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%I #19 Nov 28 2024 19:10:04
%S 9,3,1,2,6,5,1,8,4,1,6,0,0,0,4,3,3,4,3,8,9,2,3,7,2,0,5,5,5,0,6,7,6,9,
%T 8,2,5,5,8,4,2,3,7,3,4,5,8,7,8,0,1,0,5,9,0,1,6,9,8,7,7,1,5,4,5,9,5,4,
%U 3,3,6,0,2,8,6,8,2,3,8,5,1,5,8,2,5,1,2,8,9,6,4,8,1,0,8,9,5,1,5
%N Decimal expansion of Product_{p prime} (1-1/(p^5-p^4)).
%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.4, p. 105.
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%e 0.93126518416000433438923720555067698...
%t digits = 99; $MaxExtraPrecision = 400; m0 = 1000; dm = 100; Clear[s]; LR = LinearRecurrence[{2, -1, 0, 0, 1, -1}, {0, 0, 0, 0, 5, 6}, 2 m0]; r[n_Integer] := LR[[n]]; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 5, 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^5-p^4)) \\ _Amiram Eldar_, Mar 12 2021
%Y Cf. A005596, A065414, A065415.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 15 2001