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%I #8 Apr 10 2021 22:28:07
%S 5,0,3,6,8,1,8,0,7,6,2,5,6,5,8,3,1,1,1,5,0,3,2,4,8,1,5,7,1,0,4,9,1,4,
%T 5,5,6,6,5,7,0,7,0,6,0,9,9,5,1,3,3,9,8,4,0,9,7,3,8,1,7,2,1,2,8,3,1,5,
%U 0,1,9,9,3,5,3,0,1,9,4,5,9,7,2,9,5,0,2,5,8,6,3,0,2,3,5,0,5,7,2
%N Decimal expansion of least x > 0 having cos(x) = cos(3*Pi*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=0.5036818076256583111503248157104914556657070609...
%t b = 1; c = 3*Pi/2; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .5, .51}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197573 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/4}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 16 2011