%I
%S 2,1,0,9,3,5,6,9,9,5,5,7,1,0,1,6,1,2,7,2,3,1,6,9,9,2,4,7,0,5,9,2,5,7,
%T 8,8,4,1,1,5,5,3,0,3,7,9,2,8,2,6,8,5,7,5,2,0,7,4,1,9,9,4,7,4,5,1,5,9,
%U 8,2,6,1,9,7,9,8,1,1,3,6,8,1,5,0,9,9,3,5,7,0,2,0,9,0,6,7,5,4,0
%N Decimal expansion of the least x satisfying x^2+3x+1=e^x.
%C See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%e least: 2.1093569955710161272316992470592578841155...
%e nearest to 0: 0.608989103010165494835043701926011...
%e greatest: 2.99223487205393686509331145278388262181...
%t a = 1; b = 3; c = 2;
%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t Plot[{f[x], g[x]}, {x, 3, 3.1}, {AxesOrigin > {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.1}, WorkingPrecision > 110]
%t RealDigits[r] (* A201897, least *)
%t r = x /. FindRoot[f[x] == g[x], {x, .7, .6}, WorkingPrecision > 110]
%t RealDigits[r] (* A201898, nearest 0 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision > 110]
%t RealDigits[r] (* A201899 greatest *)
%Y Cf. A201741.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Dec 06 2011
