cp's OEIS Frontend

A201757 Decimal expansion of the least x satisfying -x^2+5=e^x.

%I A201757 #8 Feb 07 2025 16:44:07
%S A201757 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 A201757 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 A201757 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 A201757 Decimal expansion of the least x satisfying -x^2+5=e^x.
%C A201757 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201757 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201757 least:  -2.21143775884204234489242329233015272...
%e A201757 greatest:  1.241142758399597693572251244897788...
%t A201757 a = -1; b = 0; c = 5;
%t A201757 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201757 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A201757 r = x /. FindRoot[f[x] == g[x], {x, -2.3, -2.2}, WorkingPrecision -> 110]
%t A201757 RealDigits[r]    (* A201757 *)
%t A201757 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A201757 RealDigits[r]    (* A201758 *)
%Y A201757 Cf. A201741.
%K A201757 nonn,cons
%O A201757 1,1
%A A201757 _Clark Kimberling_, Dec 05 2011