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%I #55 Jan 16 2020 15:25:33
%S 2,0,3,1,8,7,8,6,9,9,7,9,9,7,9,9,5,3,8,3,8,4,7,9,0,6,2,0,6,2,4,1,9,8,
%T 7,9,1,0,5,4,9,8,7,8,7,5,9,0,5,7,0,3,1,7,5,0,0,2,4,7,7,4,4,1,5,1,9,5,
%U 7,5,0,7,5,9,1,9,0,6,0,2,4,8,8,3,6,2,5,0,3,6,1,6,9,0,7,7,9,6,4,2,9,1,4,6,9
%N The rumor constant: decimal expansion of the number x defined by x*e^(2 - 2*x) = 1.
%H G. C. Greubel, <a href="/A106533/b106533.txt">Table of n, a(n) for n = 0..5000</a>
%H L. Bayon, P. Fortuny Ayuso, J. M. Grau, A. M. Oller-Marcen, M. M. Ruiz, <a href="https://arxiv.org/abs/1706.07185">The Best-or-Worst and the Postdoc problems</a>, arXiv:1706.07185 [math.PR], 2017.
%H L. Bayon, J. Grau, A. M. Oller-Marcen, M. Ruiz, P. M. Suarez, <a href="http://arxiv.org/abs/1603.03928">A variant of the Secretary Problem: the Best or the Worst</a>, arXiv preprint arXiv:1603.03928 [math.PR], 2016.
%H D. J. Daley and D. G. Kendall, <a href="http://dx.doi.org/10.1093/imamat/1.1.42">Stochastic rumours</a>, Journal of the Institute of Mathematics and Its Applications 1:42-55, 1965.
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>.
%H José María Grau Ribas, <a href="https://arxiv.org/abs/1812.09255">A New Proof and Extension of the Odds-Theorem</a>, arXiv:1812.09255 [math.PR], 2018.
%H José María Grau Ribas, <a href="https://doi.org/10.1016/j.spl.2019.108591">An extension of the Last-Success-Problem</a>, Statistics & Probability Letters (2020) Vol. 156, 108591.
%H Brian Hayes, <a href="http://bit-player.org/wp-content/extras/bph-publications/AmSci-2005-05-Hayes-rumours.pdf ">Rumours and Errours</a>, American Scientist, Vol. 93, Nbr. 3, 2005, pp. 207-211.
%F Solution to x*exp(2 - 2*x) = 1 with x not equal to 1.
%F Equals -1/2*LambertW(-2*exp(-2)). - _Vladeta Jovovic_, May 30 2005
%F Constant c satisfies: exp(c*x)/(1-2*c) = Sum_{n>=0} (x + 2*n)^n * exp(-2*n)/n!. - _Paul D. Hanna_, Mar 12 2016
%e c = 0.20318786997997995383847906206241987910549878759057031750024774...
%t RealDigits[ -ProductLog[ -2/E^2]/2, 10, 111][[1]]
%o (PARI) solve(x=0, 0.5, x*exp(2-2*x)-1) \\ _Michel Marcus_, Mar 13 2016
%Y Cf. A007456, A129506, A217900, A217910.
%K cons,nonn
%O 0,1
%A _Robert G. Wilson v_, May 03 2005
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