A201749 - OEIS

%I #8 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of the number x satisfying x^2+10=e^x.

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e x=2.918826982306345343651746480540976249949094...

%t a = 1; b = 0; c = 10;

%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x

%t Plot[{f[x], g[x]}, {x, -3, 4}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201749 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 05 2011