A201752 - OEIS

%I #8 Jan 30 2025 10:43:05

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

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

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

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

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least:  -1.3159737777962901878871773873012710...

%e greatest:  0.53727444917385660425676298977967...

%t a = -1; b = 0; c = 2;

%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, -1.4, -1.3}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201751 *)

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

%t RealDigits[r]    (* A201752 *)

%Y Cf. A201741.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Dec 05 2011