Sequences

Class 2- primes (for definition see A005109).

Class 3- primes (for definition see A005109).

Class 4- primes (for definition see A005109).

Smallest prime in class n (sometimes written n+) according to the Erdős-Selfridge classification of primes.

Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function (A001065).

Let i, i+d, i+2d, ..., i+(n-1)d be an n-term arithmetic progression of primes; choose the one which minimizes the last term; then a(n) = last term i+(n-1)d.

Number of protruded partitions of n with largest part at most 10.

Squarefree numbers: numbers that are not divisible by a square greater than 1.

Number of simple allowable sequences on 1..n containing the permutation 12...n.

Infinitesimal generator of x*(x + 1).

A sixth-order linear divisibility sequence: a(n+6) = -3*a(n+5) - 5*a(n+4) - 5*a(n+3) - 5*a(n+2) - 3*a(n+1) - a(n).

Number of ultradissimilarity relations on an n-set.

Numbers k such that 8k - 1 is prime.

Numbers k such that 8k + 1 is prime.

Numbers k such that 8k + 3 is prime.

Numbers k such that 8k - 3 is prime.

a(n) = 2^n + n + 1.

Number of k for which n does not divide Stirling cycle numbers [ {n \atop k} ].

Number of k for which n does not divide Stirling_2 subset numbers S(n, k).

Theta series of {E_6}* lattice.

Robbins numbers: a(n) = Product_{k=0..n-1} (3k+1)!/(n+k)!; also the number of descending plane partitions whose parts do not exceed n; also the number of n X n alternating sign matrices (ASM's).

A generalized continued fraction for Euler's number e.

Recamán's sequence (or Recaman's sequence): a(0) = 0; for n > 0, a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n.

Number of index n subgroups of modular group PSL_2(Z).

Number of n-dimensional unimodular lattices (or quadratic forms).

Number of laminated lattices of dimension n.

Highest minimal norm of n-dimensional unimodular lattice.

Highest minimal distance of self-dual code of length 2n.

Number of n-dimensional determinant 2 lattices.

Number of n-dimensional determinant 3 lattices.

Number of n-dimensional determinant 4 lattices.

Number of genera of forms with |determinant| = n.

Number of connected bipartite graphs with n nodes.

Number of sub-Eulerian graphs with n nodes.

Number of sub-Hamiltonian graphs with n nodes.

n copies of n-th prime.

Numerators of numbers occurring in continued fraction connected with expansion of gamma function.

Denominators of numbers occurring in continued fraction connected with expansion of gamma function.

Sequence of coefficients arising in connection with a rapidly converging series for Pi.

Sequence of coefficients arising in connection with a rapidly converging series for Pi.

Look and Say sequence: describe the previous term! (method A - initial term is 1).

Summarize the previous term (digits in increasing order), starting with a(1) = 1.

Rotation distance between binary trees on n nodes.

Practical numbers: positive integers m such that every k <= sigma(m) is a sum of distinct divisors of m. Also called panarithmic numbers.

a(0) = 1, a(1) = 2; thereafter a(n) = 3*a(n-1)^2 - 2*a(n-2)^4.

Number of degree sequences of n-node graphs.

Number of alternating sign 2n+1 X 2n+1 matrices symmetric about the vertical axis (VSASM's); also 2n X 2n off-diagonally symmetric alternating sign matrices (OSASM's).

Number of totally symmetric plane partitions that fit in an n X n X n box.

Number of alternating sign n X n matrices invariant under a half-turn.

a(n) = 3^n*Catalan(n).