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 A231830 #25 Apr 22 2023 10:27:46
%S A231830 1,5,101,1020101,1061522231810040101,
%T A231830 1196154511175776540960913502483611007728163340227060101
%N A231830 a(0) = 1; for n > 0, a(n) = 1 + 4*Product_{i=1..n-1} a(i)^2.
%C A231830 Sequence designed to show that there are an infinity of primes congruent to 1 modulo 4 (A002144). Terms are not necessarily prime. Their smallest prime factors from A002144 are: 5, 101, 1020101, 53, 686743037.
%C A231830 Next term is too large to include.
%C A231830 From _Max Alekseyev_, Apr 21 2023: (Start)
%C A231830 Similarly to Sylvester's sequence (A000058), it is unknown if all terms are squarefree.
%C A231830 Primes dividing terms of this sequence are listed in A362252. Since terms are pairwise coprime, for each n prime A362252(n) divides exactly one term, whose index is A362253(n). That is, A362252(n) divides a(A362253(n)). (End)
%H A231830 S. A. Shirali, <a href="http://www.jstor.org/stable/2690862">A family portrait of primes-a case study in discrimination</a>, Math. Mag. Vol. 70, No. 4 (Oct., 1997), pp. 263-272.
%F A231830 For n > 1, a(n) = (a(n-1) - 1) * a(n-1)^2 + 1. - _Max Alekseyev_, Mar 25 2023
%o A231830 (PARI) lista(nn) = {a = vector(nn); a[1] = 5; for (n=2, nn, a[n] = 4*prod(i=1, n-1, a[i]^2) + 1;); a;}
%Y A231830 Cf. A000058, A002144, A007018, A231831, A362252, A362253.
%K A231830 nonn
%O A231830 0,2
%A A231830 _Michel Marcus_, Nov 14 2013
%E A231830 a(0)=1 prepended by _Max Alekseyev_, Mar 25 2023