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 -exp(1) - lambertw(-exp(-exp(1)). - G. C. Greubel, Nov 09 2017
EXAMPLE
x < 0: -2.64745024204996672072720122214641524...
x > 0: 1.420370118020083458458421283899772980...
MATHEMATICA
u = 1; v = E;
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, -2.7, -2.6}, WorkingPrecision -> 110]
RealDigits[r] (* A202347 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A104689 *)
RealDigits[-E - LambertW[-Exp[-E]], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)
PROG
(PARI) solve(x=-3, 0, exp(x)-exp(1)-x) \\ Michel Marcus, Nov 09 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 17 2011
STATUS
approved