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Decimal expansion of Hardy-Littlewood constant Product_{p prime >= 5} (1-(6*p^2-4*p+1)/(p-1)^4).
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%I #20 Mar 10 2021 03:18:18

%S 3,0,7,4,9,4,8,7,8,7,5,8,3,2,7,0,9,3,1,2,3,3,5,4,4,8,6,0,7,1,0,7,6,8,

%T 5,3,0,2,2,1,7,8,5,1,9,9,5,0,6,6,3,9,2,8,2,9,8,3,0,8,3,9,6,2,6,0,8,8,

%U 8,7,6,7,2,9,6,6,9,2,9,9,4,8,1,3,8,4,0,2,6,4,6,8,1,7,1,4,9,3,8

%N Decimal expansion of Hardy-Littlewood constant Product_{p prime >= 5} (1-(6*p^2-4*p+1)/(p-1)^4).

%C For comparison: Product_{n>=5} (1-(6n^2-4n+1)/(n-1)^4) = 3/32. - _R. J. Mathar_, Feb 25 2009

%H R. J. Mathar, <a href="http://arxiv.org/abs/0903.2514">Hardy-Littlewood constants embedded into infinite products over all positive integers</a>, arXiv:0903.2514 [math.NT], 2009-2011, constant C_1^(4).

%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]

%e 0.30749487875832709312335448607107685302...

%t $MaxExtraPrecision = 1000; digits = 99; terms = 1000; P[n_] := PrimeZetaP[ n] - 1/2^n - 1/3^n; LR = Join[{0, 0}, LinearRecurrence[{5, -4}, {-12, -60}, 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 (* _Jean-François Alcover_, Apr 17 2016 *)

%o (PARI) prodeulerrat(1-(6*p^2-4*p+1)/(p-1)^4, 1, 5) \\ _Amiram Eldar_, Mar 10 2021

%Y Cf. A065418, A027377, A065431.

%K cons,nonn

%O 0,1

%A _N. J. A. Sloane_, Nov 15 2001

%E A sign in the definition corrected by _R. J. Mathar_, Feb 25 2009