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%I #10 Feb 27 2013 05:50:12
%S 3,7,9,2,4,7,9,7,7,6,3,5,1,5,1,8,5,2,5,9,6,4,8,3,2,8,6,6,8,5,0,0,2,7,
%T 8,3,1,9,4,9,3,4,7,6,3,4,4,9,8,5,8,4,2,4,0,0,5,0,6,0,8,4,2,2,4,5,3,6,
%U 6,1,1,5,7,8,2,4,2,4,0,5,9,3,2,9,3,4,4,2,6,8,3,9,2,1,4,9,0,9,0
%N Decimal expansion of least x>0 having cos(3x)=(cos(6x))^2.
%C The Mathematica program includes a graph. See A197476 for a guide for the least x>0 satisfying cos(b*x)=(cos(c*x))^2 for selected b and c.
%e x=0.3792479776351518525964832866850027831...
%t b = 3; c = 6; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .37, .38}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197481 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]
%t RealDigits[ 2/3*ArcTan[ Sqrt[ Root[#^3 - 5#^2 + 19# - 7&, 1]]], 10, 100] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 15 2011
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