Sequences

Decimal expansion of Khinchin's constant.

Continued fraction for Khintchine's constant.

Number of restricted hexagonal polyominoes with n cells.

Number of tree-like polyhexes rooted at a hexagon and containing n hexagons.

Number of unrooted hexagonal polyominoes with n cells and no reflections allowed.

Number of polyhexes with n hexagons, having reflectional symmetry (see Harary and Read for precise definition).

Harary-Read numbers: restricted hexagonal polyominoes (cata-polyhexes) with n cells.

Starting with n, repeatedly calculate the sum of prime factors (with repetition) of the previous term, until reaching 0 or a fixed point: a(n) is the number of terms in the resulting sequence.

Number of unlabeled nonseparable (or 2-connected) graphs (or blocks) with n nodes.

a(n) is the number of partitions of 2n that can be obtained by adding together two (not necessarily distinct) partitions of n.

a(n) is the number of partitions of 3n that can be obtained by adding together three (not necessarily distinct) partitions of n.

a(n) is the number of partitions of 4n that can be obtained by adding together four (not necessarily distinct) partitions of n.

a(n) is the number of partitions of 5n that can be obtained by adding together five (not necessarily distinct) partitions of n.

Smallest prime p of form p = 8k-1 such that first n primes (p_1=2, ..., p_n) are quadratic residues mod p.

Smallest prime p of form p = 8k+1 such that first n primes (p_1=2, ..., p_n) are quadratic residues mod p.

a(n) is the smallest prime p such that each of the first n primes has three cube roots mod p.

Smallest prime p such that first n primes (p_1=2, ..., p_n) are quintic residues mod p.

Smallest prime p such that first n primes (p_1=2, ..., p_n) are 7th power residues mod p.

Smallest prime p such that first n primes (p_1=2, ..., p_n) are 11th power residues mod p.

Primitive roots that go with the primes in A002230.

Primes with record values of the least positive primitive root.

Primitive roots that go with the primes in A029932.

8th powers written backwards.

a(1) = 1; for n > 1, a(n) = least positive prime primitive root of n-th prime.

Numbers k such that the Woodall number k*2^k - 1 is prime.

Numbers m such that 3*2^m - 1 is prime.

Numbers k such that 9*2^k - 1 is prime.

Numbers k such that 15*2^k - 1 is prime.

Numbers k such that 21*2^k - 1 is prime.

9th powers written backwards.

Numbers k such that 33*2^k - 1 is prime.

10th powers written backwards.

Numbers k such that 45*2^k - 1 is prime.

Numbers that are not the sum of 3 distinct triangular numbers.

Numbers that are not the sum of 3 distinct nonzero triangular numbers.

A (4,2)-sequence.

a(1) = 3; for n > 1, a(n) = 4*phi(n); given a rational number r = p/q, where q>0, (p,q)=1, define its height to be max{|p|,q}; then a(n) = number of rational numbers of height n.

A (6,2)-sequence.

Number of points on y^2 + xy = x^3 + x^2 + x over GF(2^n).

a(n) = a(n-1) - 2*a(n-2) with a(0) = 2, a(1) = 1.

a(n) = 4^n - 2*3^n.

Start with the nonnegative integers; then swap L(k) and U(k) for all k >= 1, where L = A000201, U = A001950 (lower and upper Wythoff sequences).

Order of letters on standard U.S. typewriter keyboard.

Numbers k such that 3*2^k + 1 is prime.

Numbers k such that 5*2^k + 1 is prime.

Numbers k such that 7*4^k + 1 is prime.

Numbers k such that 9*2^k + 1 is prime.

Numbers k such that 13*4^k + 1 is prime.

Numbers k such that 15*2^k + 1 is prime.

Numbers k such that 17*2^k + 1 is prime.