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A276500
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Digital expansion of K_ccf, an analog of Khinchin's constant for centered continued fractions.
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0
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5, 4, 5, 4, 5, 1, 7, 2, 4, 4, 5, 4, 5, 5, 8, 5, 7, 5, 6, 9, 6, 6, 0, 5, 7, 7, 2, 4, 9, 9, 4, 3, 8, 1, 0, 1, 6, 9, 7, 3, 2, 7, 2, 4, 1, 6, 2, 5, 1, 3, 4, 7, 0, 4, 5, 3, 9, 8, 0, 3, 5, 2, 0, 4, 1, 5, 9, 8, 4, 8, 1, 4, 9, 2, 2, 4, 5, 3, 4, 4, 5, 7, 0, 4, 6, 5, 5, 1, 8, 9, 2, 4, 2, 8, 2, 3, 6, 5, 2
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OFFSET
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.8 Khinchin-Lévy constants p. 62.
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LINKS
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EXAMPLE
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5.454517244545585756966057724994381016973272416251347045398035204...
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MATHEMATICA
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digits = 35; n1 = n2 = 25; phi = GoldenRatio; L1 = (phi + 2)/(2 phi); L2 = 1/(2 phi^3); h[n_, x_] := Sum[x^k/k, {k, 1, n - 1}]; LL[N1_, N2_] := Log[3] Log[phi] + Log[2/3] Log[(5 phi + 3)/(5 phi + 2)] + NSum[Log[1 + 1/k] (Log[1 + L1/k] - Log[1 + L2/k]), {k, 3, N1}, WorkingPrecision -> digits + 5] + NSum[((-1)^n/n) Zeta[n, N1 + 1]*(L1^n h[n, 1/L1] + h[n, L1] - L2^n h[n, 1/L2] - h[n, L2]), {n, 2, N2}, WorkingPrecision -> digits + 5]; Kccf = Exp[LL[n1, n2]/Log[phi]]; RealDigits[Kccf, 10, digits][[1]]
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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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