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 A215540 #21 Feb 16 2025 08:33:18
%S A215540 1,41,7,14,67,18759,20,229,147,6838,41
%N A215540 Least k such that (2*n-1)*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m, or 0 if no such value exists.
%C A215540 (2*n-1)*2^a(n) + 1 is in A023394.
%C A215540 a(n) >= 7 for n > 1.
%C A215540 a(39279) = 0. No n < 39279 with a(n)=0 is known.
%C A215540 a(12)>2500000, a(13)>2500000, a(14)=455, a(15)=57 (see Ballinger and Keller link).
%C A215540 No, a(13)=2141884, found in 2011. - _Jeppe Stig Nielsen_, Sep 07 2019
%H A215540 Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/riesel1.html">List of primes k.2^n + 1 for k < 300</a>
%H A215540 Fermat factoring status, <a href="http://www.prothsearch.com/fermat.html">Prime factors of Fermat numbers</a>
%H A215540 FermatSearch, <a href="http://www.fermatsearch.org/index.html">Home page</a>
%H A215540 PrimeGrid, <a href="https://www.primegrid.com/download/pps-F2141884.pdf">Announcement of 25*2^2141884+1</a>, related to a(13).
%H A215540 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>
%t A215540 lst = {}; Do[k = 1; While[True, p = n*2^k + 1; If[PrimeQ[p] && IntegerQ@Log[2, MultiplicativeOrder[2, p]], AppendTo[lst, k]; Break[]]; k++], {n, 1, 9, 2}]; lst
%Y A215540 Cf. A000215, A033809.
%K A215540 nonn,hard,more
%O A215540 1,2
%A A215540 _Arkadiusz Wesolowski_, Aug 15 2012