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%I #8 Jan 22 2013 08:23:28
%S 1,1,6,1,5,5,2,1,5,7,9,6,7,2,9,1,0,2,3,9,2,1,4,5,8,8,1,7,5,1,1,9,7,2,
%T 5,3,9,8,6,0,9,3,9,7,5,5,2,5,9,9,7,6,9,7,1,9,7,4,9,1,2,9,4,7,3,6,1,3,
%U 8,5,5,7,9,8,5,8,0,4,6,5,9,7,6,3,1,7,0,0,7,1,0,1,5,6,1,6,5,1,1,4
%N Decimal expansion of least x>0 having sin(6x)=(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=0.11615521579672910239214588175119725398609...
%t b = 6; c = 8; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .1, .3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197296 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]
%Y Cf. A197133.
%K nonn,cons
%O 0,3
%A _Clark Kimberling_, Oct 13 2011