A123252 a(n) = smallest prime of the form 2^k + 2n - 1, k = 0, 1, ..., or 0 if there is none.

3, 5, 7, 11, 11, 13, 17, 17, 19, 23, 23, 31, 29, 29, 31, 47, 37, 37, 41, 41, 43, 47, 47, 79, 53, 53, 61, 59, 59, 61, 317, 67, 67, 71, 71, 73, 89, 79, 79, 83, 83, 211, 89, 89, 97, 107, 97, 97, 101, 101, 103, 107, 107, 109, 113, 113, 241, 131, 149, 127, 137, 127, 127, 131

Offset: 1

Author

Cino Hilliard, Oct 08 2006

Keywords

• nonn

Comments

If n == 0 (mod 3) then the exponent k must be odd, if n>1 and n == 1 (mod 3) then k must be even and if n == 2 (mod 3) then k can be either.

Records: 3, 5, 7, 11, 13, 17, 19, 23, 31, 47, 79, 317, 1163, 1048847, 536871199, 2^955 + 773, ..., . - Robert G. Wilson v

Examples

			For n = 4, p = 2 -> 2^2+(2*4-1) = 11, the fourth entry because 2^1+(2*4-1) which equals 9 is not a prime.
		

Crossrefs

Cf. A067760.

Programs

Mathematica

f[n_] := Block[{p = 1}, While[ !PrimeQ[2^p + 2n - 1], p++ ]; 2^p + 2n - 1]; Array[f, 64] (* Robert G. Wilson v *)

PARI

g2(n) = forstep(k=1,n,2,for(p=1,n,y=k+2^p;if(isprime(y),print1(y",");break)))

Formula

a(n) = 2^A067760(n-1) + 2n-1 if A067760(n-1) > 0, 0 if A067760(n-1) = 0. - Robert Israel, Jan 14 2017

Extensions

Edited and extended by Robert G. Wilson v, Nov 11 2006

Name edited by Robert Israel, Jan 14 2017