A201896 Decimal expansion of the greatest x satisfying x^2 + 3*x + 1 = e^x.

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

Offset: 1

Author

Clark Kimberling, Dec 06 2011

Keywords

• nonn
• cons

Comments

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least:  -2.649219887767292965348496137953408152796...
greatest:  2.8931164309252712203155349313495308853...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -4, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.7, -2.6}, WorkingPrecision -> 110]
RealDigits[r]     (* A201895 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]     (* A201896 *)  (* NOTE 3 zeros *)

Extensions

a(98) onwards corrected by Georg Fischer, Aug 03 2021