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A277136
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Numbers k such that cos(k) > 0 and cos(k+2) > 0.
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5
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5, 11, 12, 18, 24, 30, 37, 43, 49, 55, 56, 62, 68, 74, 81, 87, 93, 99, 100, 106, 112, 118, 125, 131, 137, 143, 144, 150, 156, 162, 169, 175, 181, 187, 188, 194, 200, 206, 213, 219, 225, 231, 232, 238, 244, 250, 257, 263, 269, 275, 276, 282, 288, 294, 301
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OFFSET
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1,1
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COMMENTS
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Guide to related sequences (a four-way splitting of the positive integers):
A277136: cos(k) > 0 and cos(k+2) > 0
A277137: cos(k) > 0 and cos(k+2) < 0
A277138: cos(k) < 0 and cos(k+2) > 0
A277139: cos(k) < 0 and cos(k+2) < 0
See A277093 for a related guide involving sines.
k such that floor(k/Pi + 1/2) and floor((k+2)/Pi + 1/2) are even.
The sequence has asymptotic density 1/2 - 1/Pi, so that a(n) ~ 2*Pi*n/(Pi - 2).
The scatter plot of a(n) - 2*Pi*n/(Pi-2) shows interesting patterns (see link). (End)
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LINKS
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MAPLE
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select(t -> floor(t/Pi+1/2)::even and floor((t+2)/Pi+1/2)::even, [$0..1000]); # Robert Israel, Oct 07 2016
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MATHEMATICA
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z = 400; f[x_] := Cos[x];
Select[Range[z], f[#] > 0 && f[# + 2] > 0 &] (* A277136 *)
Select[Range[z], f[#] > 0 && f[# + 2] < 0 &] (* A277137 *)
Select[Range[z], f[#] < 0 && f[# + 2] > 0 &] (* A277138 *)
Select[Range[z], f[#] < 0 && f[# + 2] < 0 &] (* A277139 *)
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PROG
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(PARI) is(n) = cos(n) > 0 && cos(n+2) > 0 \\ Felix Fröhlich, Oct 14 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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