A201758 Decimal expansion of the greatest x satisfying -x^2+5=e^x.

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

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:  -2.21143775884204234489242329233015272...
greatest:  1.2411427583995976935722512448977887...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = -1; b = 0; c = 5;
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, -2.3, -2.2}, WorkingPrecision -> 110]
RealDigits[r]     (* A201757 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
RealDigits[r]    (* A201758 *)