A202321 Decimal expansion of x > 0 satisfying x + 2 = exp(x).

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

Offset: 1

Author

Clark Kimberling, Dec 16 2011

Keywords

• nonn
• cons

Comments

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

Examples

			x < 0: -1.841405660436960637846604658012486...
x > 0:  1.1461932206205825852370610285213682...
		

Links

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

Crossrefs

Cf. A202320.

Programs

Mathematica

u = 1; v = 2;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.9, -1.8}, WorkingPrecision -> 110]
RealDigits[r]  (* A202320 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A202321 *)
RealDigits[-ProductLog[-1, -1/E^2] - 2, 10, 99] // First (* Jean-François Alcover, Feb 26 2013 *)

PARI

solve(x=1, 2, x+2-exp(x)) \\ Michel Marcus, Nov 09 2017

Formula

a(n) = -LambertW(-1, -exp(-2)) - 2. - Vaclav Kotesovec, Jan 09 2014