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
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 18 2011
STATUS
approved