A276121 Smallest odd integer k such that k*2^prime(n)-1 is a prime number.

1, 1, 1, 1, 3, 1, 1, 1, 13, 7, 1, 21, 15, 3, 31, 147, 45, 1, 43, 73, 15, 69, 91, 1, 51, 81, 3, 1, 9, 85, 1, 55, 169, 225, 109, 145, 15, 103, 615, 69, 259, 69, 63, 45, 285, 471, 9, 255, 169, 489, 69, 273, 427, 43, 391, 169, 201, 21, 159, 181, 103, 15, 339

Offset: 1

Author

Pierre CAMI, Aug 21 2016

Keywords

• nonn

Comments

When k=1 the prime k*2^prime(n)-1 is a Mersenne prime.

Examples

			1*2^7-1 = 127 prime so a(4) = 1 as prime(4)=7.
1*2^11-1 = 2047 composite, 3*2^11-1 = 6143 prime so a(5) = 3 as prime(5)=11.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A000043, A126717.

Programs

Mathematica

Table[k = 1; While[! PrimeQ[k 2^Prime@ n - 1], k += 2]; k, {n, 63}] (* Michael De Vlieger, Aug 21 2016 *)

PARI

a(n) = {my(k=1); while (!isprime(k*2^prime(n)-1), k+=2); k;} \\ Michel Marcus, Aug 21 2016

Formula

a(n) = A126717(prime(n)). - Michel Marcus, Sep 07 2016