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 A097493 #22 Jul 05 2024 08:13:38
%S A097493 7,37,457,8647,51315414607
%N A097493 Primes which are two greater than A097492 terms.
%C A097493 The next term (17866..79237) has 186 digits.
%H A097493 Amiram Eldar, <a href="/A097493/b097493.txt">Table of n, a(n) for n = 1..7</a>
%e A097493 a(4) = 8647 = (Product_{k=1..4} A006512(k)) + 2 = 5*7*13*19 + 2 = A097492(4) + 2. - _Hartmut F. W. Hoft_, Apr 27 2021
%t A097493 step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p,p+2}}, {}]], p}]
%t A097493 largerTwin[n_] := Last[Transpose[First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]]]
%t A097493 a097492[n_] := Rest[FoldList[Times, 1, largerTwin[n]]]
%t A097493 a097493[n_] := Select[Map[#+2&, a097492[n]], PrimeQ]
%t A097493 a097493[68] (* _Hartmut F. W. Hoft_, Apr 27 2021 *)
%o A097493 (PARI) fu(n) = p=1;for(x=1,n,p*=twinu(x);if(isprime(p+2),print1(p+2", ")))
%o A097493 twinu(n) = { local(c,x); c=0; x=1; while(c<n, if(isprime(prime(x)+2),c++); x++; ); return(prime(x)) }
%Y A097493 Cf. A097490, A097491, A097492.
%Y A097493 Cf. A001359, A077800, A097489.
%K A097493 nonn
%O A097493 1,1
%A A097493 _Cino Hilliard_, Aug 24 2004
%E A097493 Edited by _Don Reble_, Apr 16 2007