A262994 Smallest number k>2 such that k*2^n-1 is a prime number.

3, 3, 3, 3, 4, 3, 3, 5, 7, 5, 3, 5, 9, 5, 4, 8, 4, 3, 28, 14, 7, 26, 13, 39, 22, 11, 16, 8, 4, 20, 10, 5, 6, 3, 24, 12, 6, 3, 25, 24, 12, 6, 3, 14, 7, 20, 10, 5, 19, 11, 21, 20, 10, 5, 3, 32, 16, 8, 4, 17, 24, 12, 6, 3, 67, 63, 43, 63, 40, 20, 10, 5, 15, 12, 6, 3

Offset: 1

Author

Pierre CAMI, Oct 07 2015

Keywords

• nonn

Comments

If k=2^j then n+j is a Mersenne exponent.

a(n)=3 if and only if 3*2^n-1 is a prime; that is, n belongs to A002235. - Altug Alkan, Oct 08 2015

Examples

			3*2^1-1=5 prime so a(1)=3;
3*2^2-1=11 prime so a(2)=3;
3*2^3-1=23 prime so a(3)=3.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A247202, A002235.

Programs

Mathematica

a[n_] := For[k = 3, True, k++, If[PrimeQ[k*2^n - 1], Return[k]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 07 2015 *)

PARI

a(n) = {k=3; while (! isprime(k*2^n-1), k++); k;} \\ Michel Marcus, Oct 08 2015