A277093 Numbers k such that sin(k) > 0 and sin(k+2) > 0.

1, 7, 13, 19, 26, 32, 38, 44, 45, 51, 57, 63, 70, 76, 82, 88, 89, 95, 101, 107, 114, 120, 126, 132, 133, 139, 145, 151, 158, 164, 170, 176, 177, 183, 189, 195, 202, 208, 214, 220, 221, 227, 233, 239, 246, 252, 258, 264, 265, 271, 277, 283, 290, 296, 302, 308

Offset

1,2

Comments

Guide to related sequences (a four-way splitting of the natural numbers):

A277093: sin(k) > 0 and sin(k+2) > 0

A277094: sin(k) > 0 and sin(k+2) < 0

A277095: sin(k) < 0 and sin(k+2) > 0

A277096: sin(k) < 0 and sin(k+2) < 0

See A277136 for a related guide involving cosines.

Links

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

Formula

a(n) ~ kn, where k = 2/(1-2/Pi) = 5.50387..., by the equidistribution theorem. - Charles R Greathouse IV, Oct 01 2016

Mathematica

z = 400; f[x_] := Sin[x];
Select[Range[z], f[#] > 0 && f[# + 2] > 0 &] (* A277093 *)
Select[Range[z], f[#] > 0 && f[# + 2] < 0 &] (* A277094 *)
Select[Range[z], f[#] < 0 && f[# + 2] > 0 &] (* A277095 *)
Select[Range[z], f[#] < 0 && f[# + 2] < 0 &] (* A277096 *)
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 *)

Prog

(PARI) is(n)=n%(2*Pi) < Pi-2 \\ Charles R Greathouse IV, Oct 01 2016

Crossrefs

Cf. A277094, A277095, A277096.

Sequence in context: A348932 A184521 A123843 * A004082 A246294 A039281

Adjacent sequences: A277090 A277091 A277092 * A277094 A277095 A277096

Keyword

nonn,easy

Author

Clark Kimberling, Oct 01 2016

Status

approved