A246768 Decimal expansion of Sum_{k >= 1} log(1 + 1/2^k), a digital tree search constant.

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

Offset: 0

Author

Jean-François Alcover, Sep 03 2014

Keywords

• nonn
• cons
• easy

Examples

			0.8688766526585549981531278013138377850925800684998667964...
		

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 44.

Crossrefs

Cf. A065442, A065443, A245675.

Cf. A141848. - Gleb Koloskov, Apr 04 2021

Programs

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 *)

PARI

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

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