A201754 - OEIS

%I #5 Mar 30 2012 18:58:02

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

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

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

%N Decimal expansion of the greatest x satisfying -x^2+3=e^x.

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

%e least:  -1.677232708532537998892701011779421...

%e greatest:  0.8344868653087587860911016801273...

%t a = -1; b = 0; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -2, 1}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201753 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201754 *)

%Y Cf. A201741.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 05 2011