A201752 Decimal expansion of the greatest x satisfying -x^2+2 = e^x.

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

Offset: 0

Author

Clark Kimberling, Dec 05 2011

Keywords

• nonn
• cons

Comments

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least:  -1.3159737777962901878871773873012710...
greatest:  0.53727444917385660425676298977967...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = -1; b = 0; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
RealDigits[r]    (* A201751 *)
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201752 *)
RealDigits[x/.FindRoot[2-x^2==E^x,{x,5},WorkingPrecision->120],10,120][[1]] (* Harvey P. Dale, May 20 2025 *)