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%I #49 Apr 13 2023 12:06:17
%S 5,0,7,8,3,3,9,2,2,8,6,8,4,3,8,3,9,2,1,8,9,0,4,1,8,4,0,7,2,2,0,7,6,3,
%T 7,4,2,4,6,2,1,8,4,3,3,4,3,2,6,0,0,9,2,9,5,3,6,6,3,9,2,7,5,0,3,5,1,5,
%U 2,2,5,8,0,8,9,7,1,0,8,6,1,8,3,6,9,0,1,5,3,8,5,5,3,5,4,4,0,7,5,4,1,8,8,8,3
%N Decimal expansion of logarithm of A112302.
%H Dawei Lu and Zexi Song, <a href="https://doi.org/10.1016/j.jnt.2015.03.013">Some new continued fraction estimates of the Somos' quadratic recurrence constant</a>, Journal of Number Theory, Volume 155, October 2015, Pages 36-45.
%H Dawei Lu, Xiaoguang Wang, and Ruiqing Xu, <a href="https://doi.org/10.1007/s00025-018-0928-0">Some New Exponential-Function Estimates of the Somos' Quadratic Recurrence Constant</a>, Results in Mathematics (2019) Vol. 74, No. 1, 6.
%H Paul Erdős, Ronald L. Graham, Imre Z. Ruzsa and Ernst G. Straus, <a href="https://doi.org/10.1090/S0025-5718-1975-0369288-3">On the prime factors of C(2n, n)</a>, Mathematics of Computation, Vol. 29, No. 129 (1975), pp. 83-92.
%H Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 183.
%H Yusuke Kobayashi and Ryoga Mahara, <a href="https://doi.org/10.15807/jorsj.66.18">Approximation algorithm for Steiner tree problem with neighbor-induced cost</a>, J. Operations Res. Soc. Japan, (2023) Vol. 66, No. 1, 18-36. See p. 32.
%H Jörg Neunhäuserer, <a href="https://arxiv.org/abs/2006.02882">On the universality of Somos' constant</a>, arXiv:2006.02882 [math.DS], 2020.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SomossQuadraticRecurrenceConstant.html">Somos's Quadratic Recurrence Constant</a>
%H Xu You and Di-Rong Chen, <a href="https://doi.org/10.1016/j.jmaa.2015.12.013">Improved continued fraction sequence convergent to the Somos' quadratic recurrence constant</a>, Mathematical Analysis and Applications, Volume 436, Issue 1, 1 April 2016, Pages 513-520.
%F Sum_{n>=2} log(n)/2^n. - _Jean-François Alcover_, Apr 14 2014
%F Equals Lim_{k -> infinity} (1/k) Sum_{i=1..k} A334074(i)/A334075(i). - _Amiram Eldar_, Apr 14 2020
%F Equals Sum_{n>=1} Lambda(n)/(2^n-1), where Lambda(n) = log(A014963(n)) is the Mangoldt function. - _Amiram Eldar_, Jul 07 2021
%e 0.507833922...
%t First@ RealDigits[-Derivative[1, 0][PolyLog][0, 1/2], 10, 105] (* _Eric W. Weisstein_, edited by _Michael De Vlieger_, Jan 21 2019 *)
%o (PARI) suminf(n=2,log(n)>>n) \\ _Charles R Greathouse IV_, Sep 08 2014
%Y Cf. A014963, A112302, A334074, A334075.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Feb 08 2006
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