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A201766 Decimal expansion of the greatest x satisfying -x^2+9=e^x.

%I A201766 #8 Feb 07 2025 16:44:07
%S A201766 1,7,6,9,6,0,1,1,0,0,1,9,9,3,5,7,6,8,9,1,8,6,5,9,6,7,7,4,7,1,0,6,7,8,
%T A201766 5,1,9,9,3,5,1,5,9,4,7,9,1,3,4,5,7,5,9,2,4,5,1,3,4,1,4,7,4,3,8,1,3,3,
%U A201766 3,1,5,0,8,9,2,9,8,9,2,9,1,0,0,7,5,8,9,1,5,3,9,3,7,6,1,9,9,2,7
%N A201766 Decimal expansion of the greatest x satisfying -x^2+9=e^x.
%C A201766 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201766 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201766 least:  -2.9916206301281875052379602922929380380...
%e A201766 greatest:  1.76960110019935768918659677471067851...
%t A201766 a = -1; b = 0; c = 9;
%t A201766 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201766 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A201766 r = x /. FindRoot[f[x] == g[x], {x, -2.9, -3.0}, WorkingPrecision -> 110]
%t A201766 RealDigits[r]    (* A201765 *)
%t A201766 r = x /. FindRoot[f[x] == g[x], {x, 1.7, 1.8}, WorkingPrecision -> 110]
%t A201766 RealDigits[r]    (* A201766 *)
%Y A201766 Cf. A201741.
%K A201766 nonn,cons
%O A201766 1,2
%A A201766 _Clark Kimberling_, Dec 05 2011