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%I #13 Feb 19 2013 09:48:15
%S 1,9,5,0,7,2,1,8,5,4,6,5,2,8,5,4,5,7,6,2,8,6,6,6,5,5,1,8,2,0,4,0,1,1,
%T 5,4,4,6,4,5,0,1,6,3,4,2,9,2,8,2,1,8,2,3,0,8,4,5,4,6,0,2,4,3,6,0,3,5,
%U 8,9,9,8,7,1,5,7,0,7,0,3,3,2,5,1,5,5,4,0,3,5,5,1,6,0,0,0,4,0,8
%N Decimal expansion of least x>0 having sin(x)=(sin(2x/3))^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=1.9507218546528545762866655182040115446450...
%t b = 1; c = 2/3; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.3, 2.6}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197378 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.7}]
%t RealDigits[ 3*ArcCos[Root[1 - 8 #^2 + 16 #^6 &, 4]], 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)
%Y Cf. A197133.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Oct 14 2011
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