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

1,1

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

Links

Table of n, a(n) for n=1..64.

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A067760.

Sequence in context: A241957 A112070 A208643 * A352185 A066168 A058024

Adjacent sequences: A123249 A123250 A123251 * A123253 A123254 A123255

Keyword

nonn

Author

Cino Hilliard, Oct 08 2006

Extensions

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

Name edited by Robert Israel, Jan 14 2017

Status

approved