A201938 Decimal expansion of the greatest number x satisfying 2*x^2=e^(-x).

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

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.

Examples

			least x:  -2.617866613066812769178978059143202...
greatest negative x:  -1.487962065498177156254...
greatest x:  0.5398352769028200492118039083633...
		

Crossrefs

Cf. A201936.

Programs

Mathematica

a = 2; b = 0; c = 0;
f[x_] := a*x^2 + b*x + c; g[x_] := E^-x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3, -2}, WorkingPrecision -> 110]
RealDigits[r]  (* A201936 *)
r = x /. FindRoot[f[x] == g[x], {x, -2, -1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201937 *)
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201938 *)

Extensions

Offset corrected by Georg Fischer, Aug 10 2021