A201767 Decimal expansion of the least x satisfying 10 - x^2 = e^x.

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

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:  -3.1555323307963464469323033192658407000...
greatest:  1.87144644984680656529114045650417237...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = -1; b = 0; c = 10;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -4, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.2, -3.1}, WorkingPrecision -> 110]
RealDigits[r]     (* A201767 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.8, 1.9}, WorkingPrecision -> 110]
RealDigits[r]    (* A201768 *)

Extensions

a(93) onwards corrected by Georg Fischer, Aug 03 2021