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Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) >= 0.
4

%I #4 Aug 26 2014 15:33:02

%S 4,10,17,23,29,36,42,48,54,61,67,73,80,86,92,98,105,111,117,124,130,

%T 136,142,149,155,161,168,174,180,186,193,199,205,212,218,224,230,237,

%U 243,249,256,262,268,274,281,287,293,300,306,312,318,325,331,337,344

%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.)

%H Clark Kimberling, <a href="/A246394/b246394.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 *)

%Y Cf. A062389, A246393, A246046, A246395, A246396.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Aug 24 2014