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 A273871 #18 May 10 2025 23:14:55 %S A273871 3,5,17,257,8209,59141,65537,649801 %N A273871 Primes p such that (4^(p-1)-1) == 0 mod ((p-1)^2+1). %C A273871 Prime terms from A273870. %C A273871 The first 5 known Fermat primes from A019434 are in this sequence. %C A273871 Conjecture 1: also primes p such that ((4^k)^(p-1)-1) == 0 mod ((p-1)^2+1) for all k >= 0. %C A273871 Conjecture 2: supersequence of Fermat primes (A019434). %e A273871 5 is a term because (4^(5-1)-1) == 0 mod ((5-1)^2+1); 255 == 0 mod 17. %o A273871 (Magma) [n: n in [1..100000] | IsPrime(n) and (4^(n-1)-1) mod ((n-1)^2+1) eq 0]; %o A273871 (PARI) is(n)=isprime(n) && Mod(4,(n-1)^2+1)^(n-1)==1 \\ _Charles R Greathouse IV_, Jun 08 2016 %Y A273871 Cf. A019434, A273870. %K A273871 nonn,more %O A273871 1,1 %A A273871 _Jaroslav Krizek_, Jun 01 2016