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A217598
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Decimal expansion of the coefficient of asymptotic expression of m(n), the number of multiplicative compositions of n.
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5
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3, 1, 8, 1, 7, 3, 6, 5, 2, 2, 0, 9, 0, 5, 6, 8, 7, 4, 3, 7, 6, 4, 4, 9, 1, 6, 7, 2, 7, 5, 6, 8, 4, 7, 1, 0, 4, 5, 1, 3, 5, 1, 9, 8, 5, 4, 4, 9, 2, 9, 0, 9, 5, 3, 2, 3, 8, 9, 3, 1, 1, 5, 3, 7, 2, 5, 9, 3, 5, 3, 9, 3, 6, 2, 3, 0, 6, 7, 7, 4, 6, 6, 9, 0, 9, 7, 0, 0, 6, 7, 4, 6, 3, 4, 0, 0, 6, 0, 5
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OFFSET
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0,1
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COMMENTS
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Equals -1/(rho * zeta'(rho)), where rho is the root of zeta(rho) = 2 (A107311).
Equals lim_{k->oo} A173382(k)/k^rho. (End)
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 293.
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LINKS
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EXAMPLE
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0.318173652...
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MATHEMATICA
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rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> 100]; RealDigits[-1/(rho*Zeta'[rho])] // First
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PROG
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(PARI) a217598={my(rho=solve(x=1.1, 2, zeta(x)-2)); -1/(rho*zeta'(rho))} \\ Hugo Pfoertner, Oct 16 2020
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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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