A197513 Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/4)^2.

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

Offset

1,1

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=1..99.

Example

x=2.4052337038770365360381128025228272460264...

Mathematica

b = 2; c = Pi/4; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.4, 2.41}, WorkingPrecision -> 110]
RealDigits[t]  (* A197513 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]

Crossrefs

Cf. A197476.

Sequence in context: A221655 A221087 A279580 * A097666 A144810 A300753

Adjacent sequences: A197510 A197511 A197512 * A197514 A197515 A197516

Keyword

nonn,cons

Author

Clark Kimberling, Oct 16 2011

Status

approved