%I #9 Apr 10 2021 13:20:45
%S 5,7,8,5,4,8,9,2,5,4,2,5,7,1,8,3,8,3,2,0,4,0,7,3,6,7,3,2,4,8,8,0,2,1,
%T 1,8,2,8,6,8,1,7,0,1,7,9,2,0,6,9,1,2,1,4,6,3,7,8,2,7,3,3,1,7,8,5,0,1,
%U 2,8,6,9,6,2,4,5,6,6,9,4,3,2,0,2,7,2,4,1,7,9,2,6,8,1,8,2,6,9,0
%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=0.57854892542571838320407367324880211828681701...
%t b = 1; c = 3 Pi/2; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .56, .58}, WorkingPrecision -> 110]
%t RealDigits[t] (* A197491 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/3}]
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 15 2011
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