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%I #23 Mar 13 2021 10:05:41
%S 8,5,6,5,4,0,4,4,4,8,5,3,5,4,2,1,7,4,4,2,6,1,6,7,9,8,4,1,3,5,9,5,3,8,
%T 8,2,1,6,6,5,7,2,8,0,0,3,1,7,6,5,2,1,4,0,3,2,5,4,8,3,2,1,6,1,6,9,4,3,
%U 1,4,4,9,8,0,3,5,9,8,9,6,3,9,2,8,3,2,3,1,1,3,0,8,2,5,9,2,0,7,1
%N Decimal expansion of Product_{p prime} (1-1/(p^4-p^3)).
%H R. J. Mathar, <a href="http://arxiv.org/abs/0903.2514">Hardy-Littlewood constants embedded into infinite products over all positive integers</a>, arXiv:0903.2514 [math.NT], 2009-2011, constant A_1^(3) table 3.
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%e 0.85654044485354217442616798413595388...
%t digits = 99; $MaxExtraPrecision = 400; m0 = 1000; dm = 100; Clear[s]; LR = LinearRecurrence[{2, -1, 0, 1, -1}, {0, 0, 0, 4, 5, 6}, 2 m0]; r[n_Integer] := LR[[n]]; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 3, m}, NSumTerms -> m0, WorkingPrecision -> 400] // 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 15 2016 *)
%o (PARI) prodeulerrat(1-1/(p^4-p^3)) \\ _Amiram Eldar_, Mar 13 2021
%Y Cf. A005596, A065414, A065416.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 15 2001
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