Sequences

Numbers k such that k^2 + (k+1)^2 is prime.

Primes of the form j^2 + (j+1)^2.

Numbers k such that k^2 + (k+1)^2 + (k+2)^2 is prime.

Primes of the form k^2 + (k+1)^2 + (k+2)^2 = 3*(k+1)^2+2.

Sums of six consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2.

Numbers k such that k^2 + (k+1)^2 + (k+2)^2 + (k+3)^2 + (k+4)^2 + (k+5)^2 is prime.

Primes of the form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2.

Number of trailing zeros in n!; highest power of 5 dividing n!.

Number of 0's in n!.

Number of zero digits in 2^n.

a(n) = Product_{i=1..n} (3^i - 1).

a(n) = Product_{i=1..n} (5^i - 1).

a(n) = Product_{i=1..n} (6^i - 1).

Minimal degree path length of a tree with n leaves.

a(n) = Product_{i=1..n} (7^i - 1).

a(n) = Product_{i=1..n} (8^i - 1).

a(n) = Product_{i=1..n} (9^i - 1).

a(n) = Product_{i=1..n} (10^i - 1).

a(n) = Product_{i=1..n} (11^i - 1).

a(n) = Product_{i=1..n} (12^i - 1).

a(i)=a(i-1)+a(j_1)*a(j_2) {where j_1+j_2=i-1, j_1 <= q j_2} + a(j_1)*a(j_2)*a(j_3) {where j_1+j_2+j_3=i-1, j_1 <= q j_2 <= q j_3} +...+ a(1)^{i-1}.

a(n) = Sum_{k>=1} k^n (2/3)^k.

Positions of primes in sequence (A246655) of primes and prime powers {p^i, i >= 1}.

Figaro's opening aria in 'Le Nozze di Figaro' by Mozart.

Leporello's 'Register-Aria' from Mozart's 'Don Giovanni'.

Primes of form n + (n+1)^2 + (n+2)^3 + (n+3)^4 + (n+4)^5.

Possible hands in the card game Skat.

Possible hands in the card game Skat (abbreviated version).

Divisors of 999999999.

Divisors of 99999999.

Divisors of 9999999.

Divisors of 999999.

Divisors of 99999.

Divisors of 9999.

Divisors of 9999999999.

Divisors of 10^11 - 1.

Divisors of 10^12 - 1.

Divisors of 10^12 + 1.

Divisors of 10^11 + 1.

Divisors of 10^10 + 1.

Divisors of 10^9 + 1.

Divisors of 3^24 - 1.

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

Terminating decimals of length n of form p/2^q using at most one of each nonzero digit.

Terminating decimals of length n of form p/5^q using at most one of each nonzero digit.

Expansion of Product_{m>=1} (1+q^m)^(4*m).

Triangle of trinomial coefficients T(n,k) (n >= 0, 0 <= k <= 2*n), read by rows: n-th row is obtained by expanding (1 + x + x^2)^n.

a(n) = T(2*n, n), T given by A027907.

T(2n,n-1), T given by A027907.

T(2n,n-2), T given by A027907.