%I #11 Feb 12 2025 04:58:17
%S 1,8,3,0,7,3,3,4,5,3,2,9,0,8,6,3,5,9,9,2,1,0,2,3,5,9,5,4,7,3,4,1,4,7,
%T 8,8,4,5,3,6,6,7,8,1,2,8,3,2,4,2,1,4,9,5,2,2,9,5,8,1,6,4,2,6,7,1,0,0,
%U 0,8,5,1,1,9,4,6,2,3,6,2,0,3,8,0,5,5,4,6,3,7,8,8,4,3,4,1,1,3,7
%N Decimal expansion of greatest x satisfying x^2 - 2*cos(x) = 4*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200025/b200025.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e least x: -0.42352729471869116185741155509692883402...
%e greatest x: 1.8307334532908635992102359547341478845...
%t a = 1; b = -2; c = 4;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.43, -.42}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200024 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.83, 1.84}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200025 *)
%o (PARI) a=1; b=-2; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 13 2011