%I #13 Jun 24 2018 08:57:32

%S 2,3,7,8,1,2,8,1,6,8,6,7,3,7,6,7,9,8,5,9,6,8,2,0,1,6,6,1,4,7,2,8,8,6,

%T 2,1,5,3,6,6,2,9,9,9,1,5,8,9,3,5,4,1,0,0,2,2,0,8,2,0,2,7,0,8,1,3,7,4,

%U 7,2,2,3,6,2,6,6,4,9,9,0,1,2,4,6,4,8,9,3,9,4,0,0,3,4,4,9,9,2,7

%N Decimal expansion of greatest x satisfying x^2 + 4*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="/A199966/b199966.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: 0.943379571591794622084167020515639838...

%e greatest x: 2.3781281686737679859682016614728862...

%t a = 1; b = 4; c = 4;

%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199965 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 2.37, 2.38}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199966 *)

%o (PARI) a=1; b=4; c=4; solve(x=2, 3, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Nov 12 2011