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A202357 Decimal expansion of the number x satisfying e*x = e^(-x). 10
2, 7, 8, 4, 6, 4, 5, 4, 2, 7, 6, 1, 0, 7, 3, 7, 9, 5, 1, 0, 9, 3, 5, 8, 7, 3, 9, 0, 2, 2, 9, 8, 0, 1, 5, 5, 4, 3, 9, 4, 7, 7, 4, 8, 8, 6, 1, 9, 7, 4, 5, 7, 6, 5, 4, 5, 3, 1, 7, 8, 1, 0, 5, 5, 3, 5, 0, 2, 9, 3, 7, 5, 4, 5, 9, 9, 4, 9, 8, 9, 8, 1, 9, 2, 0, 4, 9, 8, 4, 2, 8, 1, 1, 2, 9, 9, 4, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A202322 for a guide to related sequences.  The Mathematica program includes a graph.

LINKS

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

W. Gautschi, The incomplete Gamma Function since Tricomi, Atti Conv. Lincei 147 (1999) 203, eq. (2.16)

H. J. H. Tuenter, On the generalized Poisson distribution, arXiv:math/0606238 [math.ST], 2006. Published version on On the Generalized Poisson Distribution, Statistica Neerlandica, 54(3):374-376, November 2000.

S. M. Zemyan, On the zeros of the Nth partial sum of the exponential series, Am. Math. Monthly 112 (2005) 891-909.

FORMULA

The constant in A202355 minus 1. - R. J. Mathar, Dec 21 2011

1+x+log(x)=0. - R. J. Mathar, Nov 02 2012

Equals LambertW(exp(-1)). - Vaclav Kotesovec, Jan 10 2014

EXAMPLE

x=0.2784645427610737951093587390229801554394774886...

MATHEMATICA

u = E; v = 0;

f[x_] := u*x + v; g[x_] := E^-x

Plot[{f[x], g[x]}, {x, 0, 1}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, .27, .28}, WorkingPrecision -> 110]

RealDigits[r]  (* A202357 *)

RealDigits[ ProductLog[1/E], 10, 99] // First (* Jean-François Alcover, Feb 14 2013 *)

RealDigits[LambertW[Exp[-1]], 10, 120][[1]] (* Harvey P. Dale, Dec 24 2019 *)

PROG

(PARI) lambertw(exp(-1)) \\ Michel Marcus, Mar 21 2016

CROSSREFS

Cf. A202322, A215077, A218300.

Sequence in context: A102098 A316252 A202355 * A334378 A329406 A019731

Adjacent sequences:  A202354 A202355 A202356 * A202358 A202359 A202360

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 18 2011

STATUS

approved

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Last modified December 7 06:09 EST 2021. Contains 349567 sequences. (Running on oeis4.)