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A273556
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Decimal expansion of Rosser's constant.
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0
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8, 3, 2, 4, 2, 9, 0, 6, 5, 6, 6, 1, 9, 4, 5, 2, 7, 8, 0, 3, 0, 8, 0, 5, 9, 4, 3, 5, 3, 1, 4, 6, 5, 5, 7, 5, 0, 4, 5, 4, 4, 5, 3, 1, 8, 0, 7, 7, 4, 1, 7, 0, 5, 3, 2, 4, 0, 8, 9, 3, 9, 9, 1, 2, 9, 6, 0, 3, 4, 7, 0, 7, 1, 3, 9, 4, 8, 1, 1, 4, 2, 4, 2, 1, 9, 1, 6, 2, 7, 2, 2, 5, 0, 4, 6, 3, 8, 1
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OFFSET
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0,1
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COMMENTS
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Named after the American logician and mathematician John Barkley Rosser, Sr. (1907-1989). - Amiram Eldar, Jun 20 2021
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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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FORMULA
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4*C_2/exp(2*EulerGamma), where C_2 is the twin primes constant.
Equals lim_{x->inf} Product_{2 < p <= x} (1-2/p)*log(x)^2.
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EXAMPLE
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0.832429065661945278030805943531465575045445318077417053240893991296...
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MATHEMATICA
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digits = 98; s[n_] := (1/n)*N[Sum[MoebiusMu[d]*2^(n/d), {d, Divisors[n]}], digits + 60]; C2 = (175/256)*Product[(Zeta[n]*(1 - 2^(-n))*(1 - 3^(-n) )*(1 - 5^(-n))*(1 - 7^(-n)))^(-s[n]), {n, 2, digits + 60}];
RealDigits[4*C2/Exp[2*EulerGamma], 10, digits] // First
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PROG
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(PARI) 4 * exp(-2*Euler) * prodeulerrat(1-1/(p-1)^2, 1, 3) \\ 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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