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 A373580 #24 Jun 30 2024 20:59:01 %S A373580 1,3,5,17,257,641,1605,4369,32113,65537,94945,114689,159441,164737, %T A373580 274177,319489,974849,2424833,3862465,6700417,13631489,13906833, %U A373580 16843009,26017793,42009217,45592577,63766529,70463489,167772161,175747457,825753601,1214251009,1227890731,1251711641 %N A373580 Numbers k that divide 2^(2^k) - 2^k + 1. %C A373580 Numbers k that divide A119564(k). %C A373580 A term is prime if and only if it is in A023394. %C A373580 If k is in A307843, then it is a term of this sequence. %C A373580 The terms that are not divisors of Fermat numbers are 1605, 4369, 32113, 94945, ... (they are all composite). Are there infinitely many of them? %C A373580 Note that 2^(2^k) - 2^k + 1 = (2^(2^k) - 1) - (2^k - 2). %t A373580 q[k_] := Mod[PowerMod[2, 2^k, k] - PowerMod[2, k, k] + 1, k] == 0; Select[Range[1, 10^5, 2], q] (* _Amiram Eldar_, Jun 10 2024 *) %o A373580 (PARI) isok(k) = Mod(Mod(2, k)^(2^k) - Mod(2,k)^k + 1, k) == 0; \\ _Michel Marcus_, Jun 12 2024 %Y A373580 Cf. A023394 (primes in this sequence), A119564, A307843 (subsequence). %K A373580 nonn %O A373580 1,2 %A A373580 _Thomas Ordowski_, Jun 10 2024 %E A373580 More terms from _Amiram Eldar_, Jun 10 2024