Sequences

Number of nonisomorphic commutative groupoids with no idempotents and no symmetry.

Number of nonisomorphic commutative groupoids with no idempotents and a nontrivial symmetry.

Number of nonisomorphic commutative groupoids with 1 idempotent.

Number of nonisomorphic commutative groupoids with 1 idempotent and no symmetry.

Number of nonisomorphic commutative groupoids with 1 idempotent and a nontrivial symmetry.

Shifts left under COMPOSE transform with itself.

Compose the natural numbers with themselves, A(x) = B(B(x)) where B(x) = x/(1-x)^2 is the generating function for natural numbers.

Number of nonisomorphic connected partial lattices.

Number of nonisomorphic disconnected partial lattices.

Number of nonisomorphic and nonantiisomorphic reflexive transitive and cotransitive (complement is transitive) relations.

Number of nonisomorphic groupoids with 1 idempotent and no symmetry.

Number of partitions of n^3 into distinct cubes.

Number of partitions of n^2 into distinct squares.

Numerators of sequence {b(1), b(2), ...} which when COMPOSED with itself gives {1,2,3,...}.

Denominators of sequence {b(1), b(2),...} which when COMPOSED with itself gives {1,2,3,...}.

Shifts left under COMPOSE transform.

Shifts left 2 places under COMPOSE transform.

COMPOSE primes with primes.

COMPOSE squares with squares.

COMPOSE triangular numbers with triangular numbers.

COMPOSE natural numbers with primes.

COMPOSE primes with natural numbers.

a(0) = 0; for n>0, a(n) is the smallest number greater than a(n-1) which does not use any digit used by a(n-1).

a(n) is the least prime > a(n-1) whose digits do not appear in a(n-1).

Palindromes whose digits do not appear in previous term.

Palindromic primes whose digits do not appear in previous term and that are increasing.

a(n) is the smallest k > a(n-1) such that k^2 has no digit in common with a(n-1)^2.

a(n+1) is smallest square > a(n) having no digits in common with a(n), with a(0) = 0.

a(n+1) is the next larger cube with no digits in common with a(n), a(0) = 0.

a(n) is the smallest k > a(n-1) such that k^3 has no digit in common with a(n-1)^3.

Primes with at most two different digits.

Numbers k such that k^3 has at most two different digits.

Cubes with at most two different digits.

Numbers k such that k^3 has at most three different digits.

Cubes with at most three distinct digits.

Smallest start for a run of at least n composite numbers.

a(n) = n*(n + a(n-1)) with a(0)=0.

List of permutations of 1,2,3,...,n for n=1,2,3,..., in lexicographic order.

Decimal representation of permutations of lengths 1, 2, 3, ... arranged lexicographically.

Runs have lengths 2^n, n >= 0.

n-th run has length 2^(n-1).

Write n in base 2 and juxtapose; irregular table in which row n lists the binary expansion of n.

Position of n-th 1 in A030302.

Least k such that the base-2 representation of n begins at s(k), where s=A030190 (or equally A030302).

Length of n-th run of 0's in A030302.

Length of n-th run of 1's in A030302.

(# 1's)-(# 0's) in first n terms of A030302.

Triangle T(n, k): Write n in base 2, reverse order of digits, to get the n-th row.

Position of n-th 0 in A030308.

Position of n-th 1 in A030308.