A202350 Decimal expansion of x > 0 satisfying e*x + 1 = exp(x).

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

Offset: 1

Author

Clark Kimberling, Dec 17 2011

Keywords

• nonn
• cons

Comments

See A202320 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			1.750786722680146367570014877255332...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A001113, A202320.

Programs

Mathematica

u = E; v = 1;
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, 1.7, 1.8}, WorkingPrecision -> 110]
RealDigits[r]  (* A202350 *)
(* alternate program *)
RealDigits[(-1 - E*ProductLog[-1, -E^(-1-1/E)])/E, 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

Formula

Equals -LambertW(-1, -1/exp(1+1/e)) - 1/e. - Andrea Pinos, Sep 12 2023