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A201755 Decimal expansion of the least x satisfying -x^2+4=e^x.

%I A201755 #8 Feb 07 2025 16:44:07
%S A201755 1,9,6,4,6,3,5,5,9,7,4,8,8,8,6,4,5,0,7,6,2,2,6,5,9,6,9,2,1,1,0,9,7,7,
%T A201755 5,8,8,3,7,5,3,0,7,5,0,6,3,7,9,4,2,2,8,1,1,5,2,1,9,7,9,5,8,3,2,3,5,7,
%U A201755 0,1,6,4,3,2,2,0,8,8,1,3,2,7,7,9,0,4,8,2,1,7,3,5,1,7,0,4,8,3,0
%N A201755 Decimal expansion of the least x satisfying -x^2+4=e^x.
%C A201755 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201755 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201755 least:  -1.96463559748886450762265969211097...
%e A201755 greatest:  1.058006401090636308621387446123...
%t A201755 a = -1; b = 0; c = 4;
%t A201755 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201755 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A201755 r = x /. FindRoot[f[x] == g[x], {x, -2.0, -1.9}, WorkingPrecision -> 110]
%t A201755 RealDigits[r]    (* A201755 *)
%t A201755 r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
%t A201755 RealDigits[r]    (* A201756 *)
%Y A201755 Cf. A201741.
%K A201755 nonn,cons
%O A201755 1,2
%A A201755 _Clark Kimberling_, Dec 05 2011