A201766 - OEIS

%I #5 Mar 30 2012 18:58:03

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

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

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

%N Decimal expansion of the greatest x satisfying -x^2+9=e^x.

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

%e least:  -2.9916206301281875052379602922929380380...

%e greatest:  1.76960110019935768918659677471067851...

%t a = -1; b = 0; c = 9;

%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, -2.9, -3.0}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201765 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.7, 1.8}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201766 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 05 2011