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A271780
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Decimal expansion of Product_{p odd prime} 1-2/(p*(p-1)), a constant related to Artin's conjecture in the context of quadratic fields.
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4
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5, 3, 5, 1, 0, 7, 0, 1, 2, 6, 1, 6, 6, 3, 8, 7, 3, 3, 2, 8, 3, 9, 5, 8, 6, 5, 1, 8, 6, 0, 6, 3, 2, 1, 5, 9, 8, 5, 8, 6, 3, 9, 3, 3, 9, 1, 0, 2, 8, 0, 1, 3, 4, 9, 2, 6, 6, 5, 2, 7, 2, 8, 8, 4, 8, 8, 9, 8, 2, 4, 3, 8, 8, 2, 1, 0, 0, 2, 6, 9, 0, 3, 5, 6, 1, 4, 4, 2, 0, 9, 2, 5, 2, 1, 5, 9, 4, 6, 2
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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, Section 2.4 Artin's constant, p. 105.
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LINKS
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FORMULA
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EXAMPLE
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0.5351070126166387332839586518606321598586393391028...
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MATHEMATICA
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digits = 99; $MaxExtraPrecision = 600; m0 = 1000; dm = 100; Clear[s]; LR = LinearRecurrence[{2, 1, -2}, {0, 4, 6}, 2 m0]; r[n_Integer] := LR[[n]];
s[m_] := s[m] = NSum[-r[n] (PrimeZetaP[n] - 1/2^n)/n, {n, 2, m}, NSumTerms -> m0, WorkingPrecision -> 600] // 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(1-2/(p*(p-1)), 1, 3) \\ Amiram Eldar, Mar 11 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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