A201764 Decimal expansion of the greatest x satisfying -x^2+8=e^x.

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

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:  -2.8178476944165736893772740965040641282283...
greatest:  1.65826072045249887879638437964645256434...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = -1; b = 0; c = 8;
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, -2.8, -2.9}, WorkingPrecision -> 110]
RealDigits[r]     (* A201763 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
RealDigits[r]    (* A201764 *)