A197507 Decimal expansion of least x > 0 having cos(2*x) = cos(3*Pi*x)^2.

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

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=0.3942682585355915905633091545751377409550...

Mathematica

b = 2; c = 3 Pi; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .4}, WorkingPrecision -> 110]
RealDigits[t] (* A197507 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]

Crossrefs

Cf. A197476.

Sequence in context: A130701 A202021 A342220 * A264992 A050000 A154368

Adjacent sequences: A197504 A197505 A197506 * A197508 A197509 A197510

Keyword

nonn,cons

Author

Clark Kimberling, Oct 15 2011

Status

approved