%I #8 Jul 11 2023 11:28:37

%S 2,3,8,9,15,16,21,22,27,28,33,34,35,40,41,46,47,52,53,59,60,65,66,71,

%T 72,77,78,79,84,85,90,91,96,97,103,104,109,110,115,116,121,122,123,

%U 128,129,134,135,140,141,147,148,153,154,159,160,165,166,167,172

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

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

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

%H Clark Kimberling, <a href="/A246396/b246396.txt">Table of n, a(n) for n = 0..1000</a>

%t z = 400; f[x_] := Cos[x]

%t Select[Range[0, z], f[#]*f[# + 1] <= 0 &] (* A062389 *)

%t Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &] (* A246393 *)

%t Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &] (* A246394 *)

%t Select[Range[0, z], f[#]*f[# + 1] > 0 &] (* A246046 *)

%t Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &] (* A246395 *)

%t Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &] (* A246396 *)

%t SequencePosition[Table[If[Cos[k]<=0,1,0],{k,200}],{1,1}][[;;,1]] (* _Harvey P. Dale_, Jul 11 2023 *)

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

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Aug 24 2014