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A201768 Decimal expansion of the greatest x satisfying 10-x^2=e^x.

%I A201768 #8 Feb 07 2025 16:44:07
%S A201768 1,8,7,1,4,4,6,4,4,9,8,4,6,8,0,6,5,6,5,2,9,1,1,4,0,4,5,6,5,0,4,1,7,2,
%T A201768 3,7,6,2,2,9,5,9,5,6,2,1,9,7,0,1,7,6,6,6,4,1,0,2,7,7,0,1,4,1,5,5,0,1,
%U A201768 3,6,6,8,3,3,5,0,0,9,1,5,8,7,5,2,4,9,3,6,5,2,1,0,8,9,4,4,3,4,6
%N A201768 Decimal expansion of the greatest x satisfying 10-x^2=e^x.
%C A201768 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201768 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201768 least:  -3.1555323307963464469323033192658407000...
%e A201768 greatest:  1.87144644984680656529114045650417237...
%t A201768 a = -1; b = 0; c = 10;
%t A201768 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201768 Plot[{f[x], g[x]}, {x, -4, 3}, {AxesOrigin -> {0, 0}}]
%t A201768 r = x /. FindRoot[f[x] == g[x], {x, -3.2, -3.1}, WorkingPrecision -> 110]
%t A201768 RealDigits[r]     (* A201767 *)
%t A201768 r = x /. FindRoot[f[x] == g[x], {x, 1.8, 1.9}, WorkingPrecision -> 110]
%t A201768 RealDigits[r]    (* A201768 *)
%Y A201768 Cf. A201741.
%K A201768 nonn,cons
%O A201768 1,2
%A A201768 _Clark Kimberling_, Dec 05 2011