A197486 Decimal expansion of least x>0 having cos(4x)=(cos(8x))^2.

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

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=0.284435983226363889447362465013752087396201072...

Mathematica

b = 4; c = 8; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .28, .29}, WorkingPrecision -> 100]
RealDigits[t] (* A197486 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.4}]
RealDigits[ 1/2*ArcTan[ Sqrt[ Root[#^3 - 5#^2 + 19# - 7&, 1]]], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

Crossrefs

Cf. A197476.

Sequence in context: A329661 A373098 A254446 * A086311 A194940 A195920

Adjacent sequences: A197483 A197484 A197485 * A197487 A197488 A197489

Keyword

nonn,cons

Author

Clark Kimberling, Oct 15 2011

Status

approved