A246396 Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) <= 0.

2, 3, 8, 9, 15, 16, 21, 22, 27, 28, 33, 34, 35, 40, 41, 46, 47, 52, 53, 59, 60, 65, 66, 71, 72, 77, 78, 79, 84, 85, 90, 91, 96, 97, 103, 104, 109, 110, 115, 116, 121, 122, 123, 128, 129, 134, 135, 140, 141, 147, 148, 153, 154, 159, 160, 165, 166, 167, 172

Offset: 0

Author

Clark Kimberling, Aug 24 2014

Keywords

• nonn
• easy

Comments

A246393 and A246394 partition A062389 (the nonhomogeneous Beatty sequence {floor((n-1/2)*Pi)}). Likewise, A246046, the complement of A062389, is partitioned by A246395 and A246396. (See the Mathematica program.)

Conjecture: every term t has at least one neighbor which is equal to t plus or minus one. - Harvey P. Dale, Jul 11 2023

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A062389, A246393, A246046, A246394, A246395.

Programs

Mathematica

z = 400; f[x_] := Cos[x]
Select[Range[0, z], f[#]*f[# + 1] <= 0 &]  (* A062389 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246393 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &]  (* A246394 *)
Select[Range[0, z], f[#]*f[# + 1] > 0 &]  (* A246046 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246395 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &]  (* A246396 *)
SequencePosition[Table[If[Cos[k]<=0,1,0],{k,200}],{1,1}][[;;,1]] (* Harvey P. Dale, Jul 11 2023 *)