A201757 - OEIS

%I #8 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of the least x satisfying -x^2+5=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:  -2.21143775884204234489242329233015272...

%e greatest:  1.241142758399597693572251244897788...

%t a = -1; b = 0; c = 5;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -2.3, -2.2}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201757 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201758 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 05 2011