A246390 Nonnegative integers k satisfying sin(k) <= 0 and sin(k+1) <= 0.

4, 5, 10, 11, 16, 17, 22, 23, 24, 29, 30, 35, 36, 41, 42, 48, 49, 54, 55, 60, 61, 66, 67, 68, 73, 74, 79, 80, 85, 86, 92, 93, 98, 99, 104, 105, 110, 111, 112, 117, 118, 123, 124, 129, 130, 136, 137, 142, 143, 148, 149, 154, 155, 156, 161, 162, 167, 168, 173

Offset

0,1

Comments

A246388 and A038130 (Beatty sequence for 2*Pi) partition A022844 (Beatty sequence for Pi). Likewise, A054386, the complement of A022844, is partitioned by A246389 and A246390. (See the Mathematica program.)

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ k*n where k = 2*Pi/(Pi-1) = 2.933... by Weyl's equidistribution theorem. - Charles R Greathouse IV, Mar 11 2026

Mathematica

z = 400; f[x_] := Sin[x]
Select[Range[0, z], f[#]*f[# + 1] <= 0 &] (* A022844 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246388 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &] (* A038130 *)
Select[Range[0, z], f[#]*f[# + 1] > 0 &] (* A054386 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246389 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &] (* A246390 *)
SequencePosition[Table[If[Sin[n]<=0, 1, 0], {n, 200}], {1, 1}][[;; , 1]] (* Harvey P. Dale, Apr 02 2023 *)

Prog

(PARI) is(n)=sin(n)<=0 && sin(n+1)<=0 \\ Charles R Greathouse IV, Mar 11 2026
(PARI) is(n)=my(t=n%(2*Pi)); t>=Pi && t<=2*Pi-1 \\ Charles R Greathouse IV, Mar 11 2026

Crossrefs

Cf. A022844, A038130, A054386, A246388, A246389.

Sequence in context: A285135 A037353 A269003 * A047257 A327311 A151735

Adjacent sequences: A246387 A246388 A246389 * A246391 A246392 A246393

Keyword

nonn,easy

Author

Clark Kimberling, Aug 24 2014

Status

approved