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%I #25 Apr 30 2021 23:07:26
%S 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,
%T 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,
%U 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
%N Decimal expansion of Sum_{k >= 1} log(1 + 1/2^k), a digital tree search constant.
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020, p. 44.
%F Also equals Sum_{k >= 1} (-1)^(k-1)/(k*(2^k - 1)).
%F A245675 = 1/12 + Pi^2/(6*log(2)^2) - 2*A246768/log(2) = 1.000000000001237...
%F Equals -log(1-P), where P is the Pell constant from A141848. - _Gleb Koloskov_, Apr 04 2021
%e 0.8688766526585549981531278013138377850925800684998667964...
%t digits = 103; NSum[Log[1 + 1/2^k], {k, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> 60] // RealDigits[#, 10, digits]& // First
%t N[-Log[QPochhammer[1/2, 1/4]]] (* _Gleb Koloskov_, Apr 04 2021 *)
%o (PARI) -log(prodinf(n=0, 1-2^(-2*n-1))) \\ _Gleb Koloskov_, Apr 04 2021
%Y Cf. A065442, A065443, A245675.
%Y Cf. A141848. - _Gleb Koloskov_, Apr 04 2021
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Sep 03 2014
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