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A201753 Decimal expansion of the least x satisfying -x^2+3=e^x.

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