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A337858
Integers k>=3 such that 2^k == 2 (mod k*(k-1)*(k-2)/6).
1
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
Sequence in context: A222496 A086158 A158878 * A337859 A184314 A300938
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