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 A274002 #22 Oct 06 2021 13:36:42
%S A274002 5,17,257,65537,3497539601
%N A274002 Primes p of the form (q-1)^2+1 that are a divisor of 4^(q-1)-1 where q is prime.
%C A274002 Corresponding values of primes q: 3, 5, 17, 257, 59141, ...
%C A274002 The first 4 known Fermat primes > 3 from A019434 are in this sequence.
%C A274002 Conjecture: also primes p of the form (q-1)^2+1, where q = prime, that are a divisor of (4^k)^(q-1)-1 for all k>=0. Example: 17 = (5-1)^2+1 is a term because 5 is prime and divides (4^k)^(5-1)-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 A274002 Subsequence of A274000.
%e A274002 17 = (5-1)^2+1 is a term because 17 divides 4^(5-1)-1; 255/17 = 15.
%o A274002 (PARI) listp(nn) = {forprime(p=2, nn, if (isprime(q=(p-1)^2 + 1) && (Mod(4, q)^(p-1) == 1), print1(q, ", ")););} \\ _Michel Marcus_, Jun 08 2016
%Y A274002 Cf. A019434, A273999, A274000.
%K A274002 nonn,more
%O A274002 1,1
%A A274002 _Jaroslav Krizek_, Jun 06 2016