%I
%S 3,0,2,4,0,1,4,5,0,1,1,3,5,2,9,3,7,8,4,7,7,5,5,8,9,6,2,7,7,9,7,3,9,5,
%T 3,5,1,6,5,9,8,2,8,2,8,7,1,3,2,9,0,7,9,1,9,8,7,5,0,3,5,5,4,8,2,6,2,3,
%U 8,2,5,2,4,7,0,6,6,4,3,2,9,4,3,2,4,8,4,3,4,2,4,1,0,3,3,5,6,4,2
%N Decimal expansion of the least x satisfying x^2+4x+3=e^x.
%C See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%e least: 3.024014501135293784775589627797395351659...
%e nearest to 0: 0.79522661386054079889626155638871...
%e greatest: 3.2986275628038651802559413164923413431...
%t a = 1; b = 4; c = 3;
%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t Plot[{f[x], g[x]}, {x, 3.5, 3.5}, {AxesOrigin > {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.0}, WorkingPrecision > 110]
%t RealDigits[r] (* A201924 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .8, .7}, WorkingPrecision > 110]
%t RealDigits[r] (* A201925 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision > 110]
%t RealDigits[r] (* A201926 *)
%Y Cf. A201741.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Dec 06 2011
