%I
%S 2,8,8,4,4,9,4,1,6,5,1,2,4,6,1,5,2,8,8,3,7,9,4,6,3,5,9,5,7,1,3,8,7,1,
%T 6,3,9,1,5,1,7,5,0,8,6,6,9,3,6,1,0,8,8,2,2,5,7,3,4,3,5,7,8,7,1,6,2,4,
%U 8,9,9,2,1,4,3,4,8,7,3,8,4,5,7,2,3,6,3,2,1,8,0,0,2,2,6,7,0,7,4
%N Decimal expansion of least x > 0 having sin(Pi*x/3) = sin(2*x)^2.
%C The Mathematica program includes a graph. See A197133 for a guide to least x > 0 satisfying sin(b*x) = sin(c*x)^2 for selected b and c.
%e x=0.2884494165124615288379463595713871639151750...
%t b = Pi/3; c = 2; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.2, 0.4}, WorkingPrecision > 200]
%t RealDigits[t] (* A197385 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.2}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 14 2011
