A246299 Numbers k such that sin(k) > sin(k+1) > sin(k+2) > sin(k+3) < sin(k+4).

2, 8, 14, 21, 27, 33, 39, 46, 52, 58, 65, 71, 77, 83, 90, 96, 102, 109, 115, 121, 127, 134, 140, 146, 153, 159, 165, 171, 178, 184, 190, 196, 203, 209, 215, 222, 228, 234, 240, 247, 253, 259, 266, 272, 278, 284, 291, 297, 303, 310, 316, 322, 328, 335, 341

Offset: 1

Author

Clark Kimberling, Aug 21 2014

Keywords

• nonn
• easy

Comments

The sequences A026309, A246297, A246298, A246299 partition the nonnegative integers.

Numbers like 20, 64, 108, 152, 177, 221, 265, 309, ... are in none of these 4 sequences. - R. J. Mathar, May 18 2020

Links

• R. J. Mathar, Table of n, a(n) for n = 1..987

Crossrefs

Cf. A026309, A246297, A246298, A246293 (complement of A026309).

Programs

Mathematica

z = 500; f[x_] := f[x] = Sin[x]; t = Range[0, z];
Select[t, f[#] < f[# + 1] &]  (* A026309 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A246297 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]  (* A246298 *)
Select[t, f[#] > f[# + 1] > f[# + 2] > f[# + 3] < f[# + 4] &] (* A246299 *)
Position[Partition[Table[Sin[n],{n,400}],5,1],?(#[[1]]>#[[2]]>#[[3]]>#[[4]]<#[[5]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, May 13 2023 *)

Extensions

Corrected signs in NAME. - R. J. Mathar, May 18 2020