A337858 Integers k>=3 such that 2^k == 2 (mod k*(k-1)*(k-2)/6).

3, 5, 37, 101, 44101, 3766141, 8122501, 18671941, 35772661, 36969661, 208168381, 425420101, 725862061, 778003381, 818423101, 1269342901, 9049716901, 27221068981, 60138957061, 125980182901, 137330493301, 314912454781, 315322826869, 478543291381, 667933881301

Offset: 1

Author

Benoit Cloitre, Sep 26 2020

Keywords

• nonn

Comments

Computed terms are prime. Is it always the case? If not it would be interesting to compute the smallest pseudoprime.

It seems that all larger terms are of the form 180*k + 1, starting at a(5) = 44101 = 180*245 + 1. - Hugo Pfoertner, Sep 27 2020

Other terms of the form 180*k+1 (which are all prime): 60138957061, 125980182901, 137330493301, 478543291381, 667933881301, 700212813301, 701030830501, 720023604301, 766514618101, 778382658901. - Chai Wah Wu, Oct 06 2020

Links

• Delbert L. Johnson, Table of n, a(n) for n = 1..28

Crossrefs

Cf. A337818, A337846.

Programs

Mathematica

Select[Range[3, 10^7], PowerMod[2, #, #*(# - 1)*(# - 2)/6] == 2 &] (* Amiram Eldar, Sep 27 2020 *)

PARI

is(n) = n>=3 && Mod(2, n*(n-1)*(n-2)/6)^n ==2

Extensions

a(12)-a(18) from Amiram Eldar, Sep 27 2020

a(19)-a(25) from Delbert L. Johnson, Mar 27 2024