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%I #5 Mar 30 2012 18:57:53
%S 9,0,6,3,6,2,2,3,6,5,3,8,7,2,1,4,1,7,5,1,9,6,9,1,9,2,2,7,5,8,8,4,6,9,
%T 1,0,3,1,2,0,8,8,7,1,0,3,0,1,9,2,0,1,8,0,4,1,4,4,0,8,9,3,8,8,7,3,7,2,
%U 3,9,2,8,6,2,0,8,5,9,6,8,1,5,6,0,8,2,0,2,8,8,5,2,4,6,7,6,1,3,4
%N Decimal expansion of least x>0 having cos(2*Pi*x)=(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=0.9063622365387214175196919227588469103120887...
%t b = 2 Pi; c = 3; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .9, .91}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197520 *)
%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