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 1-7 of 7 results.

A108586 Floor(2*n*Pi/(2*Pi-1)).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Comments

Beatty sequence for 2*Pi/(2*Pi-1); complement of A038130; not the same as A108120: a(37)=44 <> A108120(37)=43.

Links

Crossrefs

Cf. A054386, A140758, A108592.

Programs

  • Mathematica
    With[{c=2Pi},Floor[(c*Range[80])/(c-1)]] (* Harvey P. Dale, Apr 21 2024 *)

A108587 a(n) = floor(n/(1-sin(1))).

Original entry on oeis.org

6, 12, 18, 25, 31, 37, 44, 50, 56, 63, 69, 75, 82, 88, 94, 100, 107, 113, 119, 126, 132, 138, 145, 151, 157, 164, 170, 176, 182, 189, 195, 201, 208, 214, 220, 227, 233, 239, 246, 252, 258, 264, 271, 277, 283, 290, 296, 302, 309, 315, 321, 328, 334, 340, 346
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Comments

Beatty sequence for 1/(1-sin(1)); complement of A108120.

Links

Crossrefs

Cf. A038130, A049469, A108120, A108593, A206530.

Programs

  • Magma
    [Floor(n/(1-Sin(1))): n in [1..60]]; // G. C. Greubel, Dec 19 2022
  • Mathematica
    Table[Floor[n/(1-Sin[1])], {n, 60}] (* G. C. Greubel, Dec 19 2022 *)
  • SageMath
    [int(n/(1-sin(1))) for n in range(1,61)] # G. C. Greubel, Dec 19 2022

A108593 Self-inverse integer permutation induced by Beatty sequences for 1/sin(1) and 1/(1-sin(1)).

Original entry on oeis.org

6, 12, 18, 25, 31, 1, 37, 44, 50, 56, 63, 2, 69, 75, 82, 88, 94, 3, 100, 107, 113, 119, 126, 132, 4, 138, 145, 151, 157, 164, 5, 170, 176, 182, 189, 195, 7, 201, 208, 214, 220, 227, 233, 8, 239, 246, 252, 258, 264, 9, 271, 277, 283, 290, 296, 10, 302, 309, 315, 321
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Links

Crossrefs

Cf. A108592.

Formula

a(A108120(n))=A108587(n) and a(A108587(n))=A108120(n).

A108611 Excess of Beatty-function of 1/sin(1) over n.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16
Offset: 0

Views

Author

Zak Seidov, Jun 13 2005

Keywords

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120.

Formula

a(n) = A108120[n] - n.

A108612 Beatty-2 (or nested Beatty) sequence for 1/sin(1).

Original entry on oeis.org

1, 4, 9, 16, 25, 42, 56, 72, 90, 110, 143, 168, 195, 224, 255, 304, 340, 378, 418, 460, 504, 572, 621, 672, 725, 780, 864, 924, 986, 1050, 1116, 1216, 1287, 1360, 1435, 1512, 1591, 1710, 1794, 1880, 1968, 2058, 2193, 2288, 2385, 2484, 2585, 2736, 2842, 2950
Offset: 1

Views

Author

Zak Seidov, Jun 13 2005

Keywords

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120, A108611, A108613.

Formula

a(n) = floor(n*floor(n/sin(1))).

A108613 Excess of Beatty-2 function of 1/sin(1) over n^2.

Original entry on oeis.org

0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 22, 24, 26, 28, 30, 48, 51, 54, 57, 60, 63, 88, 92, 96, 100, 104, 135, 140, 145, 150, 155, 192, 198, 204, 210, 216, 222, 266, 273, 280, 287, 294, 344, 352, 360, 368, 376, 432, 441, 450, 459, 468, 477, 540, 550, 560, 570, 580, 649, 660
Offset: 0

Views

Author

Zak Seidov, Jun 13 2005

Keywords

Comments

Cf. A108612 Beatty-2 (or nested Beatty) function of 1/sin(1).

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120, A108611, A108612.

Formula

a(n) = A108612[n] - n^2 = floor(n*floor(n/sin(1))) - n^2.

A248850 First row of spectral array W(1/sin(1)).

Original entry on oeis.org

1, 6, 7, 37, 43, 233, 276, 1469, 1745, 9266, 11011, 58449, 69460, 368695, 438155, 2325725, 2763880, 14670658
Offset: 1

Views

Author

Colin Barker, Dec 03 2014

Keywords

Comments

1/sin(1) = 1.18839510577812121626159945237455100352782983409796262526525...
The sequence is generated from the Beatty sequence (A108120) and from the complement of the Beatty sequence (A108587) for 1/sin(1).

Links

Crossrefs

Cf. A108120, A108587.

Programs

  • PARI
    \\ Row i of the generalized Wythoff array W(h),
\\   where h is an irrational number between 1 and 2,
\\   and m is the number of terms in the vectors b and c.
row(h, i, m) = {
  if(h<=1 || h>=2, print("Invalid value for h"); return);
  my(
    b=vector(m, n, floor(n*h)),       \\ Beatty sequence for h
    c=vector(m, n, floor(n*h/(h-1))), \\ Complement of b
    w=[b[b[i]], c[b[i]]],
    j=3
  );
  while(1,
    if(j%2==1,
      if(w[j-1]<=#b, w=concat(w, b[w[j-1]]), return(w))
    ,
      if(w[j-2]<=#c, w=concat(w, c[w[j-2]]), return(w))
    );
    j++
  )
}
allocatemem(10^9)
default(realprecision, 100)
row(1/sin(1), 1, 10^7)
Showing 1-7 of 7 results.

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