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

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]
RealDigits[t] (* A197481 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]
RealDigits[ 2/3*ArcTan[ Sqrt[ Root[#^3 - 5#^2 + 19# - 7&, 1]]], 10, 100] // First (* Jean-François Alcover, Feb 27 2013 *)

Crossrefs

Cf. A197476.

Sequence in context: A090458 A131712 A072845 * A197682 A021729 A198236

Adjacent sequences: A197478 A197479 A197480 * A197482 A197483 A197484

Keyword

nonn,cons

Author

Clark Kimberling, Oct 15 2011

Status

approved