%I #10 Aug 03 2019 19:27:36

%S 4,10,16,22,23,29,35,41,48,54,60,66,67,73,79,85,92,98,104,110,111,117,

%T 123,129,136,142,148,154,155,161,167,173,180,186,192,198,199,205,211,

%U 217,224,230,236,242,243,249,255,261,268,274,280,286,287,293,299

%N Numbers k such that sin(k) < 0 and sin(k+2) < 0.

%C Guide to related sequences (a four-way splitting of the natural numbers):

%C A277093: sin(k) > 0 and sin(k+2) > 0

%C A277094: sin(k) > 0 and sin(k+2) < 0

%C A277095: sin(k) < 0 and sin(k+2) > 0

%C A277096: sin(k) < 0 and sin(k+2) < 0

%H Clark Kimberling, <a href="/A277096/b277096.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ kn, where k = 2/(1-2/Pi) = 5.50387..., by the equidistribution theorem. - _Charles R Greathouse IV_, Oct 09 2016

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

%t Select[Range[z], f[#] > 0 && f[# + 2] > 0 &] (* A277093 *)

%t Select[Range[z], f[#] > 0 && f[# + 2] < 0 &] (* A277094 *)

%t Select[Range[z], f[#] < 0 && f[# + 2] > 0 &] (* A277095 *)

%t Select[Range[z], f[#] < 0 && f[# + 2] < 0 &] (* A277096 *)

%t SequencePosition[Table[If[Sin[n]<0,1,0],{n,400}],{1,_,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 03 2019 *)

%o (PARI) is(n)=my(x=frac(n/2/Pi)); x>1/2 && x<1-1/Pi \\ _Charles R Greathouse IV_, Oct 09 2016

%Y Cf. A277093, A277094, A277095.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Oct 01 2016