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%I #20 Jul 05 2024 08:13:49
%S 5,17,167,302946354048717875530381041444257,
%T 17164738545781348456175905084853738838912866540727619406614703260339837793050935010265073947
%N Primes which are two greater than A097489 terms.
%H Amiram Eldar, <a href="/A097490/b097490.txt">Table of n, a(n) for n = 1..6</a>
%e a(3) = 167 = (Product_{k=1..3} A001359(k)) + 2 = 3 * 5 * 11 + 2 = A097489(3) + 2. - _Hartmut F. W. Hoft_, Apr 27 2021
%t step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p,p+2}}, {}]], p}]
%t smallerTwin[n_] := First[Transpose[First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]]]
%t a097489[n_] := Rest[FoldList[Times, 1, smallerTwin[n]]]
%t a097490[n_] := Select[Map[#+2&, a097489[n]], PrimeQ]
%t a097490[39] (* _Hartmut F. W. Hoft_, Apr 27 2021 *)
%o (PARI) fp(n) = p=1;for(x=1,n,p*=twinl(x);if(isprime(p+2),print1(p+2", ")))
%o twinl(n) = { local(c,x); c=0; x=1; while(c<n, if(isprime(prime(x)+2),c++); x++; ); return(prime(x-1)) }
%Y Cf. A097489, A097491.
%Y Cf. A001359, A077800.
%K nonn
%O 1,1
%A _Cino Hilliard_, Aug 24 2004
%E Edited by _Don Reble_, Apr 16 2007
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