A178995 Numbers k such that 3^k (mod 2^k) is prime.

3, 5, 7, 9, 11, 20, 28, 62, 161, 204, 471, 505, 881, 1810, 1812, 2506, 3321, 6809, 9272, 15131, 17449, 25250, 27989, 36082, 53309, 64970, 66354, 69646, 96080, 176059, 451810, 549633

Offset: 1

Author

Robert G. Wilson v, Jan 03 2011

Keywords

• nonn
• more

Crossrefs

Cf. A002380, A178985.

Programs

Mathematica

fQ[n_] := PrimeQ@ PowerMod[3, n, 2^n]; k = 1; lst = {}; While[k < 15001, If[fQ@ k, AppendTo[lst, k]]; k++]; lst

PARI

for(n=1, 10^5, if(ispseudoprime((3^n)%(2^n)), print1(n, ", "))) \\ Felix Fröhlich, Jun 05 2014

Formula

A002380(a(n)) = A178985(n). - Amiram Eldar, Jul 18 2021

Extensions

a(20)-a(23) from Felix Fröhlich, Jun 06 2014

a(24)-a(28) from Amiram Eldar, Jul 18 2021

a(29) from Michael S. Branicky, Jun 08 2024

a(30)-a(32) from Henri Lifchitz, Jun 05 2025