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A201765 Decimal expansion of the least x satisfying 9-x^2=e^x.

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