Sequences

Numbers n such that 2^n does not contain the digit 6 (probably finite).

Numbers n such that 2^n does not contain the digit 7.

Numbers n such that 2^n does not contain the digit 8 (probably finite).

Numbers k such that 2^k does not contain the digit 9 (probably finite).

Numbers k such that k! has a prime number of digits.

Prime lengths of factorials: see A035065.

n! has a palindromic prime number of digits.

Palindromic prime lengths of factorials: see A035067.

a(n) is root of square starting with digit 2: first term of runs.

a(n) is root of square starting with digit 3: first term of runs.

a(n) = ceiling(sqrt(4*10^n)).

a(n) is root of square starting with digit 5: first term of runs.

a(n) is root of square starting with digit 6: first term of runs.

a(n) is root of square starting with digit 7: first term of runs.

a(n) = ceiling(sqrt(8*10^n)).

a(n) is root of square starting with digit 9: first term of runs.

Denominators of partial sums of Bernoulli numbers B_{2n} = A000367/A002445.

Numerators of partial sums of Bernoulli numbers B_{2n} = A000367/A002445.

Weigh transform of A007561.

Number of asymmetric connected graphs where every block is a complete graph.

Number of increasing asymmetric rooted connected graphs where every block is a complete graph.

Number of rooted polygonal cacti (Husimi graphs) with n nodes.

DIK(b)-DIK[ 2 ](b)-b where b is A035082.

BIK(b)-b where b is A035082.

Number of polygonal cacti (Husimi graphs) with n nodes.

Number of increasing rooted polygonal cacti (Husimi graphs) with n nodes.

Number of labeled rooted polygonal cacti (Husimi graphs) with n nodes.

Number of labeled polygonal cacti (Husimi graphs) with n nodes.

Smallest prime of form 2^n*k + 1.

Non-palindromic squares which when written backwards remain square (and still have the same number of digits).

Smallest prime == 1 mod (n^2).

Smallest k such that (n^2)*k + 1 is prime.

Smallest k such that k*n! + 1 is prime.

Smallest prime of form (n!)*k + 1.

Smallest prime congruent to 1 (mod prime(n)).

a(n) is the smallest k such that prime(n)*k+1 is prime.

Related to 9-factorial numbers A045756.

Near-Bell numbers: partitions of an n-multiset with multiplicities 1, 1, 1, ..., 1, 2.

McKay-Thompson series of class 2B for the Monster group with a(0) = 40.

Number of bits in binary expansion of n-th prime.

E.g.f. x*(c(x/2)-1)/(1-2*x), where c(x) = g.f. for Catalan numbers A000108.

Composite binary rooted trees with external nodes.

Number of 0's in binary representation of n-th prime.

First differences give (essentially) A028242.

a(n) = LCM of Fibonacci sequence {F_1,...,F_n}.

1, together with numbers of the form k*(k+1) or k*(k+2), k > 0.

First differences give (essentially) A028242.

Denominators in expansion of a certain Dirichlet series.

Numerators in the expansion of the Dirichlet series zeta(s) * Product((1+p^-s) / (1-p^(1-s))), p > 2.

Numerators in expansion of a certain Dirichlet series.