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A065478
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Decimal expansion of Product_{p prime} (1 - p/(p^3-1)).
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2
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5, 7, 5, 9, 5, 9, 9, 6, 8, 8, 9, 2, 9, 4, 5, 4, 3, 9, 6, 4, 3, 1, 6, 3, 3, 7, 5, 4, 9, 2, 4, 9, 6, 6, 9, 2, 5, 0, 6, 5, 1, 3, 9, 6, 7, 1, 7, 6, 4, 9, 2, 3, 6, 3, 6, 0, 0, 6, 4, 0, 7, 9, 8, 6, 6, 5, 3, 7, 2, 5, 5, 1, 6, 9, 8, 8, 6, 8, 5, 2, 8, 4, 3, 6, 4, 0, 9, 8, 7, 2, 0, 9, 1, 7, 2, 6, 1, 8
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 106.
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LINKS
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 155.
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EXAMPLE
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0.57595996889294543964316337549249669...
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MATHEMATICA
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$MaxExtraPrecision = 100; m0 = 200; dm = 200; digits = 101; Clear[f]; f[m_] := f[m] = (slog = Normal[Series[Log[1 - p/(p^3 - 1)], {p, Infinity, m}]]; Exp[slog] /. Power[p, n_] -> PrimeZetaP[-n] // N[#, digits+10]&); f[m = m0]; Print[m, " ", f[m]]; f[m = m + dm]; While[Print[m, " ", f[m]]; RealDigits[f[m], 10, digits+5] != RealDigits[f[m - dm], 10, digits+5], m = m + dm]; RealDigits[f[m], 10, digits] // First (* Jean-François Alcover, Sep 15 2015 *)
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PROG
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(PARI) prodeulerrat(1 - p/(p^3-1)) \\ Amiram Eldar, Mar 17 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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