A336116 Primes of the form q*2^h - 1, where q is a Fermat prime.

2, 5, 11, 19, 23, 47, 67, 79, 191, 271, 383, 1087, 1279, 4111, 5119, 6143, 16447, 20479, 81919, 262147, 263167, 786431, 1114111, 1310719, 16842751, 17825791, 1073758207, 4295032831, 4311744511, 17180131327, 21474836479, 51539607551, 824633720831, 1168231104511

Offset: 1

Author

Antti Karttunen, Jul 09 2020

Keywords

• nonn

Crossrefs

Cf. A000265, A019434, A334092, A335874, A335885, A336117.

Programs

Mathematica

NestList[NestWhile[NextPrime, #, ! (PrimeQ[#2] && With[{p = NestWhile[BitShiftRight, #2 + 1, EvenQ] - 1}, BitAnd[p, p - 1] == 0 && With[{b = BitLength[p]}, BitAnd[b - 1, b - 2] == 0]]) &, 2] &, 2, 25] (* Jan Mangaldan, Jul 14 2020 *)

PARI

A000265(n) = (n>>valuation(n,2));
isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2,n-1));
isA336116(n) = (isprime(n)&&isA019434(A000265(1+n)));

Formula

For all n >= 1, A335885(a(n)) <= 2.

Extensions

More terms from Jinyuan Wang, Jul 11 2020