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

1,1

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

Mathematica

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

Prog

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

Crossrefs

Cf. A337818, A337846.

Sequence in context: A222496 A086158 A158878 * A337859 A184314 A300938

Adjacent sequences: A337855 A337856 A337857 * A337859 A337860 A337861

Keyword

nonn

Author

Benoit Cloitre, Sep 26 2020

Extensions

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

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

Status

approved