Sequences

Largest prime factor of n-th Mersenne number (A001348(n)).

Woodall (or Riesel) numbers: n*2^n - 1.

Let y=f(x) satisfy F(x,y)=0. a(n) is the number of terms in the expansion of (d/dx)^n y in terms of the partial derivatives of F.

Number of representations of n as a sum of distinct Lucas numbers 1, 3, 4, 7, 11, ... (A000204).

a(n) = floor((-4n)/Bernoulli(2n)).

Not representable by truncated tribonacci sequence 2, 4, 7, 13, 24, 44, 81, ....

Product of first n nonzero Fibonacci numbers F(1), ..., F(n).

Central Fibonomial coefficients.

Central Fibonomial coefficients.

a(n) = a(n-1) + a(n-4) with a(0) = 0, a(1) = a(2) = a(3) = 1.

A nonrepetitive sequence.

Smallest number that requires n iterations of the unitary totient function (A047994) to reach 1.

a(n) = ceiling((-4n)/Bernoulli(2n)).

Congruent numbers: positive integers k for which there exists a right triangle having area k and rational sides.

Number of key permutations of length n: permutations {a_i} with |a_i - a_{i-1}| = 1 or 2.

Values of phi(k) when phi(k) = phi(k+1).

Numbers k such that the multiplicative group of residues prime to k, M_k, is isomorphic to M_{k+1}.

Cyclic numbers: k such that k and phi(k) are relatively prime; also k such that there is just one group of order k, i.e., A000001(k) = 1.

Szekeres's sequence: a(n)-1 in ternary = n-1 in binary; also: a(1) = 1, a(2) = 2, and thereafter a(n) is smallest number k which avoids any 3-term arithmetic progression in a(1), a(2), ..., a(n-1), k.

High temperature series for spherical model susceptibility on 3-dimensional simple cubic lattice.

Numerators of coefficients of Green function for cubic lattice.

Numerators of coefficients of Green function for cubic lattice.

Numerators of coefficients of Green function for cubic lattice.

Denominators of coefficients of Green function for cubic lattice.

Numerators of coefficients of Green function for cubic lattice.

Period of continued fraction for square root of n (or 0 if n is a square).

Number of semi-regular digraphs (with loops) on n unlabeled nodes with each node having out-degree 2.

Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1).

Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,0,2).

Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,1).

Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,2).

Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,1).

Number of 4-line partitions of n decreasing across rows.

Number of planar partitions of n decreasing across rows.

Numbers k such that k^4 can be written as a sum of four positive 4th powers.

McKay-Thompson series of class 11A for the Monster group with a(0) = -5.

Coefficients of modular function g_2(tau).

Coefficients of modular function g_3(tau).

Denominators of coefficients of Green function for cubic lattice.

Numerators of coefficients of Green function for cubic lattice.

Denominators of coefficients of Green function for cubic lattice.

Numerators of coefficients of Green function for cubic lattice.

Denominators of coefficients of Green function for cubic lattice.

Numerators of spin-wave coefficients for cubic lattice.

Number of figure 8's with 2n edges on the square lattice.

Figure 8's with 2n edges on the square lattice.

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

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

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

Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th remaining number.