A201937 - OEIS

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

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

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

%U 6,8,0,9,4,4,6,2,7,6,8,7,4,4,2,2,8,9,2,0,8,3,0,1,2,0,9,0,1,8,8

%N Decimal expansion of the greatest negative number x satisfying 2*x^2=e^(-x).

%C See A201936 for a guide to related sequences.  The Mathematica program includes a graph.

%e least x:  -2.617866613066812769178978059143202...

%e greatest negative x:  -1.487962065498177156254...

%e greatest x:  0.5398352769028200492118039083633...

%t a = 2; b = 0; c = 0;

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

%t Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -3, -2}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A201936 *)

%t r = x /. FindRoot[f[x] == g[x], {x, -2, -1}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201937 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201938 *)

%Y Cf. A201936.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 13 2011