A201941 Decimal expansion of x>0 satisfying x^2+x=e^(-x).

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

Offset: 0

Author

Clark Kimberling, Dec 13 2011

Keywords

• nonn
• cons

Comments

See A201936 for a guide to related sequences. The Mathematica program includes a graph.

1/(x+1) is the solution for real valued z in the equations dW(z)/dz=W(z) and 1=z(W(z)+1) where W(z) is the 0 branch of the Lambert W function. - Colin Linzer, Nov 01 2024

Examples

			x=0.444130228823966590585466329490984667...
		

Crossrefs

Cf. A201936.

Programs

Mathematica

a = 1; b = 1; c = 0;
f[x_] := a*x^2 + b*x + c; g[x_] := E^-x
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201941 *)