Sequences

Sums of three consecutive primes.

Primes that are the sum of three consecutive primes.

Sums of four consecutive primes.

Sums of five consecutive primes.

Primes that are sum of five consecutive primes.

Number of different values of i^2 + j^2 + k^2 for i,j,k in [ 0,n ] (or [ -n,n ]).

Sum of digits of numbers between 0 and (10^n)-1.

Minimal number of factorials that add to n.

a(1) = a(2) = 1, a(n) is largest prime factor of concatenation of a(n - 2) and a(n - 1).

a(n) is the greatest prime factor of a(n-2)*a(n-1)-1.

a(n) = floor(E_(n+1)/E_(n)) where E_n is n-th Euler number (see A028296 and A000364).

a(n) = floor(T_(n+1)/T_(n)) where T_n is n-th tangential or "Zag" number (see A000182).

Number of distinct prime factors in central binomial coefficients C(n, floor(n/2)), the terms of A001405.

Number of divisors of binomial(n, floor(n/2)), the terms of A001405.

One seventh of octo-factorial numbers.

One eighth of octo-factorial numbers.

Expansion of 1/(1-64*x)^(1/8), related to octo-factorial numbers A045755.

a(n)^2 is smallest square starting with a string of n 1's.

Smallest square starting with a string of n 1's.

a(n)^2 is smallest positive square starting with a string of n 2's.

Smallest square starting with a string of n 2's.

a(n)^2 is smallest square starting with a string of n 3's.

Smallest square starting with a string of n 3's.

a(n)^2 is smallest square starting with a string of n 4's.

Smallest square starting with a string of n 4's.

a(n)^2 is smallest square number starting with a string of n 5's.

Smallest square starting with a string of n 5's.

a(n) is root of smallest square starting with a string of n 'digit_6's.

Smallest squares starting with a string of n 6's.

a(n)^2 is smallest square starting with a string of n 7's.

Smallest square starting with a string of n 7's.

a(n)^2 is smallest square number starting with a string of n 8's.

Smallest square starting with a string of n 8's.

Square root of smallest square starting with a string of n 9's.

Smallest square starting with a string of n 9's.

Related to octo-factorial numbers A045755.

Number of generalized retarded functions in quantum field theory.

Expansion of Product (1+q^(2k-1))^(-8)*(1+q^(4k))^(-8), k=1..inf.

Number of ways to cut a 2 X n rectangle into rectangles with integer sides.

Nontrivial trinomial coefficients.

Sorted elements of table (A035002) of a(m,n) = sum(a(m-k,n), k=1..m-1)+sum(a(m,n-k), k=1..n-1).

Square array read by antidiagonals: T(m,n) = Sum_{k=1..m-1} T(m-k,n) + Sum_{k=1..n-1} T(m,n-k).

Sorted entries in triangle in A014784.

Number of divisors of the n-th nonprime.

Number of possible queen moves on an n X n chessboard.

Number of possible rook moves on an n X n chessboard.

Duplicate of A002492.

Total number of possible knight moves on an (n+2) X (n+2) chessboard, if the knight is placed anywhere.

STIRLING transform of [1,1,2,4,8,16,32,...].

Number of prime binary rooted trees with n external nodes.