Sequences

Numbers k such that 123*2^k+1 is prime.

Numbers k such that 125*2^k+1 is prime.

Numbers k such that 127*2^k+1 is prime.

Numbers k such that 129*2^k+1 is prime.

Numbers k such that 131*2^k+1 is prime.

Numbers k such that 133*2^k+1 is prime.

Numbers k such that 135*2^k+1 is prime.

Numbers n such that 137 * 2^n + 1 is a prime.

Numbers k such that 139*2^k + 1 is prime.

Numbers k such that 141*2^k+1 is prime.

Numbers k such that 143*2^k+1 is prime.

Numbers k such that 145*2^k+1 is prime.

Numbers k such that 147*2^k+1 is prime.

Numbers k such that 149*2^k+1 is prime.

Numbers k such that 151*2^k+1 is prime.

Sum_{n>=0} a(n)/10^n = exp(1).

Coefficients of Jacobi elliptic function c(4,m).

Coefficients of Jacobi elliptic function c(5,m).

Coefficients of Jacobi elliptic function c(6,m).

Coefficients of Jacobi elliptic function c(7,m).

Coefficients of Jacobi elliptic function c(8,m).

Coefficients of Jacobi elliptic function c(9,m).

Coefficients of Jacobi elliptic function c(10,m).

Triangle read by rows: last survivors of Josephus elimination process.

Triangle of second-to-last man to survive in Josephus problem of n men in a circle with every k-th killed, with 1 <= k <= n and n >= 2.

Triangle of third-to-last man to survive in the Josephus problem of n men in a circle with every k-th killed, with 1 <= k <= n and n >= 3.

Substrings from the right are prime numbers (using only odd digits different from 5).

a(n) = n^2 - floor((n+1)/2)^2.

a(n) = Sum_{i=0..4} binomial(Fibonacci(n),i).

Sum_{i=0..3} binomial(Fibonacci(n),i).

a(n) = Sum_{i=0..2} binomial(Fibonacci(n),i).

Expansion of 1 / Product_{k >= 1} (1-q^k)^2*(1-q^(11k))^2.

a(n) = Sum_{i=0..n} binomial(2*n, i).

a(1) = 1, a(2) = 16, a(n) = lcm(48, 2n^2) for n>2.

Number the digits of the decimal expansion of Pi: 3 is the first, 1 is the second, 4 is the third and so on; a(n) gives the starting position of the first occurrence of n.

Number of solutions to phi(k) = 2n.

Inverse function of phi( ).

Smallest prime == -1 modulo prime(n).

Every suffix is prime and no digit is 0 or 5.

Period of finite sequence g(n) related to Poulet's Conjecture.

Irregular triangle read by rows: there is a row for each value of n for which the aliquot sequence starting at n eventually reaches 1, giving the part of the sequence from n to 1.

Irregular triangle read by rows: row n >= 1 contains the sequence p(n), s(p(n)), p(s(p(n))), p(p(s(p(n)))), s(p(p(s(p(n))))), ..., repeatedly applying (p,s,p) to n, where p = phi (A000010), s = sigma = (A000203), stopping after the first 1 is reached. If 1 is never reached, row n contains -1.

Numbers k such that 153*2^k+1 is prime.

Numbers k such that 155*2^k+1 is prime.

Numbers k such that 157*2^k+1 is prime.

Numbers k such that 159*2^k + 1 is prime.

Numbers k such that 161*2^k+1 is prime.

Numbers k such that 163*2^k+1 is prime.

Numbers k such that 165*2^k+1 is prime.

Numbers n such that 167*2^n+1 is prime.