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%I #7 Dec 05 2018 17:37:48
%S 3,2,2,6,4,7,7,6,3,7,7,3,4,2,4,5,9,2,6,8,1,3,8,9,6,3,4,5,6,9,9,0,8,0,
%T 9,6,5,6,1,4,9,7,0,7,3,3,5,5,0,9,3,5,7,2,3,5,6,8,7,3,3,1,4,7,4,6,2,0,
%U 8,2,0,4,1,8,1,6,7,0,3,1,6,7,3,1,3,9,0,3,7,4,6,7,0,1,3,1,1,5,4
%N Decimal expansion of least x>0 having cos(3*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=0.3226477637734245926813896345699080965614970733550...
%t b = 3*Pi; c = 1; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .32, .33}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197586 *)
%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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