A332499 Least positive integer k such that tan(n*k)*tan(n*k + k) < 0.

1, 1, 11, 1, 1, 5, 2, 1, 3, 2, 1, 2, 3, 1, 2, 5, 1, 1, 10, 1, 1, 177, 1, 1, 11, 1, 1, 5, 2, 1, 3, 2, 1, 2, 3, 1, 2, 5, 1, 1, 9, 1, 1, 88, 1, 1, 12, 1, 1, 5, 2, 1, 3, 2, 1, 2, 3, 1, 2, 5, 1, 1, 9, 1, 1, 59, 1, 1, 13, 1, 1, 6, 2, 1, 3, 2, 1, 2, 3, 1, 2, 4, 1

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..83.

Example

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

Mathematica

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

Crossrefs

Cf. A327422, A327423, A332488, A332489.

Sequence in context: A010195 A010193 A214679 * A010192 A214326 A105769

Adjacent sequences: A332496 A332497 A332498 * A332500 A332501 A332502

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2020

Status

approved