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

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

Cf. A131503, A246444, A332488, A332499.

Sequence in context: A343593 A224763 A128515 * A119569 A318475 A066083

Adjacent sequences: A332486 A332487 A332488 * A332490 A332491 A332492

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2020

Status

approved