A074040 Product of first n twin prime pair products.

15, 525, 75075, 24249225, 21800053275, 38433493923825, 138322144631846175, 716923675626858725025, 7458156997546211316435075, 86984485062381462583582279725, 1656445549042930191979157352803175

Offset

1,1

Links

Table of n, a(n) for n=1..11.

Formula

a(1) = A037074(1) and a(n) = a(n-1)*A037074(n) for n>1.

a(n) = A079164(2*n).

Example

The first two twin prime pairs are (3,5) and (5,7), their products: 15 and 35, therefore a(2)=15*35=525.

Mathematica

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}]
Rest[FoldList[Times, 1, Times@@@Select[Partition[Prime[Range[50]], 2, 1], #[[2]]-#[[1]]==2&]]] (* Harvey P. Dale, Jan 19 2015 *)
step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p, p+2}}, {}]], p}]
pairList[n_] := First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]
a037074[n_] := Map[Apply[Times, #]&, pairList[n]]
a074040[n_] := Rest[FoldList[Times, 1, a037074[n]]]
a074040[11] (* Hartmut F. W. Hoft, Apr 27 2021 *)

Crossrefs

Cf. A074041, A001359, A006512 & A014574.

Cf. A037074, A077800, A079164.

Sequence in context: A009068 A268960 A157166 * A002403 A077206 A171197

Adjacent sequences: A074037 A074038 A074039 * A074041 A074042 A074043

Keyword

nonn

Author

Reinhard Zumkeller, Aug 13 2002

Extensions

Edited by Robert G. Wilson v, Aug 17 2002

Corrections in Comment and Example, and added references. Hartmut F. W. Hoft, Apr 27 2021

Status

approved