A026311 -id:A026311 - cp's OEIS frontend

A246303 Numbers k such that cos(k) < cos(k+1).

3, 4, 5, 9, 10, 11, 12, 16, 17, 18, 22, 23, 24, 28, 29, 30, 35, 36, 37, 41, 42, 43, 47, 48, 49, 53, 54, 55, 56, 60, 61, 62, 66, 67, 68, 72, 73, 74, 79, 80, 81, 85, 86, 87, 91, 92, 93, 97, 98, 99, 100, 104, 105, 106, 110, 111, 112, 116, 117, 118, 123, 124

Offset: 1

Clark Kimberling, Aug 22 2014

The sequences A246303, A246304, A246305, A246306 partition the nonnegative integers.

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

Cf. A026304, A246305, A246306, A026311 (complement of A246303).

z = 500; f[x_] := f[x] = Cos[x]; t = Range[0, z];
Select[t, f[#] < f[# + 1] &]  (* A246303 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A246304 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]  (* A246305 *)
Select[t, f[#] > f[# + 1] > f[# + 2] > f[# + 3] < f[# + 4] &] (* A246306 *)

A246300 Numbers k such that cos(k) < cos(k+1) > cos(k+2).

Original entry on oeis.org

5, 12, 18, 24, 30, 37, 43, 49, 56, 62, 68, 74, 81, 87, 93, 100, 106, 112, 118, 125, 131, 137, 144, 150, 156, 162, 169, 175, 181, 187, 194, 200, 206, 213, 219, 225, 231, 238, 244, 250, 257, 263, 269, 275, 282, 288, 294, 301, 307, 313, 319, 326, 332, 338, 345

Offset: 1

Clark Kimberling, Aug 22 2014

The sequences A026311, A246300, A246301, A246302 partition the nonnegative integers.

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

Cf. A246294, A026311, A246301, A246302.

z = 520; f[x_] := f[x] = Cos[x]; t = Range[0, z];
Select[t, f[#] > f[# + 1] &]  (* A026311 *)
Select[t, f[#] < f[# + 1] > f[# + 2] &]  (* A246300 *)
Select[t, f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (* A246301 *)
Select[t, f[#] < f[# + 1] < f[# + 2] < f[# + 3] > f[# + 4] &] (* A246302 *)
Flatten[Position[Partition[Cos[Range[350]],3,1],?(#[[1]]<#[[2]]>#[[3]]&),1,Heads->False]] (* _Harvey P. Dale, Jan 20 2025 *)

A246301 Numbers k such that cos(k) < cos(k+1) < cos(k+2) > cos(k+3).

Original entry on oeis.org

4, 11, 17, 23, 29, 36, 42, 48, 55, 61, 67, 73, 80, 86, 92, 99, 105, 111, 117, 124, 130, 136, 143, 149, 155, 161, 168, 174, 180, 186, 193, 199, 205, 212, 218, 224, 230, 237, 243, 249, 256, 262, 268, 274, 281, 287, 293, 300, 306, 312, 318, 325, 331, 337, 344

Offset: 1

Clark Kimberling, Aug 22 2014

The sequences A026311, A246300, A246301, A246302 partition the nonnegative integers.

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

Cf. A026311, A246300, A246302, A246295.

z = 520; f[x_] := f[x] = Cos[x]; t = Range[0, z];
Select[t, f[#] > f[# + 1] &]  (* A026311 *)
Select[t, f[#] < f[# + 1] > f[# + 2] &]  (* A246300 *)
Select[t, f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (* A246301 *)
Select[t, f[#] < f[# + 1] < f[# + 2] < f[# + 3] > f[# + 4] &] (* A246302 *)

A246302 Numbers k such that cos(k) < cos(k+1) < cos(k+2) < cos(k+3) > cos(k+4).

Original entry on oeis.org

3, 10, 16, 22, 28, 35, 41, 47, 54, 60, 66, 72, 79, 85, 91, 98, 104, 110, 116, 123, 129, 135, 142, 148, 154, 160, 167, 173, 179, 185, 192, 198, 204, 211, 217, 223, 229, 236, 242, 248, 255, 261, 267, 273, 280, 286, 292, 299, 305, 311, 317, 324, 330, 336, 343

Offset: 1

Clark Kimberling, Aug 22 2014

The sequences A026311, A246300, A246301, A246302 partition the nonnegative integers.

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

Cf. A026311, A246300, A246301.

z = 520; f[x_] := f[x] = Cos[x]; t = Range[0, z];
Select[t, f[#] > f[# + 1] &]  (* A026311 *)
Select[t, f[#] < f[# + 1] > f[# + 2] &]  (* A246300 *)
Select[t, f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (* A246301 *)
Select[t, f[#] < f[# + 1] < f[# + 2] < f[# + 3] > f[# + 4] &] (* A246302 *)

A246304 Numbers k such that cos(k) > cos(k+1) < cos(k+2).

Original entry on oeis.org

2, 8, 15, 21, 27, 34, 40, 46, 52, 59, 65, 71, 78, 84, 90, 96, 103, 109, 115, 122, 128, 134, 140, 147, 153, 159, 166, 172, 178, 184, 191, 197, 203, 209, 216, 222, 228, 235, 241, 247, 253, 260, 266, 272, 279, 285, 291, 297, 304, 310, 316, 323, 329, 335, 341

Offset: 1

Clark Kimberling, Aug 22 2014

The sequences A246303, A246304, A246305, A246306 partition the nonnegative integers.

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

Cf. A026303, A246305, A246306, A026311 (complement of A246303).

z = 500; f[x_] := f[x] = Cos[x]; t = Range[0, z];
Select[t, f[#] < f[# + 1] &]  (* A246303 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A246304 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]  (* A246305 *)
Select[t, f[#] > f[# + 1] > f[# + 2] > f[# + 3] < f[# + 4] &] (* A246306 *)
Flatten[Position[Partition[Cos[Range[400]],3,1],?(#[[1]]>#[[2]] && #[[2]]< #[[3]]&),{1},Heads->False]] (* _Harvey P. Dale, Apr 23 2015 *)

A246305 Numbers k such that cos(k) > cos(k+1) > cos(k+2) < cos(k+3).

Original entry on oeis.org

1, 7, 14, 20, 26, 33, 39, 45, 51, 58, 64, 70, 77, 83, 89, 95, 102, 108, 114, 121, 127, 133, 139, 146, 152, 158, 165, 171, 177, 183, 190, 196, 202, 208, 215, 221, 227, 234, 240, 246, 252, 259, 265, 271, 278, 284, 290, 296, 303, 309, 315, 322, 328, 334, 340

Offset: 1

Clark Kimberling, Aug 22 2014

The sequences A246303, A246304, A246305, A246306 partition the nonnegative integers.

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

Cf. A026303, A246304, A246306, A026311 (complement of A246303).

z = 500; f[x_] := f[x] = Cos[x]; t = Range[0, z];
Select[t, f[#] < f[# + 1] &]  (* A246303 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A246304 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]  (* A246305 *)
Select[t, f[#] > f[# + 1] > f[# + 2] > f[# + 3] < f[# + 4] &] (* A246306 *)

Definition corrected by Georg Fischer, Apr 01 2024

A246306 Numbers k such that cos(k) > cos(k+1) > cos(k+2) > cos(k+3) < cos(k+4).

Original entry on oeis.org

0, 6, 13, 19, 25, 32, 38, 44, 50, 57, 63, 69, 76, 82, 88, 94, 101, 107, 113, 120, 126, 132, 138, 145, 151, 157, 164, 170, 176, 182, 189, 195, 201, 207, 214, 220, 226, 233, 239, 245, 251, 258, 264, 270, 277, 283, 289, 295, 302, 308, 314, 321, 327, 333, 339

Offset: 1

Clark Kimberling, Aug 22 2014

The sequences A246303, A246304, A246305, A246306 partition the nonnegative integers.

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

Cf. A026303, A246304, A246305, A026311 (complement of A246303).

z = 500; f[x_] := f[x] = Cos[x]; t = Range[0, z];
Select[t, f[#] < f[# + 1] &]  (* A246303 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A246304 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]  (* A246305 *)
Select[t, f[#] > f[# + 1] > f[# + 2] > f[# + 3] < f[# + 4] &] (* A246306 *)

Definition corrected by Georg Fischer, Apr 01 2024

cp's OEIS Frontend

A246303 Numbers k such that cos(k) < cos(k+1).

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A246300 Numbers k such that cos(k) < cos(k+1) > cos(k+2).

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A246301 Numbers k such that cos(k) < cos(k+1) < cos(k+2) > cos(k+3).

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A246302 Numbers k such that cos(k) < cos(k+1) < cos(k+2) < cos(k+3) > cos(k+4).

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A246304 Numbers k such that cos(k) > cos(k+1) < cos(k+2).

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A246305 Numbers k such that cos(k) > cos(k+1) > cos(k+2) < cos(k+3).

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A246306 Numbers k such that cos(k) > cos(k+1) > cos(k+2) > cos(k+3) < cos(k+4).

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