A202392 Decimal expansion of the number x satisfying 3x=exp(-x).

2, 5, 7, 6, 2, 7, 6, 5, 3, 0, 4, 9, 7, 3, 6, 7, 0, 4, 2, 8, 2, 9, 1, 6, 2, 0, 1, 6, 2, 6, 0, 9, 7, 7, 9, 0, 9, 0, 9, 6, 9, 2, 6, 4, 7, 5, 0, 3, 2, 0, 4, 4, 9, 1, 5, 3, 3, 9, 5, 1, 1, 4, 4, 0, 6, 6, 3, 1, 9, 1, 2, 9, 2, 7, 5, 2, 0, 4, 3, 7, 2, 4, 5, 9, 6, 3, 9, 8, 8, 7, 9, 3, 4, 1, 0, 0, 2, 5, 0

Offset: 0

Author

Clark Kimberling, Dec 18 2011

Keywords

• nonn
• cons

Comments

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

Examples

			x=0.257627653049736704282916201626097790909692...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for transcendental numbers

Crossrefs

Cf. A202322.

Programs

Mathematica

u = 3; 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, .25, .26}, WorkingPrecision -> 110]
RealDigits[r]  (* A202392 *)
(* other program *)
RealDigits[ ProductLog[1/3], 10, 99] // First (* Jean-François Alcover, Feb 14 2013 *)

PARI

lambertw(1/3) \\ G. C. Greubel, Jun 10 2017