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%I #20 Mar 12 2021 04:01:59
%S 6,9,7,5,0,1,3,5,8,4,9,6,3,6,5,9,0,3,2,8,4,6,7,0,3,5,0,8,2,0,9,2,2,9,
%T 2,4,0,7,3,1,5,3,9,4,6,2,1,4,5,1,5,3,9,5,3,5,4,3,7,8,7,5,2,8,8,6,4,5,
%U 9,1,1,0,5,9,6,0,9,5,5,6,6,6,6,6,1,5,4,8,3,8,5,1,3,0,7,1,8,7,9
%N Decimal expansion of rank 2 Artin constant Product_{p prime} (1-1/(p^3-p^2)).
%H R. J. Mathar, <a href="http://arxiv.org/abs/0903.2514">Hardy-Littlewood constants embedded into infinite products..</a>, arxiv:0903.2514 [math.NT], 2009-2011, variable A_1^(2).
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%H <a href="/index/Ar#Artin">Index entries for sequences related to Artin's conjecture</a>
%e 0.697501358496365903284670350820922924...
%t digits = 99; m0 = 1000; dm = 100; Clear[s]; r[n_] := RootSum[-1 - #^2 + #^3 &, #^n&] - 1; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 3, m}, NSumTerms -> m0, WorkingPrecision -> 300] // Exp; s[m0]; s[m = m0 + dm]; While[RealDigits[s[m], 10, digits][[1]] != RealDigits[s[m - dm], 10, digits][[1]], Print[m]; m = m + dm]; RealDigits[s[m], 10, digits][[1]] (* _Jean-François Alcover_, Apr 14 2016 *)
%o (PARI) prodeulerrat(1-1/(p^3-p^2)) \\ _Amiram Eldar_, Mar 12 2021
%Y Cf. A005596, A065417.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 15 2001
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