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%I #16 Sep 08 2021 21:37:37
%S 5,0,6,2,9,7,8,9,9,2,3,4,0,5,9,8,2,6,7,5,0,0,1,1,5,6,2,7,8,3,6,9,7,0,
%T 3,2,5,2,8,6,5,8,1,6,3,9,5,8,2,8,9,4,7,4,1,9,1,4,3,2,4,7,4,1,1,1,0,7,
%U 6,9,2,2,7,8,9,7,5,3,6,7,6,3,4,2,8,4,5
%N Decimal expansion of least x > 0 having cos(2*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=0.50629789923405982675001156278369703252865816395828...
%t b = 2; c = 3 Pi/2; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .5, .51}, WorkingPrecision -> 110]
%t RealDigits[t] (* A197508 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 15 2011
%E a(87) onward corrected by _Sean A. Irvine_, Sep 08 2021
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