A201761 - OEIS

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

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

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

%U 4,6,2,8,2,9,1,2,8,7,6,5,5,1,4,9,7,2,6,1,3,6,8,4,8,2,4,1,3,4,1

%N Decimal expansion of the least x satisfying -x^2+7=e^x.

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

%e least:  -2.6321235606142229538753076713383129343383...

%e greatest:  1.53531760234376586202692372439720620861...

%t a = -1; b = 0; c = 7;

%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, -2.6}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201761 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201762 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 05 2011