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

1,1

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A247202, A002235.

Sequence in context: A276863 A227321 A309555 * A179847 A035936 A006671

Adjacent sequences: A262991 A262992 A262993 * A262995 A262996 A262997

Keyword

nonn

Author

Pierre CAMI, Oct 07 2015

Status

approved