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Decimal expansion of Product_{p prime} (1 + 1/(p^2-p-1)).
6

%I #15 Feb 10 2022 06:01:18

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

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

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

%N Decimal expansion of Product_{p prime} (1 + 1/(p^2-p-1)).

%C This is 1/Artin's constant, see A005596.

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

%e 2.67411272557002150896041183...

%t $MaxExtraPrecision = 1200; digits = 99; terms = 1200; P[n_] := PrimeZetaP[n ]; LR = Join[{0, 0}, LinearRecurrence[{2, 0, -1}, {2, 3, 6}, term+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. A005596, A048296, A351219.

%K cons,nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 19 2001