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Decimal expansion of Product_{p prime} (1-1/(p^5-p^4)).
8

%I #16 Mar 12 2021 03:34:41

%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)).

%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