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%I #5 Mar 30 2012 18:57:52
%S 6,8,1,0,8,9,8,1,8,2,4,2,8,7,4,0,0,6,1,8,5,0,5,2,8,1,6,3,2,7,8,2,8,5,
%T 2,4,9,2,5,1,8,5,8,5,6,2,5,7,5,2,2,5,5,9,6,2,2,9,7,5,8,1,5,4,8,1,2,3,
%U 5,4,3,9,3,2,9,2,9,2,8,1,4,2,2,6,5,5,2,2,7,3,7,8,6,5,8,3,2,1,0
%N Decimal expansion of least x>0 having cos(2x)=(cos 3x)^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=0.681089818242874006185052816327828524925...
%t b = 2; c = 3; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, .8}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197479 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 15 2011
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