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

%I #4 Aug 26 2014 15:33:09

%S 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 69,74,75,81,82,87,88,93,94,99,100,101,106,107,112,113,118,119,125,

%U 126,131,132,137,138,143,144,145,150,151,156,157,162,163,169,170

%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="/A246395/b246395.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, A246394, A246396.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Aug 24 2014