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%I #20 Jun 27 2023 09:24:11
%S 1,7,6,9,7,5,5,4,9,5,5,6,4,8,0,1,2,8,0,0,5,9,5,6,1,4,5,7,9,0,5,7,8,6,
%T 6,8,3,5,2,2,2,5,1,5,1,3,0,8,8,9,7,8,6,3,0,1,5,5,1,0,1,6,8,9,6,1,4,4,
%U 1,5
%N Decimal expansion of 1 - log(2)/log(-W(-2/e^2)), where W is Lambert's W function.
%C Chang shows that a constant population of n individuals, with ancestors selected uniformly at random, converges in probability to a state where every individual leaves either no current ancestors or else is a common ancestor of all present individuals after k*log_2(n) generations, where k is this constant (see Theorem 2 in Chang link for precise statement).
%H Joseph T. Chang, <a href="http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf">Recent common ancestors of all present-day individuals</a>, Advances in Applied Probability Vol. 31, No. 4 (Dec., 1999), pp. 1002-1026.
%H James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=Fm0hOex4psA">EVERY baby is a ROYAL baby</a>, Numberphile video (2019).
%H Douglas L. T. Rohde, Steve Olson, and Joseph T. Chang, <a href="http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-Article.pdf">Modelling the recent common ancestry of all living humans</a>, Nature Vol. 431, No. 7008 (Sep. 2004), pp. 562-566.
%e 1.769755495564801280059561457905786683522251513088978630155101689614415...
%e A population of 1000 is expected to have identical ancestors after around k*log_2(1000) = 17.6... generations.
%e A population of a million is expected to have identical ancestors after around k*log_2(10^6) = 35.2... generations.
%e A population of a billion is expected to have identical ancestors after around k*log_2(10^9) = 52.9... generations.
%e A population of a trillion is expected to have identical ancestors after around k*log_2(10^12) = 70.5... generations.
%t RealDigits[1 - Log[2]/Log[-ProductLog[-2/E^2]], 10, 120][[1]] (* _Amiram Eldar_, Jun 27 2023 *)
%Y Cf. A106533, A226775.
%K nonn,cons
%O 1,2
%A _Charles R Greathouse IV_, May 07 2019
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