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 A080134 #9 Feb 16 2025 08:32:48
%S A080134 5,3,3,2,4,3,2,3,3,1,1,3,1,4,1,1
%N A080134 Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>=0.
%C A080134 Values of k <= 16 were tested. The sequence A078902 lists some of the generalized Fermat primes. Bjorn and Riesel examined generalized Fermat numbers for n <= 11 and k <= 999. The next n>1 for which (n+1)^2^k + n^2^k is prime for k=0,1,2,3,4 is n=826284.
%H A080134 Anders Björn and Hans Riesel, <a href="http://www.jstor.org/stable/2584996">Factors of Generalized Fermat Numbers</a>, Mathematics of Computation, Vol. 67, No. 221, Jan., 1998, pp. 441-446.
%H A080134 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>
%e A080134 a(1) = 5 because there are five known Fermat primes: 3, 5, 17, 257, 65537.
%t A080134 lst={}; Do[prms=0; Do[If[PrimeQ[(n+1)^2^k+n^2^k], prms++ ], {k, 0, 16}]; AppendTo[lst, prms], {n, 16}]; lst
%Y A080134 Cf. A019434, A078902, A080131, A080133.
%K A080134 nonn,hard,more
%O A080134 1,1
%A A080134 _T. D. Noe_, Jan 30 2003