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

%I #5 Aug 26 2014 15:32:53

%S 1,7,14,20,26,32,39,45,51,58,64,70,76,83,89,95,102,108,114,120,127,

%T 133,139,146,152,158,164,171,177,183,190,196,202,208,215,221,227,234,

%U 240,246,252,259,265,271,278,284,290,296,303,309,315,322,328,334,340

%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="/A246393/b246393.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, A246394, A246046, A246395, A246396, A246388.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Aug 24 2014