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A201763 Decimal expansion of the least x satisfying -x^2+8=e^x.

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