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

1,1

Links

Table of n, a(n) for n=1..34.

Formula

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

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 *)

Prog

(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)));

Crossrefs

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

Sequence in context: A157978 A282246 A045363 * A031870 A040147 A152471

Adjacent sequences: A336113 A336114 A336115 * A336117 A336118 A336119

Keyword

nonn

Author

Antti Karttunen, Jul 09 2020

Extensions

More terms from Jinyuan Wang, Jul 11 2020

Status

approved