A202324 Decimal expansion of x < 0 satisfying x + 3 = exp(x).

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

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: -2.9475309025422851275901263887139816414...
x > 0:  1.50524149579288336699862443213735394007...
		

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 = 3;
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, -1}, WorkingPrecision -> 110]
RealDigits[r]  (* A202324 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A202325 *)
RealDigits[-3 - LambertW[-Exp[-3]], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)

PARI

solve(x=-3, 0, x+3-exp(x)) \\ Michel Marcus, Nov 09 2017

Formula

Equals -3 - LambertW(-exp(-3)). - G. C. Greubel, Nov 09 2017