cp's OEIS Frontend

A246394 Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) >= 0.

%I A246394 #8 May 17 2025 08:05:49
%S A246394 4,10,17,23,29,36,42,48,54,61,67,73,80,86,92,98,105,111,117,124,130,
%T A246394 136,142,149,155,161,168,174,180,186,193,199,205,212,218,224,230,237,
%U A246394 243,249,256,262,268,274,281,287,293,300,306,312,318,325,331,337,344
%N A246394 Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) >= 0.
%C A246394 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.)
%H A246394 Clark Kimberling, <a href="/A246394/b246394.txt">Table of n, a(n) for n = 0..1000</a>
%t A246394 z = 400; f[x_] := Cos[x]
%t A246394 Select[Range[0, z], f[#]*f[# + 1] <= 0 &]  (* A062389 *)
%t A246394 Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246393 *)
%t A246394 Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &]  (* A246394 *)
%t A246394 Select[Range[0, z], f[#]*f[# + 1] > 0 &]  (* A246046 *)
%t A246394 Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246395 *)
%t A246394 Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &]  (* A246396 *)
%Y A246394 Cf. A062389, A246393, A246046, A246395, A246396.
%K A246394 nonn,easy
%O A246394 0,1
%A A246394 _Clark Kimberling_, Aug 24 2014