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%I #31 Apr 21 2021 04:26:12
%S 5,11,12,18,24,30,37,43,49,55,56,62,68,74,81,87,93,99,100,106,112,118,
%T 125,131,137,143,144,150,156,162,169,175,181,187,188,194,200,206,213,
%U 219,225,231,232,238,244,250,257,263,269,275,276,282,288,294,301
%N Numbers k such that cos(k) > 0 and cos(k+2) > 0.
%C Guide to related sequences (a four-way splitting of the positive integers):
%C A277136: cos(k) > 0 and cos(k+2) > 0
%C A277137: cos(k) > 0 and cos(k+2) < 0
%C A277138: cos(k) < 0 and cos(k+2) > 0
%C A277139: cos(k) < 0 and cos(k+2) < 0
%C See A277093 for a related guide involving sines.
%C From _Robert Israel_, Oct 07 2016: (Start)
%C k such that floor(k/Pi + 1/2) and floor((k+2)/Pi + 1/2) are even.
%C The sequence has asymptotic density 1/2 - 1/Pi, so that a(n) ~ 2*Pi*n/(Pi - 2).
%C The scatter plot of a(n) - 2*Pi*n/(Pi-2) shows interesting patterns (see link). (End)
%H Clark Kimberling, <a href="/A277136/b277136.txt">Table of n, a(n) for n = 1..10000</a>
%H Robert Israel, <a href="/A277136/a277136.png">Scatter plot of a(n) - 2*Pi*n/(Pi-2)</a>
%p select(t -> floor(t/Pi+1/2)::even and floor((t+2)/Pi+1/2)::even, [$0..1000]); # _Robert Israel_, Oct 07 2016
%t z = 400; f[x_] := Cos[x];
%t Select[Range[z], f[#] > 0 && f[# + 2] > 0 &] (* A277136 *)
%t Select[Range[z], f[#] > 0 && f[# + 2] < 0 &] (* A277137 *)
%t Select[Range[z], f[#] < 0 && f[# + 2] > 0 &] (* A277138 *)
%t Select[Range[z], f[#] < 0 && f[# + 2] < 0 &] (* A277139 *)
%o (PARI) is(n) = cos(n) > 0 && cos(n+2) > 0 \\ _Felix Fröhlich_, Oct 14 2016
%Y Cf. A277137, A277138, A277139, subsequence of A131503.
%Y Cf. A277093.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Oct 01 2016
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