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%I #12 Feb 27 2013 05:49:46
%S 4,2,4,0,3,1,0,3,9,4,9,0,7,4,0,5,0,4,0,2,6,4,7,2,1,6,9,4,9,9,2,0,9,0,
%T 4,0,0,3,6,6,8,3,1,0,6,6,3,1,5,5,6,3,2,1,4,3,0,3,5,9,0,8,1,7,8,5,1,0,
%U 0,4,1,0,6,1,4,2,3,7,1,1,7,1,7,4,5,9,4,9,0,0,8,6,5,9,7,8,6,1,5,1
%N Decimal expansion of least x>0 having sin(6x)=(sin(2x))^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=0.4240310394907405040264721694992090400...
%t b = 6; c = 2; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .6}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197291 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
%t RealDigits[ ArcTan[ (4-Sqrt[7])/3 ], 10, 100] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 13 2011
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