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A337858
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Integers k>=3 such that 2^k == 2 (mod k*(k-1)*(k-2)/6).
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1
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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Select[Range[3, 10^7], PowerMod[2, #, #*(# - 1)*(# - 2)/6] == 2 &] (* Amiram Eldar, Sep 27 2020 *)
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PROG
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(PARI) is(n) = n>=3 && Mod(2, n*(n-1)*(n-2)/6)^n ==2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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