A327140 Numbers k such that cos(2k) > cos(2k+2) > cos(2k+4) < cos(2k+6).

3, 6, 9, 22, 25, 28, 31, 44, 47, 50, 53, 66, 69, 72, 75, 88, 91, 94, 97, 110, 113, 116, 119, 132, 135, 138, 141, 154, 157, 160, 163, 179, 182, 185, 188, 201, 204, 207, 210, 223, 226, 229, 232, 245, 248, 251, 254, 267, 270, 273, 276, 289, 292, 295, 298, 311

Offset: 1

Author

Clark Kimberling, Aug 23 2019

Keywords

• nonn
• easy

Comments

The sequences A327138, A327139, A327140 partition the positive integers.

Examples

			(cos 2, cos 4, ...) = (-0.4, -0.6, 0.9, -0.1, -0.8, ...) approximately, so that the differences, in sign, are - + - - + - - + - - + +, with "+" in places 2,5,8,11,12, ... (A327138), "- +" starting in places 1,4,7,10,13,... (A327139), and "- - +" starting in places 3,6,9,22,25,... (A327140).
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A026309, A246303, A026317, A327138.

Programs

Mathematica

z = 500; f[x_] := f[x] = Cos[2 x]; t = Range[1, z];
Select[t, f[#] < f[# + 1] &]    (* A327138 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A327139 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]   (* A327140 *)