Sequences

Concatenation of 'nextprime(k) and k and prevprime(k)' is a prime.

Concatenation of 'prevprime(k) and k and prevprime(k)' is a prime.

Concatenations C1 and C2 are both prime (see the comment lines).

Concatenations C1 and C2 are both prime (see the comment lines).

Concatenations C1 and C2 are both prime (see the comment lines).

Concatenations C1 and C2 are both prime (see the comment lines).

Concatenations C1 and C2 and C3 are all prime (see the comment lines).

Concatenations C1 and C2 and C3 are all prime (see the comment lines).

Concatenations C1 and C2 and C3 and C4 are all prime (see the comment lines).

Concatenations C1 and C2 and C3 and C4 are all prime (see the comment lines).

Concatenations C1 and C2 are both prime (see the comment lines).

Numbers k such that there are no palindromic squares of length k.

Number of n-node rooted trees of height at most 6.

Number of n-node rooted trees of height at most 7.

Number of n-node rooted trees of height at most 8.

Number of n-node rooted trees of height at most 9.

a(n) = 2*binomial(n,4).

a(n) = floor(n^2/4)*(n/2).

a(n) = n-th sept-factorial number divided by 2.

a(n) = n-th sept-factorial number divided by 3.

a(n) = n-th sept-factorial number divided by 4.

a(n) = n-th sept-factorial number divided by 5.

a(n) = n-th sept-factorial number divided by 6.

One seventh of sept-factorial numbers.

Expansion of 1/(1-49*x)^(1/7); related to sept-factorial numbers A045754.

Number of ways to write n as n = x*y*z with 1 <= x <= y <= z.

Numbers that are divisible by the first, i.e., the leftmost, digit.

Numbers k that are divisible by every digit of k.

Triangular array formed by taking every other term of each row of Pascal's triangle.

Concatenation of 3 or more numbers in arithmetic progression.

a(n) = (n^2)! / (n!)^n.

Number of divisors = last digit.

Number of divisors = first digit.

Primes with only nonprime decimal digits.

Primes of the form iii...ijjj...j, i != j.

a(n) = P(n,6) = 1+6*K(n,6)=1+6*A034783(n). P(n,6) are special primes of 6k+1. The relevant values of k are given by A034783.

a(n) = 1 + 4*A034780(n).

a(n) = 1 + 3*A034782(n).

a(n) = 1 + 2*A034784(n).

Triangular array formed by taking every other term of Pascal's triangle.

Rows of Losanitsch's triangle T(n, k), n >= 0, 0 <= k <= n.

Rows of (Pascal's triangle - Losanitsch's triangle) (n >= 0, k >= 0).

Triangle giving number of trees with n >= 3 nodes and diameter d >= 2.

Triangle giving number of labeled trees with n >= 3 nodes and diameter d >= 2.

Triangle read by rows giving number of rooted labeled trees with n >= 2 nodes and height d >= 1.

a(n) = binomial(n+1, 2) + n - 1 = n*(n+3)/2 - 1.

a(n) = C(n+2,3) + 2*C(n,2) + 2*(n-2).

a(n) = C(n+3,4) + 3*C(n+1,3) + 5*C(n-1,2) + 7*n - 15.

a(n) = C(n+3,4) + 3*C(n+1,3) + 5*C(n-1,2) + 7*n - 15 for n >= 3; a(1)=1, a(2)=10.

a(n) = n!*(2*n-5)/2.