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A065416
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Decimal expansion of Product_{p prime} (1-1/(p^5-p^4)).
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8
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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, 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, 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
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OFFSET
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0,1
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LINKS
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EXAMPLE
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0.93126518416000433438923720555067698...
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MATHEMATICA
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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 *)
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PROG
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(PARI) prodeulerrat(1-1/(p^5-p^4)) \\ Amiram Eldar, Mar 12 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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