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%I #5 Mar 30 2012 18:57:53
%S 1,6,5,1,9,5,8,3,1,3,6,2,2,5,0,0,7,8,9,7,6,4,6,7,8,2,8,5,7,3,4,4,4,7,
%T 2,0,3,8,1,2,6,5,5,8,3,9,5,5,9,0,7,8,4,0,3,0,1,0,6,8,1,8,8,8,7,1,2,5,
%U 4,2,3,1,3,9,5,6,6,8,9,4,5,8,7,7,0,0,5,2,4,1,4,1,2,3,4,4,1,1,1
%N Decimal expansion of least x>0 having cos(Pi*x)=(cos x/2)^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=1.6519583136225007897646782857344472038126558395...
%t b = Pi; c = 1/2; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.65, 1.66},
%t WorkingPrecision -> 200]
%t RealDigits[t] (* A197517 *)
%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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