A277096 Numbers k such that sin(k) < 0 and sin(k+2) < 0.

4, 10, 16, 22, 23, 29, 35, 41, 48, 54, 60, 66, 67, 73, 79, 85, 92, 98, 104, 110, 111, 117, 123, 129, 136, 142, 148, 154, 155, 161, 167, 173, 180, 186, 192, 198, 199, 205, 211, 217, 224, 230, 236, 242, 243, 249, 255, 261, 268, 274, 280, 286, 287, 293, 299

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) ~ kn, where k = 2/(1-2/Pi) = 5.50387..., by the equidistribution theorem. - Charles R Greathouse IV, Oct 09 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, Aug 03 2019 *)

Prog

(PARI) is(n)=my(x=frac(n/2/Pi)); x>1/2 && x<1-1/Pi \\ Charles R Greathouse IV, Oct 09 2016

Crossrefs

Cf. A277093, A277094, A277095.

Sequence in context: A310514 A190060 A328986 * A043385 A277570 A310515

Adjacent sequences: A277093 A277094 A277095 * A277097 A277098 A277099

Keyword

nonn,easy

Author

Clark Kimberling, Oct 01 2016

Status

approved