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%I #16 Mar 11 2021 04:47:13
%S 3,6,9,4,3,7,5,1,0,3,8,6,4,9,8,6,8,9,3,2,3,1,9,0,7,4,9,8,7,6,7,5,0,7,
%T 7,7,0,5,5,3,7,2,9,1,3,8,9,3,0,3,1,8,2,5,2,9,1,0,1,2,3,0,2,9,0,7,7,3,
%U 9,2,9,9,5,7,3,9,1,7,7,7,8,4,2,8,2,7,6,8,3,3,5,0,0,0,6,9,3,1,7
%N Decimal expansion of Hardy-Littlewood constant C_7 = Product_{p prime > 7} 1/(1-1/p)^7 (1-7/p).
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 86.
%e 0.3694375103864986893231907498767507770553729138930318252910123...
%t $MaxExtraPrecision = 1100; digits = 99; terms = 1000; P[n_] := PrimeZetaP[ n] - 1/2^n - 1/3^n - 1/5^n - 1/7^n; LR = Join[{0, 0}, LinearRecurrence[ {8, -7}, {-42, -336}, terms+10]]; r[n_Integer] := LR[[n]]; Exp[ NSum[ r[n]*P[n-1]/(n-1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First
%o (PARI) prodeulerrat(1/(1-1/p)^7*(1-7/p), 1, 11) \\ _Amiram Eldar_, Mar 11 2021
%Y Cf. A005597, A065418, A065419, A269843, A269846.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Apr 17 2016
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