OFFSET
1,1
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
Equals -3 - LambertW(-exp(-3)). - G. C. Greubel, Nov 09 2017
EXAMPLE
x < 0: -2.9475309025422851275901263887139816414...
x > 0: 1.50524149579288336699862443213735394007...
MATHEMATICA
u = 1; v = 3;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2, -1}, WorkingPrecision -> 110]
RealDigits[r] (* A202324 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r] (* A202325 *)
RealDigits[-3 - LambertW[-Exp[-3]], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)
PROG
(PARI) solve(x=-3, 0, x+3-exp(x)) \\ Michel Marcus, Nov 09 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 16 2011
STATUS
approved