A065476 Decimal expansion of Product_{p prime >= 3} (1 - (p+2)/p^3).
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, 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, 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
Offset: 0
Examples
0.7236484022982000094088491498...
Links
- G. Niklasch, Some number theoretical constants: 1000-digit values. [Cached copy]
- Peter C. Sarnak, Class Numbers of Indefinite Binary Quadratic Forms II, Journal of Number Theory, Vol. 21, No. 3 (1985), pp. 333-346.
- Eric Weisstein's World of Mathematics, Sarnak's Constant.
Programs
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Mathematica
$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 *) -
PARI
prodeulerrat(1 - (p+2)/p^3, 1, 3) \\ Amiram Eldar, Mar 15 2021