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

%I A246396 #12 May 17 2025 08:04:32
%S A246396 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 A246396 72,77,78,79,84,85,90,91,96,97,103,104,109,110,115,116,121,122,123,
%U A246396 128,129,134,135,140,141,147,148,153,154,159,160,165,166,167,172
%N A246396 Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) <= 0.
%C A246396 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.)
%C A246396 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 A246396 Clark Kimberling, <a href="/A246396/b246396.txt">Table of n, a(n) for n = 0..1000</a>
%t A246396 z = 400; f[x_] := Cos[x]
%t A246396 Select[Range[0, z], f[#]*f[# + 1] <= 0 &]  (* A062389 *)
%t A246396 Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246393 *)
%t A246396 Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &]  (* A246394 *)
%t A246396 Select[Range[0, z], f[#]*f[# + 1] > 0 &]  (* A246046 *)
%t A246396 Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246395 *)
%t A246396 Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &]  (* A246396 *)
%t A246396 SequencePosition[Table[If[Cos[k]<=0,1,0],{k,200}],{1,1}][[;;,1]] (* _Harvey P. Dale_, Jul 11 2023 *)
%Y A246396 Cf. A062389, A246393, A246046, A246394, A246395.
%K A246396 nonn,easy
%O A246396 0,1
%A A246396 _Clark Kimberling_, Aug 24 2014