A246298 -id:A246298 - cp's OEIS frontend

A026309 a(n) = n-th nonnegative integer k satisfying sin(k) < sin(k+1).

0, 1, 5, 6, 7, 11, 12, 13, 17, 18, 19, 24, 25, 26, 30, 31, 32, 36, 37, 38, 42, 43, 44, 45, 49, 50, 51, 55, 56, 57, 61, 62, 63, 68, 69, 70, 74, 75, 76, 80, 81, 82, 86, 87, 88, 89, 93, 94, 95, 99, 100, 101, 105, 106, 107, 112, 113, 114, 118

Offset: 1

Clark Kimberling

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

Clark Kimberling, Table of n, a(n) for n = 1..4000

Cf. A246297, A246298, A246299, A246293 (complement of A026309).

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 *)

a(n) ~ 2n by the Equidistribution Theorem. - Charles R Greathouse IV, Dec 11 2024

Comment, Mathematica, and Crossrefs by Clark Kimberling, Aug 21 2014

A246297 Numbers k such that sin(k) > sin(k+1) < sin(k+2).

Original entry on oeis.org

4, 10, 16, 23, 29, 35, 41, 48, 54, 60, 67, 73, 79, 85, 92, 98, 104, 111, 117, 123, 129, 136, 142, 148, 155, 161, 167, 173, 180, 186, 192, 198, 205, 211, 217, 224, 230, 236, 242, 249, 255, 261, 268, 274, 280, 286, 293, 299, 305, 312, 318, 324, 330, 337, 343

Offset: 1

Clark Kimberling, Aug 21 2014

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

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

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A026309, A246298, A246299, A246293 (complement of A026309).

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 *)

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

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

Original entry on oeis.org

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

Clark Kimberling, Aug 21 2014

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

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

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

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 *)

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

cp's OEIS Frontend

A026309 a(n) = n-th nonnegative integer k satisfying sin(k) < sin(k+1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A246297 Numbers k such that sin(k) > sin(k+1) < sin(k+2).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions