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A197494 Decimal expansion of least x>0 having cos(x)=(cos(Pi*x/3))^2. 2

%I

%S 1,5,6,6,0,2,3,6,1,3,6,2,2,2,8,9,7,0,2,3,0,3,8,2,0,8,2,3,9,4,8,9,4,6,

%T 1,1,0,5,0,0,2,3,7,1,8,4,2,4,8,4,9,7,1,8,2,1,8,6,5,9,9,3,4,1,5,9,8,6,

%U 8,2,4,0,3,9,2,3,5,2,3,3,2,6,4,2,1,9,4,2,2,7,2,3,3,1,9,9,4,8,2

%N Decimal expansion of least x>0 having cos(x)=(cos(Pi*x/3))^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=1.566023613622289702303820823948946110500...

%t b = 1; c = Pi/3; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.5, 1.6}, WorkingPrecision -> 110]

%t RealDigits[t] (* A197494 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]

%Y Cf. A197476.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 15 2011

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Last modified October 16 20:23 EDT 2019. Contains 328103 sequences. (Running on oeis4.)