Sequences

Numerators of continued fraction convergents to cube root of 6.

Denominators of continued fraction convergents to fifth root of 2.

Numerators of continued fraction convergents to fifth root of 2.

Denominators of continued fraction convergents to fifth root of 5.

Numerators of continued fraction convergents to fifth root of 5.

Numbers y such that p^2 = x^2 + y^2, 0 < x < y, p = A002144(n).

Numbers x such that x^2 + y^2 = p^2 = A002144(n)^2, x < y.

Let p = A007645(n) be the n-th generalized cuban prime and write p^2 = x^2 + 3*y^2 with y > 0; a(n) = x.

Let p = A007645(n) be the n-th generalized cuban prime and write p^2 = x^2 + 3*y^2 with y > 0; a(n) = y.

Number of ways of folding a strip of n rectangular stamps.

a(n) = (2*n-1)^2 * a(n-1) - 3*C(2*n-1,3) * a(n-2) for n>1; a(0) = a(1) = 1.

Period of decimal expansion of 1/(n-th prime) (0 by convention for the primes 2 and 5).

Goldbach conjecture: number of decompositions of 2n into ordered sums of two odd primes.

Smallest prime in decomposition of 2n into sum of two odd primes.

Largest prime <= n in any decomposition of 2n into a sum of two odd primes.

From Goldbach conjecture: number of decompositions of 2n into an unordered sum of two odd primes.

Least number of positive cubes needed to sum to n.

Least number of 4th powers needed to represent n.

Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1).

a(n) = floor(3^n / 2^n).

a(n) = 3^n reduced modulo 2^n.

Numbers of the form (p^2 - 1)/120 where p is 1 or prime.

Numbers of the form (p^2 - 49)/120 where p is prime.

Primes of form k^2 + k + 1.

Numbers m such that m^2 + m + 1 is prime.

Palindromic primes: prime numbers whose decimal expansion is a palindrome.

Primes (lower end) with record gaps to the next consecutive prime: primes p(k) where p(k+1) - p(k) exceeds p(j+1) - p(j) for all j < k.

Least k such that H(k) > n, where H(k) is the harmonic number Sum_{i=1..k} 1/i.

Decimal expansion of Pi^2.

Decimal expansion of -log(gamma), where gamma is Euler's constant A001620.

Decimal expansion of natural logarithm of golden ratio.

Decimal expansion of natural logarithm of 3.

Decimal expansion of natural logarithm of 10.

Weight distribution of [8,4,4] Hamming code omitting 0 terms.

Weight distribution of [ 7,4,3 ] Hamming code.

a(n) is the number of crystal forms in n dimensions.

Inverse of reduced totient function.

a(n) = n! * lcm({1, 2, ..., n+1}).

Coefficients for step-by-step integration.

Coefficients for step-by-step integration.

Coefficients for step-by-step integration.

Coefficients for step-by-step integration.

Coefficients for step-by-step integration.

Coefficients for step-by-step integration.

Coefficients for step-by-step integration.

Coefficients for step-by-step integration.

Coefficients for step-by-step integration.

Cuban primes: primes which are the difference of two consecutive cubes.

Expansion of 8-dimensional cusp form.

a(n) = 2^n*C(n+6,6). Number of 6D hypercubes in an (n+6)-dimensional hypercube.