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 A178428 #12 May 23 2024 00:54:11
%S A178428 5,7,37,1297,1679617,2821109907457,7958661109946400884391937,
%T A178428 63340286662973277706162286946811886609896461828097
%N A178428 5 followed by the generalized Fermat numbers 6^(2^n)+1 (A078303).
%C A178428 If a(0) = 3, the recursion formula gives the Fermat numbers (A000215).
%C A178428 With a(0) = 3 instead of 5; a(n) = 2 + product_{i=0..n-1} a(i), n >= 1.
%C A178428 The recurrence equation for generalized Fermat numbers F_n(a) = a^(2^n)+1,
%C A178428 a >= 2, n >= 0, is F_{n}(a) = (F_{n-1}(a)-1)^2 + 1. - _Daniel Forgues_, Jun 22 2011
%F A178428 a(0) = 5; a(n) = 2 + product_{i=0..n-1} a(i), n >= 1.
%F A178428 From _Daniel Forgues_, Jun 22 2011: (Start)
%F A178428 The motivation for this sequence comes from the recurrence for generalized Fermat numbers 6^(2^n)+1 (A078303)
%F A178428 a(n) = 5*a(n-1)*a(n-2)*...*a(1)*a(0) + 2, n >= 0, where for n = 0, we get 5*(empty product, i.e., 1)+ 2 = 7 = a(0). This implies that the terms are pairwise coprime. (End)
%t A178428 a[0] := 5;
%t A178428 a[n_] := a[n] = Product[a[i], {i, 0, n - 1}] + 2;
%t A178428 Table[a[n], {n, 0, 10}]
%Y A178428 Cf. A000215, A178427, A178426.
%K A178428 nonn,less
%O A178428 0,1
%A A178428 _Roger L. Bagula_, May 27 2010
%E A178428 Definition simplified by the Assoc. Eds. of the OEIS - May 28 2010
%E A178428 Edited by _Daniel Forgues_, Jun 22 2011