A058500 Primes of the form p*2^k + 1, where p is an odd prime and k > 0.

7, 11, 13, 23, 29, 41, 47, 53, 59, 83, 89, 97, 107, 113, 137, 149, 167, 173, 179, 193, 227, 233, 263, 269, 293, 317, 347, 353, 359, 383, 389, 449, 467, 479, 503, 509, 557, 563, 569, 587, 593, 641, 653, 719, 769, 773, 797, 809, 839, 857, 863, 887, 929, 977

Offset: 1

Author

Labos Elemer, Dec 20 2000

Keywords

• nonn

Examples

			719 is a term because 719 = 2*359 + 1 and 359 is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from T. D. Noe)

Crossrefs

Cf. A057023, A006093.

Cf. A074781 (this sequence and the Fermat primes), A147545.

Programs

Mathematica

mx = 1000; Select[ Sort@ Flatten@ Table[Prime[p] 2^k + 1, {p, 2, PrimePi[ mx/2]}, {k, Log2[ mx/Prime[ p]]}], PrimeQ] (* or *)
fQ[n_] := Block[{m = n -1}, PrimeQ[m/2^IntegerExponent[m, 2]]]; Select[
Prime@ Range@ PrimePi@ mx, fQ] (* Robert G. Wilson v, Feb 09 2018 *)

PARI

isoka(p) = isprime(p) && (pp=p-1) && isprime(pp/2^valuation(pp, 2)); \\ Michel Marcus, Feb 09 2018

Extensions

Revised definition from T. D. Noe, Nov 03 2008