%I #9 Oct 09 2016 01:41:50
%S 5,6,11,12,17,18,24,25,30,31,36,37,42,43,49,50,55,56,61,62,68,69,74,
%T 75,80,81,86,87,93,94,99,100,105,106,112,113,118,119,124,125,130,131,
%U 137,138,143,144,149,150,156,157,162,163,168,169,174,175,181,182
%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="/A277095/b277095.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ Pi*n 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 *)
%o (PARI) is(n)=frac(n/2/Pi) > 1-1/Pi \\ _Charles R Greathouse IV_, Oct 09 2016
%Y Cf. A277093, A277094, A277096.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Oct 01 2016