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.
%I A226366 #39 Feb 16 2025 08:33:19
%S A226366 7,25,39,75,127,1947,3313,23473,125413
%N A226366 Numbers k such that 5*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m.
%C A226366 No other terms below 5330000.
%C A226366 The reason all terms are odd is that if k is even, then 5*2^k + 1 == (-1)*(-1)^k + 1 = (-1)*1 + 1 = 0 (mod 3). So if k is even, then 3 divides 5*2^k + 1, and since 3 divides no other Fermat number than F_0=3 itself, we do not have a Fermat factor. - _Jeppe Stig Nielsen_, Jul 21 2019
%H A226366 Wilfrid Keller, <a href="http://www.prothsearch.com/fermat.html">Fermat factoring status</a>
%H A226366 J. C. Morehead, <a href="https://doi.org/10.1090/S0002-9904-1906-01371-4">Note on the factors of Fermat's numbers</a>, Bull. Amer. Math. Soc., Volume 12, Number 9 (1906), pp. 449-451.
%H A226366 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>
%t A226366 lst = {}; Do[p = 5*2^n + 1; If[PrimeQ[p] && IntegerQ@Log[2, MultiplicativeOrder[2, p]], AppendTo[lst, n]], {n, 7, 3313, 2}]; lst
%o A226366 (PARI) isok(n) = my(p = 5*2^n + 1, z = znorder(Mod(2, p))); isprime(p) && ((z >> valuation(z, 2)) == 1); \\ _Michel Marcus_, Nov 10 2018
%Y A226366 Subsequence of A002254.
%Y A226366 Cf. A000215, A050526, A057775, A057778, A201364, A204620.
%K A226366 nonn,hard,more
%O A226366 1,1
%A A226366 _Arkadiusz Wesolowski_, Jun 05 2013