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%I #8 Jan 22 2013 08:23:37
%S 1,6,4,5,6,3,8,0,7,2,7,9,3,5,6,6,8,7,8,2,4,4,0,5,9,7,8,5,5,1,8,8,8,5,
%T 7,9,0,0,9,1,1,9,6,3,4,1,0,0,0,7,3,6,1,0,7,9,2,9,5,0,9,5,0,8,8,4,4,0,
%U 9,3,4,1,6,0,9,4,4,5,6,1,0,1,3,6,4,0,0,3,9,6,2,5,2,7,9,2,1,8,4,1
%N Decimal expansion of least x>0 having sin(6x)=(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=0.164563807279356687824405978551888579009...
%t b = 6; c = 7; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .15, .2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197295 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 13 2011
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