A277094 Numbers k such that sin(k) > 0 and sin(k+2) < 0.

2, 3, 8, 9, 14, 15, 20, 21, 27, 28, 33, 34, 39, 40, 46, 47, 52, 53, 58, 59, 64, 65, 71, 72, 77, 78, 83, 84, 90, 91, 96, 97, 102, 103, 108, 109, 115, 116, 121, 122, 127, 128, 134, 135, 140, 141, 146, 147, 152, 153, 159, 160, 165, 166, 171, 172, 178, 179, 184

Offset

1,1

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

Links

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

Formula

a(n) ~ Pi*n 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 *)
Position[Partition[Sin[Range[200]], 3, 1], _?(#[[1]]>0&&#[[3]]<0&), 1, Heads-> False]// Flatten (* Harvey P. Dale, Sep 04 2022 *)

Prog

(PARI) is(n)=my(x=frac(n/(2*Pi))); 1/2-1/Pi<x && x<1/2 \\ Charles R Greathouse IV, Oct 01 2016

Crossrefs

Cf. A277093, A277095, A277096.

Sequence in context: A301917 A327312 A047243 * A099148 A309423 A029787

Adjacent sequences: A277091 A277092 A277093 * A277095 A277096 A277097

Keyword

nonn,easy

Author

Clark Kimberling, Oct 01 2016

Status

approved