092181 (program): Figurate numbers based on the 24-cell (4-D polytope with Schlaefli symbol 3,4,3 ).
  • A092184 (program): Sequence S_6 of the S_r family.
  • A092185 (program): a(n) = (5/6)n^3+(5/2)n^2+(8/3)*n.
  • A092196 (program): Number of letters in “old style” Roman numeral representation of n (e.g., IIII rather than IV).
  • A092200 (program): Expansion of (1+2x)/((1-x)(1-x^3)).
  • A092202 (program): Expansion of (x - x^3) / (1 - x^5) in powers of x.
  • A092205 (program): Number of units in the imaginary quadratic field Q(sqrt(-n)).
  • A092220 (program): Expansion of x(1-x)/ ((1+x)(1-x+x^2)) in powers of x.
  • A092242 (program): Numbers that are congruent to 5, 7 mod 12.
  • A092246 (program): Odd “odious” numbers (A000069).
  • A092248 (program): Parity of number of distinct primes dividing n (function omega(n)) parity of A001221.
  • A092249 (program): Positions of the integers in the standard diagonal enumeration of the rationals (with the integers in the first column and diagonals moving up to the right).
  • A092259 (program): Numbers that are congruent to 4, 8 mod 12.
  • A092261 (program): Sum of unitary, squarefree divisors of n, including 1.
  • A092263 (program): a(1)=1, a(n+1)=ceiling(phia(n))+1 if a(n) is odd, a(n+1)=ceiling(phia(n)) if a(n) is even, where phi=(1+sqrt(5))/2.
  • A092266 (program): Expansion of (1+4x)/AGM(1+4x,1-4x) where AGM denotes the arithmetic-geometric mean.
  • A092270 (program): If n mod 2 == 0 then 3^n else 2^n.
  • A092277 (program): a(n) = 7*n^2 + n.
  • A092278 (program): Floor( (3*n+4)/16 ).
  • A092279 (program): a(n) = floor(7*n/16) + 5.
  • A092283 (program): Triangular array read by rows: T(n,k)=n+k^2, 1<=k<=n.
  • A092286 (program): Fourth diagonal (m=3) of triangle A084938; a(n) = A084938(n+3,n) = (n^3 + 9n^2 + 26n)/6.
  • A092292 (program): a(n) = 3*n + A053838(n).
  • A092293 (program): a(n) = 3*n + A090239(n).
  • A092296 (program): a(n) = 3*n + A090193(n).
  • A092297 (program): Number of ways of 3-coloring an annulus consisting of n zones joined like a pearl necklace.
  • A092323 (program): 2^m - 1 appears 2^m times.
  • A092327 (program): a(n) = (1/12)(n+1)(n^3+19n^2+118n+228).
  • A092338 (program): a(n) = number of numbers d with n mod d <= 1.
  • A092339 (program): Number of adjacent identical digits in the binary representation of n.
  • A092341 (program): a(0)=1, a(n) = sigma_3(3n).
  • A092342 (program): a(n) = sigma_3(3n+1).
  • A092343 (program): a(n) = sigma_3(3n+2).
  • A092348 (program): a(n) = sigma_3(n) - sigma_1(n).
  • A092349 (program): a(n) = sigma_3(n) - sigma_2(n).
  • A092352 (program): G.f.: (1+3x^3)/((1-x)^2(1-x^3)^2).
  • A092353 (program): Expansion of (1+x^3)/((1-x)^2*(1-x^3)^2).
  • A092364 (program): a(n) = n^2*binomial(n,2).
  • A092365 (program): Coefficient of X^2 in expansion of (1 + nX + nX^2)^n.
  • A092383 (program): Sum of digits of n if n odd, else sum of digits of 2n.
  • A092384 (program): Sum of digits of n if n even, else sum of digits of 2n.
  • A092387 (program): a(n) = Fibonacci(2n+1) + Fibonacci(2n-1) + 2.
  • A092391 (program): a(n) = n + wt(n), where wt(n) = A000120(n) = binary weight of n.
  • A092396 (program): Row 2 of array in A288580.
  • A092403 (program): a(n) = sigma(n) + sigma(n+1).
  • A092404 (program): phi(n)+phi(n+1).
  • A092405 (program): a(n) = tau(n) + tau(n+1), where tau(n) = A000005(n), the number of divisors of n.
  • A092412 (program): Fixed point of the morphism 0->11, 1->12, 2->13, 3->10, starting from a(1) = 1.
  • A092420 (program): a(n+2) = 9*a(n+1) - a(n) + 1, with a(1)=1, a(2)=10.
  • A092431 (program): Numbers having in binary representation a leading 1 followed by n zeros and n-1 ones.
  • A092434 (program): Number of words X=x(1)x(2)x(3)…x(n) of length n in three digits 0,1,2 that are invariant under the mapping X -> Y, where y(i)=((AD)^(i-1))x(1) and where (AD) denotes the absolute difference (AD)x(i)=abs(x(i+1)-x(i)) (in other words, y(i) is the i-th element in the diagonal of leading entries in the table of absolute differences of x(1), x(2),…,x(n)).
  • A092436 (program): a(n) = 1/2 + (-1)^n*(1/2 - A010060(floor(n/2))).
  • A092438 (program): Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.
  • A092440 (program): a(n) = 2^(2n+1) - 2^(n+1) + 1.
  • A092442 (program): Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.
  • A092443 (program): Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.
  • A092444 (program): a(n+1) = 11*a(n) - a(n-1) - 3, a(0)=a(1)=1.
  • A092459 (program): Numbers that are not Catalan numbers (A000108).
  • A092460 (program): Numbers that are not Bell numbers (A000110).
  • A092464 (program): Numbers n congruent to 4 or 9 mod 13.
  • A092476 (program): Numbers that are congruent to 1, 3, 9 mod 13.
  • A092486 (program): Take natural numbers, exchange first and third quadrisection.
  • A092498 (program): G.f.: (1+x+2x^2)/((1-x)^3*(1-x^3)).
  • A092499 (program): Chebyshev polynomials S(n-1,21) with Diophantine property.
  • A092503 (program): a(n) = n^floor(n/2).
  • A092514 (program): Decimal expansion of e^(1/5).
  • A092515 (program): Decimal expansion of e^(1/6).
  • A092516 (program): Decimal expansion of e^(1/7).
  • A092517 (program): Product of tau-values for consecutive integers.
  • A092521 (program): a(n) = 8a(n-1) - 8a(n-2) + a(n-3).
  • A092523 (program): Number of distinct prime factors of n-th odd number.
  • A092525 (program): To binary representation of n, append as many ones as there are trailing zeros.
  • A092530 (program): a(0) = 0; for n > 0, a(n) = T(n) + k where T(n) is the n-th triangular number (A000217) and k (see A026741) is the smallest positive number such that a(n) is divisible by n.
  • A092532 (program): G.f.: 1/((1-x)(1-x^4)(1-x^8)).
  • A092533 (program): G.f.: (1+x^8)/((1-x)*(1-x^4)).
  • A092534 (program): Expansion of (1-x+x^2)(1+x^4)/((1-x)^2(1-x^2)).
  • A092535 (program): G.f.: (1+x^2)(1+x^3)/((1-x)(1-x^2)).
  • A092542 (program): Table below read by antidiagonals alternately upwards and downwards.
  • A092543 (program): Table below read by antidiagonals alternately upwards and downwards.
  • A092557 (program): Triangle read by rows: T(1,1) = 1; for n>=2, write the first n^2 integers in an n X n array beginning with 1 in the upper left proceeding left to right and top to bottom; then T(n,k) is the last prime in the k-th row.
  • A092596 (program): Natural numbers n for which sum of decimal digits is greater than n/2.
  • A092598 (program): Natural numbers n for which sum of decimal digits is greater than n/4.
  • A092605 (program): Decimal expansion of e^(-1/2).
  • A092634 (program): a(n) = 1 - Sum_ k=2..n k*k!.
  • A092693 (program): Sum of iterated phi(n).
  • A092694 (program): Product of iterated phi(n).
  • A092695 (program): Number of positive integers less than or equal to n which are not divisible by the primes 2,3,5,7.
  • A092724 (program): Disk degeneracies for brane III in the O(K)->P^1 x P^1 geometry.
  • A092754 (program): a(1)=1, a(2n)=2a(n)+1, a(2n+1)=2a(n)+2.
  • A092755 (program): Partial sums of A000195 (floor(log(n))).
  • A092757 (program): Partial sums of round(log_2(n)).
  • A092759 (program): a(n) = prime(n)^7.
  • A092763 (program): a(n) = floor(3^n / n).
  • A092769 (program): Squares of A006450: a(n) = prime(prime(n))^2.
  • A092770 (program): Cubes of A006450: a(n) = prime(prime(n))^3.
  • A092771 (program): Prime(prime(n))^2-1.
  • A092772 (program): (Prime(prime(n))^2-1)/24.
  • A092773 (program): Prime(prime(n))^2+1)/2.
  • A092774 (program): Prime(prime(n))^2+1
  • A092775 (program): (prime(prime(n))^4-1)/120.
  • A092780 (program): Sum(prime(k),k=1..n)^2-1.
  • A092788 (program): USUP perfect numbers.
  • A092790 (program): a(n) = (n+1)*phi(n-1)/2.
  • A092803 (program): Expansion of (1-5x)/((1-2x)(1-6x)).
  • A092804 (program): Expansion of (1+10x)/((1-1000x^3)).
  • A092805 (program): Expansion of (1+10x)/((1-x)(1-1000x^3)).
  • A092807 (program): Expansion of (1-6x+4x^2)/((1-2x)(1-6*x)).
  • A092808 (program): Pair reversal of Jacobsthal numbers.
  • A092809 (program): Expansion of (1+x-x^2) / ((1-x^2)(1-4x^2)).
  • A092810 (program): Binomial transform of a Jacobsthal trisection.
  • A092811 (program): Expansion of (1-4x)/(1-8x).
  • A092812 (program): Number of closed walks of length 2*n on the 4-cube.
  • A092841 (program): Numerator of I(n) = Integral_ x=0..1/(4^n) (1-sqrt(x))^2 dx; e.g., I(3) = 323/24576. The denominator is b(n) = 96*16^(n-1); e.g., b(3) = 24576.
  • A092860 (program): “3 times the prime sequence”.
  • A092896 (program): Related to random walks on the 4-cube.
  • A092898 (program): Expansion of (1 - 4x + 4x^2 - 4x^3)/(1 - 4x).
  • A092899 (program): Expansion of (1+2x+3x^2+6x^3)/((1+x)(1-x)^2).
  • A092906 (program): Number of iterations of the sine function to be less than 1/n with an initial argument of Pi/2 radians.
  • A092919 (program): Partial sums of A000193 (round(log(n))).
  • A092929 (program): n-th partial arithmetic mean is equal to the n-th noncomposite number or to prime(n-1) for n>1.
  • A092930 (program): n-th partial arithmetic mean is equal to the n-th composite number.
  • A092936 (program): Area of n-th triple of hexagons around a triangle.
  • A092942 (program): A Fibonacci sequence with “corrections” at every third step: -++-++-++-++-++…, i.e., at every 3rd step there is a subtraction instead of an addition.
  • A092949 (program): Numbers of the form prime(n+1) + prime(n) + 1.
  • A092956 (program): a(n) = (2n+2)!/((n+2)n!).
  • A092966 (program): Number of interior balls in a truncated tetrahedral arrangement.
  • A092979 (program): Least k such that (n+1)(n+2)(k-1)k >= n!.
  • A092984 (program): a(n) = the least k >= 1 such that n! + k is squarefree.
  • A092985 (program): a(n) = Arithofactorial(n) = AF(n) is the product of first n terms of an arithmetic progression with the first term 1 and common difference n.
  • A093001 (program): Least k such that Sum_ r=n+1..k r is greater than or equal to the sum of the first n positive integers (i.e., the n-th triangular number, A000217(n)). Or, least k such that (sum of first n positive integers) <= (sum of numbers from n+1 up to k).
  • A093005 (program): a(n) = n * ceiling(n/2).
  • A093007 (program): First nonprime number reached when iterating n under x->2*x+1.
  • A093033 (program): Number of interior balls in a truncated octahedral arrangement.
  • A093039 (program): Sequence resulting from a sum of three repeated binomial(n+3,4) sequences.
  • A093040 (program): Expansion of (1+x)/((1+x+x^2)(1-x-x^2)).
  • A093041 (program): Expansion of (1-4x+6x^2-3x^3)/(1-5x+9x^2-8x^3+4x^4).
  • A093048 (program): a(n) = n minus exponent of 2 in n, with a(0) = 0.
  • A093049 (program): n-1 minus exponent of 2 in n, a(0) = 0.
  • A093050 (program): Exponent of 2 in (3^n-3)*2^(n-1).
  • A093051 (program): Exponent of 2 in (3^n-3)*2^n.
  • A093052 (program): Exponent of 2 in 6^n - 2^n.
  • A093057 (program): Triangle T(j,k) read by rows, where T(j,k) = number of matrix elements remaining at fixed position in the in-situ transposition of a rectangular j X k matrix (singleton cycles).
  • A093061 (program): 6 * Sum_ d n (d mod 3).
  • A093064 (program): Decimal expansion of (4 + 3*log(3))/20.
  • A093069 (program): a(n) = (2^n + 1)^2 - 2.
  • A093074 (program): Greatest prime factor of n and its direct neighbors.
  • A093083 (program): Partial sums of digits of decimal expansion of golden ratio phi.
  • A093101 (program): Cancellation factor in reducing Sum_ k=0…n 1/k! to lowest terms.
  • A093112 (program): a(n) = (2^n-1)^2 - 2.
  • A093119 (program): Number of convex polyominoes with a 3 X n+1 minimal bounding rectangle.
  • A093129 (program): Binomial transform of Fibonacci(2n-1) (A001519).
  • A093130 (program): Third binomial transform of Fibonacci(3n).
  • A093131 (program): Binomial transform of Fibonacci(2n).
  • A093132 (program): Third binomial transform of Fibonacci(3n+2).
  • A093134 (program): A Jacobsthal trisection.
  • A093135 (program): Expansion of (1-8x)/((1-x)(1-10*x)).
  • A093136 (program): Expansion of (1 - 8x)/(1 - 10x).
  • A093137 (program): Expansion of (1-7x)/((1-x)(1-10x)).
  • A093138 (program): Expansion of (1-7x)/(1-10x).
  • A093140 (program): Expansion of (1-6x)/((1-x)(1-10*x)).
  • A093141 (program): Expansion of (1-6x)/(1-10x).
  • A093142 (program): Expansion of (1-5x)/((1-x)(1-10x)).
  • A093143 (program): Expansion of (1-5x)/(1-10x).
  • A093145 (program): Third binomial transform of Fibonacci(3n)/Fibonacci(3).
  • A093148 (program): a(n) = gcd(Fibonacci(n+5), Fibonacci(n+1)).
  • A093149 (program): a(1) = 4; a(n) = (n^(n+1)+2*n-3)/(n-1) for n > 1.
  • A093178 (program): If n is even then 1, otherwise n.
  • A093191 (program): Primes congruent to 4 mod 13.
  • A093194 (program): Minimal values of m=a^2+b^2=c^2+d^2 for each x=a+b+c+d=6*p (p=any odd prime).
  • A093197 (program): Number of labeled plane 2-trees on n triangles.
  • A093198 (program): Number of 4 X 4 symmetric magic squares with line sum 2n.
  • A093220 (program): a(n) is the largest number such that all of a(n)’s length-n substrings are distinct and divisible by 20.
  • A093230 (program): a(n) is the largest number such that all of a(n)’s length-n substrings are distinct and divisible by 30.
  • A093260 (program): a(n) is the largest number such that all of a(n)’s length-n substrings are distinct and divisible by 60.
  • A093270 (program): a(n) is the largest number such that all of a(n)’s length-n substrings are distinct and divisible by 70.
  • A093275 (program): a(n) is the largest number such that all of a(n)’s length-n substrings are distinct and divisible by 75.
  • A093302 (program): a(n) = (a(n-1)+(2n-1))*(2n) with a(0) = 0.
  • A093303 (program): a(n) = a(n-1)*(2n-1) + 2n with a(0)=0.
  • A093308 (program): a(n) = Fibonacci(prime(prime(n))).
  • A093328 (program): a(n) = 2*n^2 + 3.
  • A093337 (program): Penultimate digits of the primes.
  • A093350 (program): Primes congruent to 6 mod 13.
  • A093353 (program): a(n) = (n + n mod 2)*(n + 1)/2.
  • A093356 (program): Number of occurrences of pattern 1-2 after n iterations of morphism A007413.
  • A093357 (program): Number of occurrences of pattern 2-1 after n iterations of morphism A007413.
  • A093360 (program): a(n) = prime(n)^(n-1).
  • A093361 (program): Add/multiply sequence, see example.
  • A093379 (program): Expansion of x(1-2x-2x^2)/((1+x)(1-2x)(1-3x)).
  • A093380 (program): Expansion of (1+4x+x^2-10x^3)/((1-x)(1-x-2x^2)).
  • A093383 (program): One of the 16 sequences illustrating the fact that A093382(2) = 31.
  • A093384 (program): Another of the 16 sequences illustrating the fact that A093382(2) = 31.
  • A093390 (program): a(n) = floor(n/9) + floor((n+1)/9) + floor((n+2)/9).
  • A093391 (program): a(n) = floor(n/16) + floor((n+1)/16) + floor((n+2)/16) + floor((n+3)/16).
  • A093434 (program): a(n) = Product_ i=1..n (2n-i)(2*n+i).
  • A093450 (program): Number of consecutive integers whose product = A093449(n).
  • A093460 (program): a(n) = 2n^(n-1) - 1.
  • A093461 (program): a(1)=1, a(n) = 2*(n^(n-1)-1)/(n-1) for n >= 2.
  • A093462 (program): a(1)=1, a(n) = 2(n^(n-1)-1)/(n-1)^2.
  • A093467 (program): a(1) = 1, a(2) = 2; for n >= 2, a(n+1) = a(n) + Sum_ i = 1..n (a(i) - a(1)).
  • A093468 (program): a(1) = 1, a(2) = 2; for n >= 2, a(n+1) = a(n) + Sum a(n)-a(i), i = 1 to n .
  • A093479 (program): Number of regular (infinite) apeirotopes of full rank in n-dimensional space.
  • A093485 (program): a(n) = (27n^2 + 9n + 2)/2.
  • A093500 (program): a(n) = (15n^2 + 5n + 2)/2.
  • A093505 (program): a(n) = floor(A001969(n)/2 + 1/2).
  • A093509 (program): Multiples of 5 or 6.
  • A093515 (program): Numbers k such that either k or k-1 is a prime.
  • A093518 (program): Number of ways of representing n as exactly 2 generalized pentagonal numbers.
  • A093526 (program): Numerators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.
  • A093527 (program): Denominators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.
  • A093528 (program): Numerators of odd raw moments in the distribution of line lengths for lines picked at random in the unit disk.
  • A093544 (program): Numerator of (4n-3)/A000265(n). Numerator of pairwise quotients of A004130.
  • A093545 (program): Sorted mapping of A093544 onto the integers.
  • A093566 (program): a(n) = n(n-1)(n-2)(n-3)(n^2-3*n-2)/48.
  • A093581 (program): Numerators of odd moments in the distribution of chord lengths for picked at random on the circumference of a unit circle.
  • A093602 (program): Decimal expansion of Pi/sqrt(3) = sqrt(2*zeta(2)).
  • A093609 (program): Upper Beatty sequence for e^G, G = Euler’s gamma constant.
  • A093610 (program): Lower Beatty sequence for e^G, G = Euler’s gamma constant.
  • A093616 (program): a(n) = smallest k such that k*n has exactly as many divisors as n^2.
  • A093620 (program): Values of Laguerre polynomials: a(n) = 2^nn!LaguerreL(n,-1/2,-2).
  • A093646 (program): Higher dimensional figurate numbers based on 12-gonal numbers A051624.
  • A093659 (program): First column of lower triangular matrix A093658; factorial of the number of 1’s in binary expansion of n.
  • A093660 (program): Row sums of lower triangular matrix A093658.
  • A093661 (program): Partial sums of A093660.
  • A093709 (program): Characteristic function of squares or twice squares.
  • A093718 (program): a(n) = (n mod 3)^(n mod 2).
  • A093719 (program): a(n) = (n mod 2)^(n mod 3).
  • A093722 (program): Integers of the form (n^2 - 1) / 120.
  • A093801 (program): a(n) = b(n)Integral_ x=0..1/(4^n) (1 - sqrt(x)) dx, where b(n) = 324^n.
  • A093803 (program): Greatest odd proper divisor of n; a(1)=1.
  • A093828 (program): Decimal expansion of (3*Pi)/8.
  • A093833 (program): 3^n-J