%I
%S 4,0,5,4,1,2,8,9,5,5,4,0,0,0,9,1,7,9,6,9,6,0,8,2,1,7,1,5,3,1,2,4,8,1,
%T 7,2,2,7,5,4,4,8,9,0,5,2,5,2,2,8,5,8,9,2,2,1,7,0,7,1,2,8,7,3,9,0,1,9,
%U 2,8,1,7,9,3,2,9,5,7,2,7,8,2,9,8,5,1,7,6,8,9,3,3,2,2,4,9,1,8,0,8
%N Decimal expansion of least x>0 having sin(x)=(sin 5x)^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=0.04054128955400091796960821715312481722...
%t b = 1; c = 5; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .03, .1}, WorkingPrecision > 100]
%t RealDigits[t] (* A197251 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 12 2011
