cp's OEIS Frontend

A201938 Decimal expansion of the greatest number x satisfying 2*x^2=e^(-x).

%I A201938 #9 Feb 07 2025 16:44:07
%S A201938 5,3,9,8,3,5,2,7,6,9,0,2,8,2,0,0,4,9,2,1,1,8,0,3,9,0,8,3,6,3,3,3,8,7,
%T A201938 2,0,0,9,3,0,1,3,0,7,9,8,7,4,4,2,7,4,2,8,6,2,7,3,2,2,0,2,7,1,2,1,8,2,
%U A201938 5,4,5,7,5,2,4,9,9,2,0,3,8,2,5,8,3,8,3,8,1,2,2,3,8,6,6,7,2,2,7
%N A201938 Decimal expansion of the greatest number x satisfying 2*x^2=e^(-x).
%C A201938 See A201936 for a guide to related sequences. The Mathematica program includes a graph.
%e A201938 least x:  -2.617866613066812769178978059143202...
%e A201938 greatest negative x:  -1.487962065498177156254...
%e A201938 greatest x:  0.5398352769028200492118039083633...
%t A201938 a = 2; b = 0; c = 0;
%t A201938 f[x_] := a*x^2 + b*x + c; g[x_] := E^-x
%t A201938 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A201938 r = x /. FindRoot[f[x] == g[x], {x, -3, -2}, WorkingPrecision -> 110]
%t A201938 RealDigits[r]  (* A201936 *)
%t A201938 r = x /. FindRoot[f[x] == g[x], {x, -2, -1}, WorkingPrecision -> 110]
%t A201938 RealDigits[r]   (* A201937 *)
%t A201938 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201938 RealDigits[r]   (* A201938 *)
%Y A201938 Cf. A201936.
%K A201938 nonn,cons
%O A201938 0,1
%A A201938 _Clark Kimberling_, Dec 13 2011
%E A201938 Offset corrected by _Georg Fischer_, Aug 10 2021