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 1-3 of 3 results.

A108120 Floor[n*1/Sin[1]], or Beatty sequence for 1/sin(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, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 83, 84, 85
Offset: 1

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Author

Zak Seidov, Jun 04 2005

Keywords

Comments

Complement of A108587; not the same as A108586: a(37)=43 <> A108586(37)=44. - Reinhard Zumkeller, Jun 11 2005

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253.
Cf. A108593.

Programs

  • Mathematica
    a[n_]:=Floor[n*1/Sin[1]];Table[a[n], {n, 90}]

Formula

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

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).

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 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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