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A271869
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Decimal expansion of Matthews' constant C_3, an analog of Artin's constant for primitive roots.
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1
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0, 6, 0, 8, 2, 1, 6, 5, 5, 1, 2, 0, 3, 0, 5, 0, 8, 6, 0, 0, 5, 6, 3, 2, 2, 7, 5, 4, 6, 1, 9, 2, 0, 8, 5, 5, 4, 3, 1, 3, 3, 7, 3, 7, 3, 4, 7, 5, 7, 6, 7, 9, 4, 1, 9, 8, 2, 6, 4, 3, 4, 0, 3, 1, 5, 0, 4, 0, 8, 0, 4, 3, 5, 0, 7, 2, 1, 2, 5, 6, 1, 6, 9, 5, 8, 6, 1, 8, 8, 8, 7, 3, 4, 8, 5, 8, 6, 6, 2, 4, 6, 8, 7, 3, 4, 0
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OFFSET
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0,2
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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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C_3 = Product_{p prime} 1 - (p^3 - (p - 1)^3)/(p^3*(p - 1)).
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EXAMPLE
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0.0608216551203050860056322754619208554313373734757679419826434...
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MATHEMATICA
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digits = 70; $MaxExtraPrecision = 1000; m0 = 2000; dm = 200; Clear[s]; LR =
LinearRecurrence[{2, 2, -6, 4, -1}, {0, 6, 0, 22, 5}, 2 m0]; r[n_Integer] := LR[[n]]; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 2, m}, NSumTerms -> 2 m0, WorkingPrecision -> digits+10] // 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]; Join[{0}, RealDigits[ s[m], 10, digits][[1]]]
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PROG
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(PARI) prodeulerrat(1 - (p^3 - (p - 1)^3)/(p^3*(p - 1))) \\ Amiram Eldar, Mar 16 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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