A337859 k-1 for integers k>=4 such that 2^k == 4 (mod k*(k-1)*(k-2)*(k-3)/24).

3, 5, 37, 44101, 157081, 2031121, 7282801, 8122501, 18671941, 78550201, 208168381, 770810041, 2658625201, 2710529641, 5241663001, 14643783001, 18719308441, 56181482281, 73303609681, 74623302001, 110102454001, 140659081201

Offset: 1

Author

Benoit Cloitre, Sep 26 2020

Keywords

• nonn
• more

Comments

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

It seems that all larger terms are of the form 60*k + 1, starting at a(4) = 44101 = 60*735 + 1. Further terms of this form after a(17) are 56181482281, 73303609681, 74623302001, 110102454001, 140659081201, 283268822761, 469078212241, 530106748081, 570417709681, 701030830501, 720023604301; all are prime. - Hugo Pfoertner, Sep 28 2020

Crossrefs

Cf. A337818, A337846.

Programs

Mathematica

Select[Range[4, 10^7], (t = #*(# - 1)*(# - 2)*(# - 3)/24) == 1 || PowerMod[2, #, t] == 4 &] - 1 (* Amiram Eldar, Sep 27 2020 *)

PARI

is(k) = k>=4 && Mod(2,k*(k-1)*(k-2)*(k-3)/24)^k == 4

Extensions

a(13)-a(17) from Amiram Eldar, Sep 27 2020

a(18)-a(22) from Chai Wah Wu, Oct 09 2020