|
%I #14 Feb 15 2024 18:55:29
%S 1,3,15,105,1155,15015,255255,4849845,140645505,4360010655,
%T 178760436855,7686698784765,453515228301135,27664428926369235,
%U 1964174453772215685,143384735125371745005,14481858247662546245505
%N Partial products of the sequence (A001097) of twin primes.
%e a(0) = 1 by the usual convention for an empty product. - _N. J. A. Sloane_, Feb 15 2024
%e a(5) = 15015 because 3 * 5 * 7 * 11 * 13 = 15015.
%t nextTwin[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p-2]||PrimeQ[p+2], {p}, {}]], p}]
%t a001097[n_] := First[NestWhile[nextTwin, {{3}, 3}, Length[First[nextTwin[#]]]<=n&]]
%t a048599[n_] := FoldList[Times, 1, a001097[n]]
%t a048599[16] (* _Hartmut F. W. Hoft_, Apr 27 2021 *)
%t Join[{1},FoldList[Times,Union[Flatten[Select[Partition[Prime[Range[30]],2,1],#[[2]]-#[[1]]==2&]]]]] (* _Harvey P. Dale_, Feb 15 2024 *)
%Y Cf. A048598, A001097.
%K easy,nonn
%O 0,2
%A Den Roussel (DenRoussel(AT)webtv.net)
%E More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999
|
