%I
%S 2,4,0,3,4,7,6,9,7,8,9,9,9,9,2,5,2,2,5,4,5,1,2,9,6,4,6,3,2,4,8,1,1,8,
%T 3,1,0,8,3,7,9,2,0,0,5,2,9,0,9,6,8,0,9,5,2,8,3,5,5,5,5,7,2,2,5,3,4,8,
%U 5,7,9,3,2,2,9,5,8,4,4,3,5,5,2,3,2,9,9,5,9,4,6,7,9,3,2,7,9,3,5
%N Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/6)^2.
%C The Mathematica program includes a graph. See A197476 for a guide for the least x > 0 satisfying cos(b*x) = cos(c*x)^2 for selected b and c.
%e x=2.40347697899992522545129646324811831083...
%t b = 2; c = Pi/6; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.4, 2.41}, WorkingPrecision > 110]
%t RealDigits[t] (* A197514 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]
%Y Cf. A197476.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 16 2011
