%I
%S 3,8,0,7,9,8,4,5,0,3,8,6,1,9,1,2,5,4,6,8,0,8,5,5,5,4,4,9,1,1,1,3,6,6,
%T 4,2,2,1,9,3,6,1,3,8,3,2,0,1,4,2,5,8,3,0,4,3,5,5,0,6,7,5,4,8,6,5,9,7,
%U 6,5,7,0,8,0,0,1,4,9,2,9,4,6,2,3,0,4,7,5,5,3,0,0,5,5,5,0,9,9,2
%N Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(x/3)^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=3.80798450386191254680855544911136642219361383...
%t b = Pi/6; c = 1/3; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3.8, 3.9}, WorkingPrecision > 200]
%t RealDigits[t] (* A197417 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 4}]
%Y Cf. A197133.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 14 2011
