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%I #14 Mar 15 2021 03:41:42
%S 7,1,5,4,6,8,2,3,5,9,8,9,9,5,5,8,4,5,0,9,4,7,7,4,7,0,5,7,1,1,7,2,8,0,
%T 7,7,6,7,5,9,7,6,2,4,8,9,8,3,7,6,7,7,6,7,4,2,6,7,2,4,7,6,9,4,4,2,4,9,
%U 5,3,5,5,5,5,1,9,7,5,5,8,5,6,8,3,3,1,5,5,5,4,0,9,0,9,0,1,1,3
%N Decimal expansion of Product_{p prime >= 3} (1 - 1/(p^2-p-1)).
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%e 0.715468235989955845094774705711728...
%t $MaxExtraPrecision = 600; digits = 98; terms = 600; P[n_] := PrimeZetaP[n] - 1/2^n;LR = LinearRecurrence[{2, 2, -3, -2}, {0, 0, -2, -3}, 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 - 1/(p^2-p-1), 1, 3) \\ _Amiram Eldar_, Mar 15 2021
%Y Cf. A065491, A078089.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 19 2001
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