A201754 Decimal expansion of the greatest x satisfying -x^2+3=e^x.

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

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:  -1.677232708532537998892701011779421...
greatest:  0.8344868653087587860911016801273...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = -1; b = 0; c = 3;
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, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201753 *)
r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]
RealDigits[r]    (* A201754 *)