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A200024 Decimal expansion of least x satisfying x^2 - 2*cos(x) = 4*sin(x), negated.

%I A200024 #13 Feb 12 2025 04:58:25
%S A200024 4,2,3,5,2,7,2,9,4,7,1,8,6,9,1,1,6,1,8,5,7,4,1,1,5,5,5,0,9,6,9,2,8,8,
%T A200024 3,4,0,2,6,1,3,5,4,6,3,4,7,0,2,5,0,3,2,6,3,0,0,0,1,8,3,3,2,6,9,9,7,3,
%U A200024 3,7,4,3,5,0,7,9,3,7,1,8,8,5,4,1,2,8,7,9,0,5,6,9,6,1,6,7,8,1,2
%N A200024 Decimal expansion of least x satisfying x^2 - 2*cos(x) = 4*sin(x), negated.
%C A200024 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200024 G. C. Greubel, <a href="/A200024/b200024.txt">Table of n, a(n) for n = 0..10000</a>
%H A200024 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200024 least x:  -0.42352729471869116185741155509692883402...
%e A200024 greatest x: 1.8307334532908635992102359547341478845366...
%t A200024 a = 1; b = -2; c = 4;
%t A200024 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200024 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200024 r = x /. FindRoot[f[x] == g[x], {x, -.43, -.42}, WorkingPrecision -> 110]
%t A200024 RealDigits[r]  (* A200024 *)
%t A200024 r = x /. FindRoot[f[x] == g[x], {x, 1.83, 1.84}, WorkingPrecision -> 110]
%t A200024 RealDigits[r]  (* A200025 *)
%o A200024 (PARI) a=1; b=-2; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200024 Cf. A199949.
%K A200024 nonn,cons
%O A200024 0,1
%A A200024 _Clark Kimberling_, Nov 13 2011
%E A200024 a(87)-a(98) corrected by _G. C. Greubel_, Jun 24 2018