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A271742
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Decimal expansion of Hardy-Littlewood constant C_7 = Product_{p prime > 7} 1/(1-1/p)^7 (1-7/p).
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2
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3, 6, 9, 4, 3, 7, 5, 1, 0, 3, 8, 6, 4, 9, 8, 6, 8, 9, 3, 2, 3, 1, 9, 0, 7, 4, 9, 8, 7, 6, 7, 5, 0, 7, 7, 7, 0, 5, 5, 3, 7, 2, 9, 1, 3, 8, 9, 3, 0, 3, 1, 8, 2, 5, 2, 9, 1, 0, 1, 2, 3, 0, 2, 9, 0, 7, 7, 3, 9, 2, 9, 9, 5, 7, 3, 9, 1, 7, 7, 7, 8, 4, 2, 8, 2, 7, 6, 8, 3, 3, 5, 0, 0, 0, 6, 9, 3, 1, 7
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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 2.1 Hardy-Littlewood Constants, p. 86.
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LINKS
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EXAMPLE
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0.3694375103864986893231907498767507770553729138930318252910123...
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MATHEMATICA
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$MaxExtraPrecision = 1100; digits = 99; terms = 1000; P[n_] := PrimeZetaP[ n] - 1/2^n - 1/3^n - 1/5^n - 1/7^n; LR = Join[{0, 0}, LinearRecurrence[ {8, -7}, {-42, -336}, terms+10]]; r[n_Integer] := LR[[n]]; Exp[ NSum[ r[n]*P[n-1]/(n-1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First
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PROG
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(PARI) prodeulerrat(1/(1-1/p)^7*(1-7/p), 1, 11) \\ 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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