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%I #11 Feb 19 2013 07:05:08
%S 2,2,1,4,2,9,7,4,3,5,5,8,8,1,8,1,0,0,6,0,3,4,1,3,0,9,2,0,3,5,7,0,7,4,
%T 0,8,0,1,4,0,0,9,5,2,9,0,8,0,2,8,6,5,2,9,3,3,5,3,0,7,8,4,1,4,8,6,7,4,
%U 2,0,6,7,7,9,5,4,7,2,5,5,8,8,0,2,6,8,3,4,2,5,7,3,7,2,3,4,1,2,8
%N Decimal expansion of least x>0 having sin(x)=(sin x/2)^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=2.2142974355881810060341309203570740...
%t b = 1; c = 1/2; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2, 2.5}, WorkingPrecision -> 200]
%t RealDigits[t] (* *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.5}]
%t RealDigits[ 2*ArcCos[ 1/Sqrt[5] ], 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)
%Y Cf. A197133.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 14 2011
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