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 A079139 #16 Aug 05 2024 07:55:33
%S A079139 1,5,45,218,506,538,1027,8153
%N A079139 Numbers n such that (Product of first n twin prime pair averages [A014574] ) + 1 is prime.
%C A079139 a(3) and a(4) certified prime with Primo.
%e A079139 a(2) = 5 because the product of the first five terms of A014574 + 1, 4*6*12*18*30 + 1 = 155521, is prime.
%t A079139 seq = {1}; prod = 4; k = 1; Do[If[AllTrue[6 n + {-1, 1}, PrimeQ], prod *= 6 n; k++; If[PrimeQ[prod + 1], AppendTo[seq, k]]], {n, 1, 5000}]; seq (* _Amiram Eldar_, Dec 14 2019 *)
%o A079139 (PARI) { atp(N)= local(t, c); t=1; c=0; forprime(p=2,N,if(isprime(p+2), t*=p+1; c++; if(isprime(t+1), print1(c, ", ")))) }
%Y A079139 Cf. A014574.
%K A079139 nonn,more
%O A079139 1,2
%A A079139 _Jason Earls_, Dec 26 2002
%E A079139 a(7) from _Amiram Eldar_, Dec 14 2019
%E A079139 a(8) from _Michael S. Branicky_, Aug 05 2024