%I #8 Feb 07 2025 16:44:07
%S 2,7,4,2,0,5,7,1,9,7,2,5,8,6,5,1,5,9,5,5,1,9,1,6,7,3,7,8,7,9,0,0,2,3,
%T 5,8,5,1,6,8,0,2,5,4,9,1,4,3,6,1,4,1,9,6,5,8,3,5,0,3,4,4,2,5,5,8,2,5,
%U 1,3,3,8,6,4,2,9,5,0,1,5,2,3,3,6,2,7,0,1,5,3,4,1,5,0,7,2,8,0,5
%N Decimal expansion of the number x satisfying x^2+8=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=2.7420571972586515955191673787900235851680254...
%t a = 1; b = 0; c = 8;
%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, 2.7, 2.8}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201747 *)
%Y Cf. A201741.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Dec 05 2011