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A307715
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Decimal expansion of Sum_{t>0} log((t + 1)/t)^2.
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0
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9, 7, 7, 1, 8, 9, 1, 8, 3, 2, 6, 8, 9, 3, 6, 5, 5, 4, 4, 5, 7, 8, 8, 5, 7, 4, 9, 4, 7, 6, 4, 3, 4, 7, 4, 8, 0, 7, 7, 3, 9, 2, 5, 0, 6, 4, 7, 4, 7, 2, 3, 9, 0, 1, 7, 7, 0, 2, 0, 9, 8, 9, 7, 5, 5, 3, 1, 8, 4, 4, 5, 2, 9, 3, 9, 2, 3, 9, 3, 3, 5, 6, 2, 9, 0, 1, 2, 3, 2, 1, 0, 7, 9, 7, 4, 3, 2, 0, 3, 3, 5, 9, 2, 3, 2
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OFFSET
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0,1
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COMMENTS
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This constant appears in the asymptotic formula of the number of minimal covering systems with exactly n elements (see Theorem 1.1 in Balister, Bollobás, Morris, Sahasrabudhe and Tiba).
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LINKS
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FORMULA
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Equals 2 * Sum_{k>=1} H(k) * (zeta(k+1)-1) / (k+1), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
Equals -Sum_{k>=1} zeta'(2*k) / k. (End)
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EXAMPLE
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0.9771891832689365544578857494764347480773925064747239017702...
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MATHEMATICA
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First[RealDigits[NSum[(Log[(t + 1)/t])^2, {t, 1, Infinity}, NSumTerms -> 100, Method -> {"NIntegrate", "MaxRecursion" -> 10}, WorkingPrecision -> 100]]]
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PROG
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(PARI) sumpos(t=1, log((t + 1)/t)^2) \\ Michel Marcus, Apr 26 2019
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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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