%I
%S 0,4,1,9,6,1,4,0,5,6,7,7,5,6,5,8,5,0,8,5,6,3,0,0,3,6,1,6,5,8,7,5,4,1,
%T 2,3,6,9,2,8,2,8,5,7,1,3,6,7,0,1,3,4,1,4,0,0,9,3,9,3,3,1,9,0,6,1,8,4,
%U 6,7,5,0,3,0,8,5,6,8,4,5,1,2,1,1,7,1,0,2,9,5,9,6,4,7,4,8,9,5,2,3,8
%N Decimal expansion of least x>0 having sin(2x)=(sin 7x)^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=0.0419614056775658508563003616587541236...
%t b = 2; c = 7; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .03, .05}, WorkingPrecision > 100]
%t RealDigits[t] (* A197258 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, .06}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 12 2011
