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 A274000 #29 Oct 06 2021 16:03:41 %S A274000 5,17,257,65537,148997,405458497,3497539601,139251776898727937 %N A274000 Primes p of the form k^2 + 1 that divide 4^k - 1. %C A274000 Prime terms from A273999. %C A274000 The first 4 known Fermat primes > 3 from A019434 are in this sequence. %C A274000 Conjecture: also primes p of the form n^2+1 such that divides (4^k)^n-1 for all k >= 0. Example: 17 = 4^2+1 is a term because divides (4^k)^4-1 for all k>=0: 0/17 = 0 (k=0); 255/17 = 15 (k=1); 65535/17 = 3855 (k=2); 16777215/17 = 986895 (k=3); 4294967295/17 = 252645135 (k=4); 1099511627775/17 = 64677154575 (k=5); ... %C A274000 a(8) > 10^15. - _Jacques Tramu_, Sep 17 2018 %C A274000 a(9) > 1.7*10^18. - _Giovanni Resta_, Nov 12 2018 %e A274000 17 = 4^2 + 1 is a term because it divides 4^4 - 1; 255/17 = 15. %o A274000 (PARI) is(n) = ceil(sqrt(n-1))==sqrtint(n-1) && Mod(4, n)^(sqrtint(n))==1 %o A274000 for(n=0, 1e12, if(is(n^2+1), if(ispseudoprime(n^2+1), print1(n^2+1, ", ")))) \\ _Felix Fröhlich_, Jun 12 2016 %Y A274000 Cf. A000215, A002496, A019434, A273999. %Y A274000 Subsequence of A002496 (primes of the form n^2+1). %Y A274000 Supersequence of A274002. %K A274000 nonn,more %O A274000 1,1 %A A274000 _Jaroslav Krizek_, Jun 06 2016 %E A274000 a(8) from _Giovanni Resta_, Nov 12 2018