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%I #5 Mar 30 2012 18:57:53
%S 1,7,9,8,5,9,1,0,3,7,0,2,8,6,9,8,4,4,2,7,7,5,5,7,2,9,2,8,4,5,2,1,6,1,
%T 3,1,1,7,0,8,8,7,0,5,1,1,1,7,5,7,5,5,6,1,5,0,4,0,8,7,1,5,6,4,2,6,4,7,
%U 6,4,6,4,9,7,8,2,0,0,6,9,9,0,1,9,0,4,3,4,6,4,0,4,9,1,3,8,5,3,2
%N Decimal expansion of least x>0 having cos(Pi*x)=(cos 2x)^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=1.79859103702869844277557292845216131170...
%t b = Pi; c = 2; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.7, 1.8}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197516 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]
%Y Cf. A197476.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Oct 16 2011
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