cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling

Keywords

Comments

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

Links

Crossrefs

Cf. A246297, A246298, A246299, 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 *)

Formula

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

Extensions

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

A026311 n-th nonnegative integer k satisfying cos(k) > cos(k+1).

Original entry on oeis.org

0, 1, 2, 6, 7, 8, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 33, 34, 38, 39, 40, 44, 45, 46, 50, 51, 52, 57, 58, 59, 63, 64, 65, 69, 70, 71, 75, 76, 77, 78, 82, 83, 84, 88, 89, 90, 94, 95, 96, 101, 102, 103, 107, 108, 109, 113, 114, 115
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

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

Links

Crossrefs

Cf. A246293, A246300, A246301, A246302, A246303 (complement of A026311).

Programs

Extensions

Comment, Mathematica, Crossrefs by Clark Kimberling, Aug 22 2014

A246294 Numbers k such that sin(k) < sin(k+1) > sin(k+2).

Original entry on oeis.org

1, 7, 13, 19, 26, 32, 38, 45, 51, 57, 63, 70, 76, 82, 89, 95, 101, 107, 114, 120, 126, 133, 139, 145, 151, 158, 164, 170, 176, 183, 189, 195, 202, 208, 214, 220, 227, 233, 239, 246, 252, 258, 264, 271, 277, 283, 290, 296, 302, 308, 315, 321, 327, 334, 340
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2014

Keywords

Comments

The sequences A246293, A246294, A246295, A246296 partition the nonnegative integers.
Numbers like 42, 86, 130, 199, 243, 287,.. are in none of these 4 sequences. - R. J. Mathar, May 18 2020

Links

Crossrefs

Cf. A246293, A246295, A246296, A026309 (complement of A246293).

Programs

A246295 Numbers k such that sin(k) < sin(k+1) < sin(k+2) > sin(k+3).

Original entry on oeis.org

0, 6, 12, 18, 25, 31, 37, 44, 50, 56, 62, 69, 75, 81, 88, 94, 100, 106, 113, 119, 125, 132, 138, 144, 150, 157, 163, 169, 175, 182, 188, 194, 201, 207, 213, 219, 226, 232, 238, 245, 251, 257, 263, 270, 276, 282, 289, 295, 301, 307, 314, 320, 326, 333, 339
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2014

Keywords

Comments

The sequences A246293, A246294, A246295, A246296 partition the nonnegative integers.
Numbers like 42, 86, 130, 199, 243, 287,.. are in none of these 4 sequences. - R. J. Mathar, May 18 2020

Links

Crossrefs

Cf. A246293, A246294, A246296, A026309 (complement of A246293).

Programs

  • Mathematica
    z = 500; f[x_] := f[x] = Sin[x]; t = Range[0, z];
Select[t, f[#] > f[# + 1] &]  (* A246293 *)
Select[t, f[#] < f[# + 1] > f[# + 2] &]  (* A246294 *)
Select[t, f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (* A246295 *)
Select[t, f[#] < f[# + 1] < f[# + 2] < f[# + 3] > f[# + 4] &] (* A246296 *)

A246296 Numbers k such that sin(k) < sin(k+1) < sin(k+2) < sin(k+3) > sin(k+4).

Original entry on oeis.org

5, 11, 17, 24, 30, 36, 43, 49, 55, 61, 68, 74, 80, 87, 93, 99, 105, 112, 118, 124, 131, 137, 143, 149, 156, 162, 168, 174, 181, 187, 193, 200, 206, 212, 218, 225, 231, 237, 244, 250, 256, 262, 269, 275, 281, 288, 294, 300, 306, 313, 319, 325, 332, 338, 344
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2014

Keywords

Comments

The sequences A246293, A246294, A246295, A246296 partition the nonnegative integers.
Numbers like 42, 86, 130, 199, 243, 287,.. are in none of these 4 sequences. - R. J. Mathar, May 18 2020

Links

Crossrefs

Cf. A246293, A246294, A246295, A026309 (complement of A246293).

Programs

  • Mathematica
    z = 500; f[x_] := f[x] = Sin[x]; t = Range[0, z];
Select[t, f[#] > f[# + 1] &]  (* A246293 *)
Select[t, f[#] < f[# + 1] > f[# + 2] &]  (* A246294 *)
Select[t, f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (* A246295 *)
Select[t, f[#] < f[# + 1] < f[# + 2] < f[# + 3] > f[# + 4] &] (* A246296 *)

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

Views

Author

Clark Kimberling, Aug 21 2014

Keywords

Comments

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

Links

Crossrefs

Cf. A026309, A246298, A246299, 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 *)

Extensions

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

A246298 Numbers k such that sin(k) > sin(k+1) > sin(k+2) < sin(k+3).

Original entry on oeis.org

3, 9, 15, 22, 28, 34, 40, 47, 53, 59, 66, 72, 78, 84, 91, 97, 103, 110, 116, 122, 128, 135, 141, 147, 154, 160, 166, 172, 179, 185, 191, 197, 204, 210, 216, 223, 229, 235, 241, 248, 254, 260, 267, 273, 279, 285, 292, 298, 304, 311, 317, 323, 329, 336, 342
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2014

Keywords

Comments

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

Links

Crossrefs

Cf. A246297, A246299, 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 *)
Flatten[Position[Partition[Sin[Range[350]],4,1],?(#[[1]]>#[[2]]>#[[3]]<#[[4]]&),1,Heads->False]] (* _Harvey P. Dale, Aug 03 2017 *)
  • PARI
    q(n)=my(s0=sin(n),s1=sin(n+1),s2=sin(n+2),s3=sin(n+3));if( (s0>s1) && (s1>s2) && (s2Joerg Arndt, Aug 03 2017
  • PARI
    list(lim)=my(v=List(),u=vector(4,x,sin(x+2))); forstep(k=3,lim-3,4, u[4]=sin(k+3); if(u[1]>u[2]&&u[2]>u[3]&&u[3]u[3]&&u[3]>u[4]&&u[4]u[4]&&u[4]>u[1]&&u[1]u[1]&&u[1]>u[2]&&u[2]sin(k+1)&&sin(k+1)>sin(k+2)&&sin(k+2)Charles R Greathouse IV, Aug 03 2017
  • Python
    from sympy import sin
def ok(n):
    s0, s1, s2, s3 = sin(n), sin(n + 1), sin(n + 2), sin(n + 3)
    return s0>s1 and s1>s2 and s2Indranil Ghosh, Aug 03 2017

Extensions

Name corrected by Harvey P. Dale, Aug 03 2017

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

Views

Author

Clark Kimberling, Aug 21 2014

Keywords

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

Crossrefs

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

Programs

Extensions

Corrected signs in NAME. - R. J. Mathar, May 18 2020
Showing 1-8 of 8 results.

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