A202323 Decimal expansion of the number x satisfying x+3=exp(-x).

7, 9, 2, 0, 5, 9, 9, 6, 8, 4, 3, 0, 6, 7, 7, 0, 0, 1, 4, 1, 8, 3, 9, 5, 8, 7, 7, 8, 8, 5, 4, 2, 2, 0, 6, 1, 8, 6, 5, 9, 2, 2, 1, 9, 3, 1, 7, 0, 0, 9, 7, 8, 8, 2, 9, 0, 8, 0, 5, 0, 5, 5, 9, 7, 9, 3, 6, 2, 7, 3, 7, 2, 1, 0, 8, 5, 5, 1, 5, 4, 5, 7, 3, 2, 8, 1, 5, 0, 0, 8, 7, 3, 2, 3, 8, 3, 5, 4, 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=-0.7920599684306770014183958778854220...
		

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, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 0.6, 0.7}, WorkingPrecision -> 110]
RealDigits[r] (* A202351 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r] (* A202352 *)
(* other program *)
RealDigits[ ProductLog[E^3] - 3, 10, 99] // First (* Jean-François Alcover, Feb 14 2013 *)

PARI

lambertw(exp(3)) - 3 \\ G. C. Greubel, Jun 10 2017

Extensions

a(97)-a(98) corrected by Jean-François Alcover, Feb 14 2013