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%I #11 Apr 10 2021 20:31:33
%S 4,0,5,7,4,6,6,6,0,7,5,1,2,4,8,2,1,5,1,1,6,0,8,4,7,7,7,0,5,8,3,0,6,9,
%T 0,5,3,2,0,0,0,9,9,3,9,1,6,2,0,4,6,8,7,5,5,3,2,0,7,0,4,0,3,4,6,6,4,6,
%U 2,8,5,6,9,4,4,5,2,2,0,0,8,0,0,4,8,5,5,7,2,3,3,2,0,0,5,7,6,2,9
%N Decimal expansion of least x > 0 having cos(2*x) = cos(2*Pi*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=0.40574666075124821511608477705830690...
%t b = 2; c = 2 Pi; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .5}, WorkingPrecision -> 110]
%t RealDigits[t] (* A197509 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 15 2011
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