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%I #17 Mar 15 2021 03:41:56
%S 7,2,3,6,4,8,4,0,2,2,9,8,2,0,0,0,0,9,4,0,8,8,4,9,1,4,9,8,0,9,1,2,7,5,
%T 9,9,0,4,1,7,8,3,7,5,1,5,7,3,0,7,7,0,2,9,1,7,6,1,1,9,8,8,9,7,9,1,2,5,
%U 8,8,3,5,2,5,1,4,3,1,5,2,6,2,6,9,2,8,5,2,1,4,9,7,7,3,1,3,2,9
%N Decimal expansion of Product_{p prime >= 3} (1 - (p+2)/p^3).
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%H Peter C. Sarnak, <a href="https://doi.org/10.1016/0022-314X(85)90060-5">Class Numbers of Indefinite Binary Quadratic Forms II</a>, Journal of Number Theory, Vol. 21, No. 3 (1985), pp. 333-346.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SarnaksConstant.html">Sarnak's Constant</a>.
%e 0.7236484022982000094088491498...
%t $MaxExtraPrecision = 500; digits = 98; terms = 500; P[n_] := PrimeZetaP[n] - 1/2^n; LR = Join[{0, 0}, LinearRecurrence[{0, 1, 2}, {-2, -6, -2}, 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 18 2016 *)
%o (PARI) prodeulerrat(1 - (p+2)/p^3, 1, 3) \\ _Amiram Eldar_, Mar 15 2021
%Y Cf. A065477, A078090.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 19 2001
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