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%I #8 Jan 22 2013 05:26:46
%S 0,1,5,7,0,6,8,4,9,5,3,1,6,2,0,0,6,5,0,5,8,1,7,7,0,3,0,2,0,8,5,2,6,0,
%T 3,6,3,9,0,0,4,1,7,7,4,8,8,0,0,3,1,2,6,3,1,0,8,5,0,9,0,7,6,7,8,4,2,7,
%U 2,2,6,1,5,7,2,8,2,6,5,4,9,2,5,7,5,8,5,7,0,8,2,0,4,1,2,7,0,4,4,9,0
%N Decimal expansion of least x>0 having sin(x)=(sin 8x)^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=0.0157068495316200650581770302085260363...
%t b = 1; c = 8; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .01, .1}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197254 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.05}]
%Y Cf. A197133.
%K nonn,cons
%O 0,3
%A _Clark Kimberling_, Oct 12 2011
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