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A332489
Least positive integer k such that cos(n*k)*cos(n*k + k) < 0.
2
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.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 21 2020
STATUS
approved