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 A023395 #37 Feb 17 2023 15:14:41 %S A023395 0,1,2,3,5,4,12,6,11,11,9,5,18,12,10,12,23,16,15,10,19,12,19,13,36,21, %T A023395 38,32,25,17,39,6,26,27,30,30,8,12,15,29,38,7,25,27,36,42,25,13,13,55 %N A023395 Only Fermat number divisible by A023394(n) is 2^2^a(n) + 1. %C A023395 From _Jianing Song_, Mar 02 2021: (Start) %C A023395 2^(a(n)+1) is the multiplicative order of 2 modulo A023394(n). %C A023395 Each k occurs A046052(k) times in this sequence provided that F(k) = 2^2^k + 1 is squarefree (no counterexamples are known). (End) %C A023395 Alternatively, a(n) is the only k such that A023394(n) divides A000215(k). - _Lorenzo Sauras Altuzarra_, Feb 01 2023 %H A023395 Wilfrid Keller, <a href="http://www.prothsearch.com/fermat.html">Prime factors k.2^n + 1 of Fermat numbers F_m</a> %H A023395 Lorenzo Sauras-Altuzarra, <a href="https://doi.org/10.26493/2590-9770.1473.ec5">Some properties of the factors of Fermat numbers</a>, Art Discrete Appl. Math. (2022). %H A023395 <a href="/index/Pri">Index entries for sequences that are related to primes dividing Fermat numbers</a> %o A023395 (PARI) forprime(p=3,,r=znorder(Mod(2,p));hammingweight(r)==1&&print1(logint(r,2)-1,", ")) \\ _Jeppe Stig Nielsen_, Mar 04 2018 %Y A023395 Cf. A000215, A023394, A046052. %K A023395 nonn,more %O A023395 1,3 %A A023395 _David W. Wilson_ %E A023395 a(25)-a(41) computed using data from Wilfrid Keller by _T. D. Noe_, Feb 01 2009 %E A023395 Three more terms by _T. D. Noe_, Feb 03 2009 %E A023395 Six more terms from Wilfrid Keller by _T. D. Noe_, Jan 14 2013