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A201758 Decimal expansion of the greatest x satisfying -x^2+5=e^x.

%I A201758 #8 Feb 07 2025 16:44:07
%S A201758 1,2,4,1,1,4,2,7,5,8,3,9,9,5,9,7,6,9,3,5,7,2,2,5,1,2,4,4,8,9,7,7,8,8,
%T A201758 7,2,9,5,6,2,5,3,8,9,9,9,3,8,5,7,2,1,6,3,2,1,1,7,4,5,5,9,0,4,6,6,7,3,
%U A201758 3,4,1,2,8,7,1,5,6,0,9,7,6,8,1,4,8,7,1,2,6,0,0,2,0,5,3,6,9,2,2
%N A201758 Decimal expansion of the greatest x satisfying -x^2+5=e^x.
%C A201758 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201758 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201758 least:  -2.21143775884204234489242329233015272...
%e A201758 greatest:  1.2411427583995976935722512448977887...
%t A201758 a = -1; b = 0; c = 5;
%t A201758 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201758 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A201758 r = x /. FindRoot[f[x] == g[x], {x, -2.3, -2.2}, WorkingPrecision -> 110]
%t A201758 RealDigits[r]     (* A201757 *)
%t A201758 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A201758 RealDigits[r]    (* A201758 *)
%Y A201758 Cf. A201741.
%K A201758 nonn,cons
%O A201758 1,2
%A A201758 _Clark Kimberling_, Dec 05 2011