A202357 Decimal expansion of the number x satisfying e*x = e^(-x).

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

Offset

0,1

Comments

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

References

Heine Halberstam and Hans Egon-Richert, Sieve Methods, Dover Publications (2011). See Theorem 2.1.

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 A360441

Adjacent sequences: A202354 A202355 A202356 * A202358 A202359 A202360

Keyword

nonn,cons

Author

Clark Kimberling, Dec 18 2011

Status

approved