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A201759 Decimal expansion of the least x satisfying -x^2+6=e^x.

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