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A197511 Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/2)^2. 2

%I #11 Sep 08 2021 21:17:20

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

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

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

%N Decimal expansion of least x > 0 having cos(2*x) = cos(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=0.63919919283722484044364786615341828833...

%t b = 2; c = Pi/2; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .63, .64}, WorkingPrecision -> 110]

%t RealDigits[t] (* A197511 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]

%Y Cf. A197476.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 15 2011

%E a(98) corrected by _Sean A. Irvine_, Sep 08 2021

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