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%I #14 May 01 2021 22:06:09
%S 15,525,75075,24249225,21800053275,38433493923825,138322144631846175,
%T 716923675626858725025,7458156997546211316435075,
%U 86984485062381462583582279725,1656445549042930191979157352803175
%N Product of first n twin prime pair products.
%F a(1) = A037074(1) and a(n) = a(n-1)*A037074(n) for n>1.
%F a(n) = A079164(2*n).
%e The first two twin prime pairs are (3,5) and (5,7), their products: 15 and 35, therefore a(2)=15*35=525.
%t a = {4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150} (* A014574 *); Table[ Product[a[[k]]^2 - 1, {k, 1, n}], {n, 1, 12}]
%t Rest[FoldList[Times,1,Times@@@Select[Partition[Prime[Range[50]],2,1],#[[2]]-#[[1]]==2&]]] (* _Harvey P. Dale_, Jan 19 2015 *)
%t step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p,p+2}}, {}]], p}]
%t pairList[n_] := First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]
%t a037074[n_] := Map[Apply[Times, #]&, pairList[n]]
%t a074040[n_] := Rest[FoldList[Times, 1, a037074[n]]]
%t a074040[11] (* _Hartmut F. W. Hoft_, Apr 27 2021 *)
%Y Cf. A074041, A001359, A006512 & A014574.
%Y Cf. A037074, A077800, A079164.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Aug 13 2002
%E Edited by _Robert G. Wilson v_, Aug 17 2002
%E Corrections in Comment and Example, and added references. _Hartmut F. W. Hoft_, Apr 27 2021
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