A135980 Numbers k such that the Mersenne number 2^prime(k)-1 is composite.

5, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78

Offset: 1

Author

Artur Jasinski, Dec 09 2007

Keywords

• nonn

Comments

A135979 is a subsequence of this sequence.

Crossrefs

Cf. A000225, A065341, A054723, A134852, A135975, A135976, A135977, A135978, A135979.

Programs

Mathematica

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], AppendTo[k, n]], {n, 1, 40}]; k
m = PrimePi @ MersennePrimeExponent @ Range[13]; Complement[Range[m[[-1]]], m] (* Amiram Eldar, Mar 12 2020 *)

PARI

isok(k) = !isprime(2^prime(k)-1); \\ Michel Marcus, Mar 12 2020

Formula

prime(a(n)) = A054723(n).

a(n) = pi(A054723(n)).

Extensions

More terms from Amiram Eldar, Mar 12 2020