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A201764 Decimal expansion of the greatest x satisfying -x^2+8=e^x.

%I A201764 #8 Feb 07 2025 16:44:07
%S A201764 1,6,5,8,2,6,0,7,2,0,4,5,2,4,9,8,8,7,8,7,9,6,3,8,4,3,7,9,6,4,6,4,5,2,
%T A201764 5,6,4,3,4,8,2,8,5,7,0,8,4,4,4,2,2,7,3,0,9,1,1,5,4,0,2,8,3,5,2,2,7,6,
%U A201764 1,8,9,0,1,2,8,8,9,4,1,0,6,5,4,4,8,8,5,6,1,7,1,8,5,8,5,8,5,7,3
%N A201764 Decimal expansion of the greatest x satisfying -x^2+8=e^x.
%C A201764 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201764 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201764 least:  -2.8178476944165736893772740965040641282283...
%e A201764 greatest:  1.65826072045249887879638437964645256434...
%t A201764 a = -1; b = 0; c = 8;
%t A201764 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201764 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A201764 r = x /. FindRoot[f[x] == g[x], {x, -2.8, -2.9}, WorkingPrecision -> 110]
%t A201764 RealDigits[r]     (* A201763 *)
%t A201764 r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
%t A201764 RealDigits[r]    (* A201764 *)
%Y A201764 Cf. A201741.
%K A201764 nonn,cons
%O A201764 1,2
%A A201764 _Clark Kimberling_, Dec 05 2011