cp's OEIS Frontend

A271886 Decimal expansion of the constant D related to the conjectured asymptotic expression of the counting function of prime triples as D*n/log(n)^3.

%I A271886 #8 Mar 11 2021 04:44:42
%S A271886 2,8,5,8,2,4,8,5,9,5,7,1,9,2,2,0,4,3,2,4,3,0,1,3,4,6,6,0,7,2,6,3,5,0,
%T A271886 8,7,8,0,3,9,2,9,5,5,9,2,9,9,5,6,7,6,0,2,9,0,4,8,8,0,5,0,7,2,1,9,0,5,
%U A271886 3,0,7,5,9,0,2,2,6,2,6,3,4,6,9,3,6,1,3,1,1,2,4,0,4,3,8,2
%N A271886 Decimal expansion of the constant D related to the conjectured asymptotic expression of the counting function of prime triples as D*n/log(n)^3.
%D A271886 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 85.
%F A271886 D = (9/2) Product_{p prime > 3} p^2(p-3)/(p-1)^3.
%e A271886 2.8582485957192204324301346607263508780392955929956760290488...
%t A271886 $MaxExtraPrecision = 800; digits = 96; terms = 1000; P[n_] := PrimeZetaP[n] - 1/2^n - 1/3^n; LR = Join[{0, 0}, LinearRecurrence[{4, -3}, {-6, -24}, terms + 10]]; r[n_Integer] := LR[[n]]; (9/2)*Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First
%o A271886 (PARI) (9/2) * prodeulerrat(p^2*(p-3)/(p-1)^3, 1, 5) \\ _Amiram Eldar_, Mar 11 2021
%Y A271886 Cf. A005597.
%K A271886 nonn,cons
%O A271886 1,1
%A A271886 _Jean-François Alcover_, Apr 16 2016