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A097491 Primes which are two greater than the terms of A079164.

%I A097491 #22 Jul 05 2024 08:13:43
%S A097491 5,17,21800053277,72409291238312731227527,
%T A097491 86984485062381462583582279727,
%U A097491 21679097826151232817152558557032490897727272048343000297777,107025222275017133994159705286756083545279583250537082122450588876727
%N A097491 Primes which are two greater than the terms of A079164.
%C A097491 A097491(8) = 2948...794027 has 76 digits and A097491(9) = 152400...802327 has 288 digits. - _Hartmut F. W. Hoft_, Apr 27 2021
%H A097491 Amiram Eldar, <a href="/A097491/b097491.txt">Table of n, a(n) for n = 1..9</a>
%e A097491 a(3) = 21800053277 = A079164(17) + 2 = 3*5*5*7*11*13*17*19*29*31 + 2. - _Hartmut F. W. Hoft_, Apr 27 2021
%t A097491 step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p,p+2}}, {}]], p}]
%t A097491 pairList[n_] := First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]
%t A097491 a079164[n_] := Rest[FoldList[Times, 1, Take[Flatten[pairList[n]], n]]]
%t A097491 a097491[n_] := Select[Map[#+2&, a079164[n]], PrimeQ]
%t A097491 a097491[39] (* _Hartmut F. W. Hoft_, Apr 27 2021 *)
%o A097491 (PARI) ft(n) = p=1;for(x=1,n,p*=twinl(x);if(isprime(p+2),print1(p+2", ")); p*=twinu(x);if(isprime(p+2),print1(p+2", ")))
%o A097491 twinl(n) = { local(c,x); c=0; x=1; while(c<n, if(isprime(prime(x)+2),c++); x++; ); return(prime(x-1)) }
%o A097491 twinu(n) = { local(c,x); c=0; x=1; while(c<n, if(isprime(prime(x)+2),c++); x++; ); return(prime(x)) }
%Y A097491 Cf. A048599, A097490, A097493.
%Y A097491 Cf. A037074, A077800, A079164.
%K A097491 nonn
%O A097491 1,1
%A A097491 _Cino Hilliard_, Aug 24 2004
%E A097491 Edited by _Don Reble_, Apr 16 2007
%E A097491 Name corrected by _Hartmut F. W. Hoft_, Apr 27 2021