A277136 Numbers k such that cos(k) > 0 and cos(k+2) > 0.

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

Offset

1,1

Comments

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.

From Robert Israel, Oct 07 2016: (Start)

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)

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Robert Israel, Scatter plot of a(n) - 2*Pi*n/(Pi-2)

Maple

select(t -> floor(t/Pi+1/2)::even and floor((t+2)/Pi+1/2)::even, [$0..1000]); # Robert Israel, Oct 07 2016

Mathematica

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 *)

Prog

(PARI) is(n) = cos(n) > 0 && cos(n+2) > 0 \\ Felix Fröhlich, Oct 14 2016

Crossrefs

Cf. A277137, A277138, A277139, subsequence of A131503.

Cf. A277093.

Sequence in context: A139200 A102181 A103068 * A176821 A070369 A357995

Adjacent sequences: A277133 A277134 A277135 * A277137 A277138 A277139

Keyword

nonn,easy

Author

Clark Kimberling, Oct 01 2016

Status

approved