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A106533 The rumor constant: decimal expansion of the number x defined by x*e^(2 - 2*x) = 1. 8
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

L. Bayon, P. Fortuny Ayuso, J.M. Grau, A.M. Oller-Marcen, M.M. Ruiz, The Best-or-Worst and the Postdoc problems, arXiv:1706.07185 [math.PR], 2017.

L. Bayon, J. Grau, A. M. Oller-Marcen, M. Ruiz, P. M. Suarez, A variant of the Secretary Problem: the Best or the Worst, arXiv preprint arXiv:1603.03928 [math.PR], 2016.

D. J. Daley and D. G. Kendall, Stochastic rumours, Journal of the Institute of Mathematics and Its Applications 1:42-55, 1965.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 56.

Brian Hayes, Rumours and Errours, American Scientist, Vol. 93, Nbr. 3, 2005, pp. 207-211.

FORMULA

Solution to x*exp(2 - 2*x) = 1 with x not equal to 1.

Equals -1/2*LambertW(-2*exp(-2)). - Vladeta Jovovic, May 30 2005

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

EXAMPLE

c = 0.20318786997997995383847906206241987910549878759057031750024774...

MATHEMATICA

RealDigits[ -ProductLog[ -2/E^2]/2, 10, 111][[1]]

PROG

(PARI) solve(x=0, 0.5, x*exp(2-2*x)-1) \\ Michel Marcus, Mar 13 2016

CROSSREFS

Cf. A007456, A129506, A217900, A217910.

Sequence in context: A241644 A241640 A158449 * A192421 A035223 A035184

Adjacent sequences:  A106530 A106531 A106532 * A106534 A106535 A106536

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, May 03 2005

STATUS

approved

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Last modified November 16 15:42 EST 2018. Contains 317274 sequences. (Running on oeis4.)