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A201754 Decimal expansion of the greatest x satisfying -x^2+3=e^x.

%I A201754 #8 Feb 07 2025 16:44:07
%S A201754 8,3,4,4,8,6,8,6,5,3,0,8,7,5,8,7,8,6,0,9,1,1,0,1,6,8,0,1,2,7,3,3,7,7,
%T A201754 8,9,8,3,5,7,0,3,0,3,8,0,7,9,9,2,5,9,1,2,5,9,7,5,0,6,4,1,0,8,7,8,7,0,
%U A201754 4,2,2,0,8,0,0,5,2,3,6,6,5,4,6,8,2,1,0,9,5,1,3,5,6,5,6,3,4,6,9
%N A201754 Decimal expansion of the greatest x satisfying -x^2+3=e^x.
%C A201754 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201754 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201754 least:  -1.677232708532537998892701011779421...
%e A201754 greatest:  0.8344868653087587860911016801273...
%t A201754 a = -1; b = 0; c = 3;
%t A201754 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201754 Plot[{f[x], g[x]}, {x, -2, 1}, {AxesOrigin -> {0, 0}}]
%t A201754 r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
%t A201754 RealDigits[r]    (* A201753 *)
%t A201754 r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]
%t A201754 RealDigits[r]    (* A201754 *)
%Y A201754 Cf. A201741.
%K A201754 nonn,cons
%O A201754 0,1
%A A201754 _Clark Kimberling_, Dec 05 2011