A197481 - OEIS

A197481

Decimal expansion of least x>0 having cos(3x)=(cos(6x))^2.

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

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OFFSET

0,1

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=0..98.

EXAMPLE

x=0.3792479776351518525964832866850027831...

MATHEMATICA

b = 3; c = 6; f[x_] := Cos[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .37, .38}, WorkingPrecision -> 100]