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A201937 Decimal expansion of the greatest negative number x satisfying 2*x^2=e^(-x).

%I A201937 #6 Feb 07 2025 16:44:07
%S A201937 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 A201937 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 A201937 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 A201937 Decimal expansion of the greatest negative number x satisfying 2*x^2=e^(-x).
%C A201937 See A201936 for a guide to related sequences. The Mathematica program includes a graph.
%e A201937 least x:  -2.617866613066812769178978059143202...
%e A201937 greatest negative x:  -1.487962065498177156254...
%e A201937 greatest x:  0.5398352769028200492118039083633...
%t A201937 a = 2; b = 0; c = 0;
%t A201937 f[x_] := a*x^2 + b*x + c; g[x_] := E^-x
%t A201937 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A201937 r = x /. FindRoot[f[x] == g[x], {x, -3, -2}, WorkingPrecision -> 110]
%t A201937 RealDigits[r]  (* A201936 *)
%t A201937 r = x /. FindRoot[f[x] == g[x], {x, -2, -1}, WorkingPrecision -> 110]
%t A201937 RealDigits[r]   (* A201937 *)
%t A201937 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201937 RealDigits[r]   (* A201938 *)
%Y A201937 Cf. A201936.
%K A201937 nonn,cons
%O A201937 1,2
%A A201937 _Clark Kimberling_, Dec 13 2011