cp's OEIS Frontend

A246395 Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) >= 0.

%I A246395 #8 May 17 2025 08:04:53
%S A246395 0,5,6,11,12,13,18,19,24,25,30,31,37,38,43,44,49,50,55,56,57,62,63,68,
%T A246395 69,74,75,81,82,87,88,93,94,99,100,101,106,107,112,113,118,119,125,
%U A246395 126,131,132,137,138,143,144,145,150,151,156,157,162,163,169,170
%N A246395 Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) >= 0.
%C A246395 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 A246395 Clark Kimberling, <a href="/A246395/b246395.txt">Table of n, a(n) for n = 0..1000</a>
%t A246395 z = 400; f[x_] := Cos[x]
%t A246395 Select[Range[0, z], f[#]*f[# + 1] <= 0 &]  (* A062389 *)
%t A246395 Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246393 *)
%t A246395 Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &]  (* A246394 *)
%t A246395 Select[Range[0, z], f[#]*f[# + 1] > 0 &]  (* A246046 *)
%t A246395 Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246395 *)
%t A246395 Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &]  (* A246396 *)
%Y A246395 Cf. A062389, A246393, A246046, A246394, A246396.
%K A246395 nonn,easy
%O A246395 0,2
%A A246395 _Clark Kimberling_, Aug 24 2014