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A337859 k-1 for integers k>=4 such that 2^k == 4 (mod k*(k-1)*(k-2)*(k-3)/24). 0
3, 5, 37, 44101, 157081, 2031121, 7282801, 8122501, 18671941, 78550201, 208168381, 770810041, 2658625201, 2710529641, 5241663001, 14643783001, 18719308441, 56181482281, 73303609681, 74623302001, 110102454001, 140659081201 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A086158 A158878 A337858 * A184314 A300938 A183258
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

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)