Sequences

Generated by a sieve.

Write down the numbers from 3 to infinity. Take next number, M say, that has not been crossed off. Counting through the numbers that have not yet been crossed off after that M, cross off the first, (M+1)st, (2M+1)st, (3M+1)st, etc. Repeat. The numbers that are left form the sequence.

a(1) = 3; for n>0, a(n+1) = a(n) + floor((a(n)-1)/2).

Length of shortest addition chain for n.

Binary entropy function: a(1)=0; for n > 1, a(n) = n + min { a(k)+a(n-k) : 1 <= k <= n-1 }.

Representing n as sum of increasing powers.

Sum of lengths of longest increasing subsequences of all permutations of n elements.

Number of unlabeled minimally 2-connected graphs with n nodes (also called "blocks").

a(n+1) = 1 + a( floor(n/1) ) + a( floor(n/2) ) + ... + a( floor(n/n) ).

Number of connected permutations of [1..n] (those not fixing [1..j] for 0 < j < n). Also called indecomposable permutations, or irreducible permutations.

a(n) = max_{k=0..n} k^(n-k).

Smallest n-th order perfect digital invariant or PDI: smallest number > 1 equal to sum of n-th powers of its digits, or 0 if no such number exists.

Necklace permutations.

Multicolor Ramsey numbers R(3,3,...,3), where there are n 3's.

A nonrepetitive sequence.

Numbers that are the sum of 2 positive cubes.

Nearest integer to Bernoulli(2n)/(-4n).

Numbers that are the sum of 4 positive cubes in 1 or more way.

Numbers that are the sum of 5 positive cubes.

Numbers that are the sum of 6 positive cubes.

Numbers that are the sum of 7 positive cubes.

Numbers that are the sum of 8 positive cubes.

Numbers that are the sum of 9 positive cubes.

Numbers that are the sum of 10 positive cubes.

Numbers that are the sum of 11 positive cubes.

Numbers that are the sum of 12 positive cubes.

Numbers that are the sum of 2 positive 4th powers.

Numbers which are the sum of 3 nonzero 4th powers.

Numbers that are the sum of 4 nonzero 4th powers.

Numbers that are the sum of 5 positive 4th powers.

Numbers that are the sum of 6 positive 4th powers.

Numbers that are the sum of 7 positive 4th powers.

Numbers that are the sum of 8 positive 4th powers.

Numbers that are the sum of 9 positive 4th powers.

Numbers that are the sum of 10 positive 4th powers.

Numbers that are the sum of 11 positive 4th powers.

Numbers that are the sum of 12 positive 4th powers.

Numbers that are the sum of 2 positive 5th powers.

Numbers that are the sum of 3 positive 5th powers.

Numbers that are the sum of 4 positive 5th powers.

Numbers that are the sum of 5 positive 5th powers.

Numbers that are the sum of 6 positive 5th powers.

Numbers that are the sum of 7 positive 5th powers.

Numbers that are the sum of 8 positive 5th powers.

Numbers that are the sum of 9 positive 5th powers.

Numbers that are the sum of 10 positive 5th powers.

Numbers that are the sum of 11 positive 5th powers.

Numbers that are the sum of 12 positive 5th powers.

Numbers that are the sum of 2 nonzero 6th powers.

Numbers that are the sum of 3 nonzero 6th powers.