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A201760 Decimal expansion of the greatest x satisfying -x^2+6 = e^x.

%I A201760 #10 Feb 07 2025 16:44:07
%S A201760 1,3,9,7,7,8,0,5,3,5,4,2,4,1,7,6,8,7,4,1,6,4,6,8,5,4,7,4,6,0,6,2,3,3,
%T A201760 3,6,8,9,4,8,0,7,2,4,1,0,7,6,4,9,2,3,5,6,6,8,8,0,1,4,3,3,1,1,4,7,4,5,
%U A201760 1,6,8,9,1,1,2,4,0,3,2,1,6,3,4,2,4,9,7,5,9,7,5,1,8,6,4,9,5,7,2
%N A201760 Decimal expansion of the greatest x satisfying -x^2+6 = e^x.
%C A201760 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201760 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201760 least:  -2.431479659723036039736539014083415082...
%e A201760 greatest:  1.3977805354241768741646854746062333...
%t A201760 a = -1; b = 0; c = 6;
%t A201760 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201760 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A201760 r = x /. FindRoot[f[x] == g[x], {x, -2.5, -2.4}, WorkingPrecision -> 110]
%t A201760 RealDigits[r]     (* A201759 *)
%t A201760 r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
%t A201760 RealDigits[r]    (* A201760 *)
%Y A201760 Cf. A201741.
%K A201760 nonn,cons
%O A201760 1,2
%A A201760 _Clark Kimberling_, Dec 05 2011