%I #9 Apr 10 2021 15:05:30
%S 4,6,7,4,5,6,3,7,6,3,3,3,3,5,8,1,6,7,5,0,9,6,3,7,3,3,8,0,1,6,9,4,6,7,
%T 0,5,9,7,5,0,8,5,9,6,6,4,0,8,8,4,0,9,3,6,3,9,4,4,0,1,1,2,8,3,5,1,6,4,
%U 6,2,4,2,5,7,1,7,0,2,2,5,2,8,4,3,2,4,7,6,5,9,1,0,7,4,6,8,2,0,2
%N Decimal expansion of least x > 0 having cos(2*Pi*x) = cos(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=0.4674563763333581675096373380169467059750...
%t b = 2*Pi; c = 1; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .46, .47}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197585 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 16 2011
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