OFFSET
1,3
COMMENTS
See A202320 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = -LambertW(-1, -exp(-2)) - 2. - Vaclav Kotesovec, Jan 09 2014
EXAMPLE
x < 0: -1.841405660436960637846604658012486...
x > 0: 1.1461932206205825852370610285213682...
MATHEMATICA
u = 1; v = 2;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.9, -1.8}, WorkingPrecision -> 110]
RealDigits[r] (* A202320 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r] (* A202321 *)
RealDigits[-ProductLog[-1, -1/E^2] - 2, 10, 99] // First (* Jean-François Alcover, Feb 26 2013 *)
PROG
(PARI) solve(x=1, 2, x+2-exp(x)) \\ Michel Marcus, Nov 09 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 16 2011
STATUS
approved