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%I #5 Mar 30 2012 18:57:53
%S 8,2,5,9,7,9,1,5,6,8,1,1,2,5,0,3,9,4,8,8,2,3,3,9,1,4,2,8,6,7,2,2,3,6,
%T 0,1,9,0,6,3,2,7,9,1,9,7,7,9,5,3,9,2,0,1,5,0,5,3,4,0,9,4,4,3,5,6,2,7,
%U 1,1,5,6,9,7,8,3,4,4,7,2,9,3,8,5,0,2,6,2,0,7,0,6,1,7,2,0,5,5,6
%N Decimal expansion of least x>0 having cos(2*Pi*x)=(cos x)^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=0.825979156811250394882339142867223601906327919779...
%t b = 2 Pi; c = 1; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, .9}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197518 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 16 2011
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