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A246768 Decimal expansion of Sum_{k >= 1} log(1 + 1/2^k), a digital tree search constant. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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.

FORMULA

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

EXAMPLE

0.8688766526585549981531278013138377850925800684998667964...

MATHEMATICA

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 *)

PROG

(PARI) -log(prodinf(n=0, 1-2^(-2*n-1))) \\ Gleb Koloskov, Apr 04 2021

CROSSREFS

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

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Sep 03 2014

STATUS

approved

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Last modified August 2 01:19 EDT 2021. Contains 346408 sequences. (Running on oeis4.)