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A246393 Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) <= 0.

%I A246393 #9 May 17 2025 03:10:49
%S A246393 1,7,14,20,26,32,39,45,51,58,64,70,76,83,89,95,102,108,114,120,127,
%T A246393 133,139,146,152,158,164,171,177,183,190,196,202,208,215,221,227,234,
%U A246393 240,246,252,259,265,271,278,284,290,296,303,309,315,322,328,334,340
%N A246393 Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) <= 0.
%C A246393 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 A246393 Clark Kimberling, <a href="/A246393/b246393.txt">Table of n, a(n) for n = 0..1000</a>
%t A246393 z = 400; f[x_] := Cos[x]
%t A246393 Select[Range[0, z], f[#]*f[# + 1] <= 0 &]  (* A062389 *)
%t A246393 Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246393 *)
%t A246393 Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &]  (* A246394 *)
%t A246393 Select[Range[0, z], f[#]*f[# + 1] > 0 &]  (* A246046 *)
%t A246393 Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246395 *)
%t A246393 Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &]  (* A246396 *)
%Y A246393 Cf. A062389, A246394, A246046, A246395, A246396, A246388.
%K A246393 nonn,easy
%O A246393 0,2
%A A246393 _Clark Kimberling_, Aug 24 2014