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%I #19 Mar 15 2021 04:24:27
%S 1,4,1,9,5,6,2,8,8,0,5,0,5,4,8,5,9,1,9,3,1,7,2,3,5,8,6,1,7,8,9,7,3,5,
%T 3,5,9,1,6,6,0,7,1,5,8,6,3,0,5,1,2,2,5,4,2,6,9,8,9,8,3,6,9,5,5,6,4,3,
%U 3,0,9,7,1,3,3,9,4,7,1,6,0,8,6,3,9,9,4,0,3,6,9,4,8,0,2,7,9,4,9
%N Decimal expansion of Product_{p prime} (1 + 1/(p^2+p-1)).
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%F 1 divided by A065463. - _R. J. Mathar_, Mar 26 2011
%e 1.419562880505485919317235861789735359... = 1/0.704442200999....
%t $MaxExtraPrecision = 1200; digits = 99; terms = 1200; P[n_] := PrimeZetaP[n ]; LR = Join[{0, 0}, LinearRecurrence[{-2, 0, 1}, {2, -3, 6}, 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)) \\ _Amiram Eldar_, Mar 15 2021
%Y Cf. A065463, A078077.
%K cons,nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 19 2001
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