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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

%I #16 Oct 12 2020 00:30:59

%S 3,5,37,44101,157081,2031121,7282801,8122501,18671941,78550201,

%T 208168381,770810041,2658625201,2710529641,5241663001,14643783001,

%U 18719308441,56181482281,73303609681,74623302001,110102454001,140659081201

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

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

%C 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

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

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

%Y Cf. A337818, A337846.

%K nonn,more

%O 1,1

%A _Benoit Cloitre_, Sep 26 2020

%E a(13)-a(17) from _Amiram Eldar_, Sep 27 2020

%E a(18)-a(22) from _Chai Wah Wu_, Oct 09 2020

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Last modified August 11 10:40 EDT 2024. Contains 375068 sequences. (Running on oeis4.)