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A087497
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Decimal expansion of Khinchin mean K_{-7}.
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10
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1, 1, 3, 3, 3, 2, 3, 3, 6, 3, 9, 5, 0, 8, 6, 5, 7, 9, 4, 9, 1, 0, 2, 8, 9, 6, 9, 4, 9, 0, 8, 8, 6, 8, 3, 6, 3, 5, 9, 9, 0, 9, 8, 2, 8, 2, 4, 1, 1, 7, 9, 7, 7, 5, 2, 5, 9, 6, 1, 3, 0, 8, 1, 7, 9, 4, 4, 2, 5, 7, 4, 1, 9, 8, 7, 6, 2, 6, 7, 4, 4, 5, 0, 1, 0, 3, 5, 4, 4, 5, 8, 0, 4, 9, 0, 0, 2, 0, 2, 6
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OFFSET
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1,3
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COMMENTS
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Khinchin's constant is K_0.
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LINKS
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EXAMPLE
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1.13332336...
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MATHEMATICA
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m = 7; digits = 100; exactEnd = 1000; f[n_] = -(Log[1 - (1 + n)^(-2)]/(n^m*Log[2])); s[n_] = Series[f[n], {n, Infinity, digits}] // Normal // N[#, digits]&; exactSum = Sum[f[n], {n, 1, exactEnd}] // N[#, digits]&; extraSum = Sum[s[n], {n, exactEnd + 1, Infinity}] // N[#, digits]&; (exactSum + extraSum)^(-1/m) // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 14 2013 *)
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CROSSREFS
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Cf. A002210, A087491, A087492, A087493, A087494, A087495, A087496, A087497, A087498, A087499, A087500.
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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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