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A246768
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Decimal expansion of Sum_{k >= 1} log(1 + 1/2^k), a digital tree search constant.
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1
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8, 6, 8, 8, 7, 6, 6, 5, 2, 6, 5, 8, 5, 5, 4, 9, 9, 8, 1, 5, 3, 1, 2, 7, 8, 0, 1, 3, 1, 3, 8, 3, 7, 7, 8, 5, 0, 9, 2, 5, 8, 0, 0, 6, 8, 4, 9, 9, 8, 6, 6, 7, 9, 6, 4, 0, 1, 2, 6, 5, 7, 2, 7, 7, 9, 8, 2, 2, 5, 4, 1, 7, 0, 8, 8, 0, 5, 0, 4, 6, 4, 3, 7, 4, 9, 1, 5, 9, 9, 7, 9, 3, 6, 6, 3, 5, 0, 0, 6, 3, 8, 8, 3
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..102.
Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 44.
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FORMULA
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Also equals Sum_{k >= 1} (-1)^(k-1)/(k*(2^k - 1)).
A245675 = 1/12 + Pi^2/(6*log(2)^2) - 2*A246768/log(2) = 1.000000000001237...
Equals -log(1-P), where P is the Pell constant from A141848. - Gleb Koloskov, Apr 04 2021
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EXAMPLE
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0.8688766526585549981531278013138377850925800684998667964...
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MATHEMATICA
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digits = 103; NSum[Log[1 + 1/2^k], {k, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> 60] // RealDigits[#, 10, digits]& // First
N[-Log[QPochhammer[1/2, 1/4]]] (* Gleb Koloskov, Apr 04 2021 *)
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PROG
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(PARI) -log(prodinf(n=0, 1-2^(-2*n-1))) \\ Gleb Koloskov, Apr 04 2021
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CROSSREFS
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Cf. A065442, A065443, A245675.
Cf. A141848. - Gleb Koloskov, Apr 04 2021
Sequence in context: A282152 A191909 A247559 * A088541 A110214 A305709
Adjacent sequences: A246765 A246766 A246767 * A246769 A246770 A246771
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Jean-François Alcover, Sep 03 2014
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STATUS
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approved
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