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Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) <= 0.
5

%I #7 Aug 26 2014 06:00:53

%S 3,9,15,21,28,34,40,47,53,59,65,72,78,84,91,97,103,109,116,122,128,

%T 135,141,147,153,160,166,172,179,185,191,197,204,210,216,223,229,235,

%U 241,248,254,260,267,273,279,285,292,298,304,311,317,323,329,336,342

%N Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) <= 0.

%C A246388 and A038130 (Beatty sequence for 2*Pi) partition A022844 (Beatty sequence for Pi). Likewise, A054386, the complement of A022844, is partitioned by A246389 and A246390. (See the Mathematica program.)

%H Clark Kimberling, <a href="/A246388/b246388.txt">Table of n, a(n) for n = 0..1000</a>

%t z = 400; f[x_] := Sin[x]

%t Select[Range[0, z], f[#]*f[# + 1] <= 0 &] (* A022844 *)

%t Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &] (* A246388 *)

%t Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &] (* A038130 *)

%t Select[Range[0, z], f[#]*f[# + 1] > 0 &] (* A054386 *)

%t Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &] (* A246389 *)

%t Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &] (* A246390 *)

%Y Cf. A022844, A038130, A054386, A246389, A246390.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Aug 24 2014