%I #8 Apr 10 2021 20:31:45
%S 6,6,3,4,9,0,0,4,6,0,5,6,6,3,7,3,2,0,7,8,9,8,3,6,1,6,6,9,1,5,1,9,0,2,
%T 1,3,3,2,1,5,0,3,2,7,9,6,4,5,8,6,8,0,6,0,0,9,3,9,2,7,8,8,8,1,7,1,0,9,
%U 3,2,8,4,7,9,2,1,9,4,6,9,2,3,6,6,4,7,1,7,6,8,4,0,2,6,3,8,9,5,1
%N Decimal expansion of least x > 0 having cos(2*x) = cos(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=0.66349004605663732078983616691519021...
%t b = 2; c = Pi; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, .7}, WorkingPrecision -> 110]
%t RealDigits[t] (* A197510 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 15 2011
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