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

1,1

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

Links

Table of n, a(n) for n=1..22.

Mathematica

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

Prog

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

Crossrefs

Cf. A337818, A337846.

Sequence in context: A086158 A158878 A337858 * A184314 A300938 A183258

Adjacent sequences: A337856 A337857 A337858 * A337860 A337861 A337862

Keyword

nonn,more

Author

Benoit Cloitre, Sep 26 2020

Extensions

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

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

Status

approved