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Least positive integer k such that cos(n*k)*cos(n*k + k) < 0.
2

%I #4 Apr 28 2020 00:18:22

%S 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,

%T 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,

%U 1,13,1,2,1,1,1,3,2,2,1,1,2,2,4,1,2,1

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

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

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

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

%Y Cf. A131503, A246444, A332488, A332499.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Apr 21 2020