A201761 Decimal expansion of the least x satisfying -x^2+7=e^x.

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

Offset: 1

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:  -2.6321235606142229538753076713383129343383...
greatest:  1.53531760234376586202692372439720620861...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = -1; b = 0; c = 7;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.7, -2.6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201761 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201762 *)