A201751 - OEIS

%I #9 Feb 07 2025 16:44:07

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

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

%U 8,0,0,4,3,3,5,4,6,2,5,1,1,2,1,4,4,0,1,5,4,4,0,8,3,8,5,5,4,1,6

%N Decimal expansion of the least 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

%O 1,2

%A _Clark Kimberling_, Dec 05 2011