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%I #10 Jun 02 2018 18:19:02
%S 1,7,13,19,26,32,38,44,45,51,57,63,70,76,82,88,89,95,101,107,114,120,
%T 126,132,133,139,145,151,158,164,170,176,177,183,189,195,202,208,214,
%U 220,221,227,233,239,246,252,258,264,265,271,277,283,290,296,302,308
%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
%C See A277136 for a related guide involving cosines.
%H Clark Kimberling, <a href="/A277093/b277093.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 01 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_, Jun 02 2018 *)
%o (PARI) is(n)=n%(2*Pi) < Pi-2 \\ _Charles R Greathouse IV_, Oct 01 2016
%Y Cf. A277094, A277095, A277096.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Oct 01 2016
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