A332489 - OEIS

A332489

Least positive integer k such that cos(n*k)*cos(n*k + k) < 0.

1, 2, 1, 2, 1, 5, 2, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 10, 1, 2, 1, 2, 1, 11, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 2, 2, 5, 1, 2, 1, 2, 1, 88, 1, 2, 1, 2, 1, 5, 2, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 9, 1, 2, 1, 2, 1, 13, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 2, 2, 4, 1, 2, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(n) = least positive integer k such that cos(n*k) and cos(n*k + k) have opposite signs.

LINKS

Table of n, a(n) for n=1..85.

EXAMPLE

The signs of cos(6), cos(12), ..., sin(36) are indicated by + + + + + -; that's five +'s followed by -, so that a(6) = 5.

MATHEMATICA

Table[First[Map[Length, Split[Table[Sign[Cos[k n]], {k, 1, 500}]]]], {n, 1, 100}]

CROSSREFS