A201894 Decimal expansion of the number x satisfying x^2 + 2x + 5 = e^x.

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

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

			2.9928845903382044191145349078323342337040238211311...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 2; c = 5;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]    (* A201894 *)

Extensions

a(85) onwards corrected by Georg Fischer, Aug 03 2021