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%I #8 Apr 10 2021 20:32:02
%S 3,0,8,1,3,7,3,5,9,9,2,8,2,3,2,6,4,6,2,3,1,7,7,0,5,6,9,9,4,5,5,4,1,1,
%T 1,9,3,9,0,5,4,8,4,3,4,9,6,7,8,8,9,4,1,4,9,5,9,3,0,9,7,0,7,6,0,3,0,2,
%U 3,7,2,0,2,2,2,4,8,1,5,5,7,2,2,9,9,5,9,9,0,2,1,0,2,1,6,1,6,9,6
%N Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/3)^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=3.0813735992823264623177056994554111...
%t b = 2; c = Pi/3; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3, 3.1}, WorkingPrecision -> 110]
%t RealDigits[t] (* A197512 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 4}]
%Y Cf. A197476.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 16 2011
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