A197506 - OEIS

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A197506

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

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

x=1.101969565544068669496912835886267221998...

MATHEMATICA

b = 1; c = 2 Pi/3; f[x_] := Cos[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.1, 1.2}, WorkingPrecision -> 110]