A337846 Odd integers k such that 2^((k-1)/2) == 1 (mod k*(k-2)).

17, 257, 457, 1297, 6481, 11953, 26321, 47521, 47881, 49681, 65537, 74449, 157081, 165601, 278497, 333433, 476737, 557041, 560737, 576721, 1033057, 1266841, 1329337, 1463617, 1468897, 2291041, 2422201, 2754481, 2851633, 2969137, 3255281

Offset: 1

Author

Benoit Cloitre, Sep 26 2020

Keywords

• nonn

Comments

Computed terms are prime. Is this a possible primality test or are there pseudo primes? Terms are of the form 8k+1.

The Fermat number F(5) = A000215(5) = 4294967297 = 641*6700417 is the smallest composite counterexample. - Hugo Pfoertner, Sep 26 2020

Crossrefs

Cf. A081762, A337818.

Programs

Mathematica

Select[Range[3, 10^6, 2], PowerMod[2, (# - 1)/2, #*(# - 2)] == 1 &] (* Amiram Eldar, Sep 26 2020 *)

PARI

is(n) = n%2 && n>=3 && Mod(2, n*(n-2))^((n-1)/2) == 1