cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A296104 Numbers k such that 2^k == 3 (mod k-1).

This page as a plain text file.
%I A296104 #54 Jul 12 2021 02:00:41
%S A296104 2,111482,465794,79036178,1781269903308,250369632905748,
%T A296104 708229497085910,15673900819204068
%N A296104 Numbers k such that 2^k == 3 (mod k-1).
%C A296104 Also, numbers k such that 2^k - 2 is a Fermat pseudoprime, i.e., 2^k - 2 belongs to A015919 and A006935.
%C A296104 a(3) was found by McDaniel (1989).
%C A296104 Some larger terms (maybe not in order): 2338990834231272653582, 341569682872976768698011746141903924998969680638.
%C A296104 Discovered huge even PSP(2) numbers of the form 2*M(n), where n=p*q and M(n)=2^n-1, ensure that the following numbers are also even pseudoprimes of the form 2*M(p)*M(q): 2*M(37)*M(12589), 2*M(131)*M(17854891864360859951), 2*M(179)*M(1398713032993), 2*M(2111)*M(335494787819), 2*M(35267)*M(50508121). - _Krzysztof Ziemak_, Jan 01 2018
%H A296104 W. L. McDaniel, <a href="https://doi.org/10.1090/S0025-5718-1989-0968152-6">Some Pseudoprimes and Related Numbers Having Special Forms</a>, Math. Comp. 53:187 (1989), 407-409.
%F A296104 a(n) = A296370(n) + 1.
%t A296104 k = 2; lst = {2}; While[k < 1000000001, If[ PowerMod[2, k, k -1] == 3, AppendTo[lst, k]]; k += 10; If[ PowerMod[2, k, k -1] == 3, AppendTo[lst, k]]; k += 2]; lst (* _Robert G. Wilson v_, Jan 01 2018 *)
%o A296104 (Python)
%o A296104 A296104_list = [n for n in range(2,10**6) if pow(2,n,n-1) == 3 % (n-1)] # _Chai Wah Wu_, Dec 06 2017
%o A296104 (PARI) is_A296104(n) = Mod(2, n-1)^n == 3; \\ _Iain Fox_, Dec 07 2017
%Y A296104 Cf. A000079, A015919, A006935, A014741, A050259, A055685, A296370.
%K A296104 nonn,more
%O A296104 1,1
%A A296104 _Krzysztof Ziemak_ and _Max Alekseyev_, Dec 04 2017