A201746 Decimal expansion of the number x satisfying x^2+7=e^x.

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

			x=2.634989915759347918394747743738596543736254...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 0; c = 7;
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, 2.6, 2.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A201746 *)
RealDigits[x/.FindRoot[x^2+7==E^x,{x,2.6},WorkingPrecision->120],10,120][[1]] (* Harvey P. Dale, Jun 11 2025 *)