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Nonnegative integers k satisfying sin(k) <= 0 and sin(k+1) <= 0.
3

%I #7 Apr 02 2023 13:50:17

%S 4,5,10,11,16,17,22,23,24,29,30,35,36,41,42,48,49,54,55,60,61,66,67,

%T 68,73,74,79,80,85,86,92,93,98,99,104,105,110,111,112,117,118,123,124,

%U 129,130,136,137,142,143,148,149,154,155,156,161,162,167,168,173

%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="/A246390/b246390.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 *)

%t SequencePosition[Table[If[Sin[n]<=0,1,0],{n,200}],{1,1}][[;;,1]] (* _Harvey P. Dale_, Apr 02 2023 *)

%Y Cf. A022844, A038130, A054386, A246388, A246389.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Aug 24 2014