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.

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A110119 Self-inverse integer permutation induced by Beatty sequences for x and (x+1)/(2*sqrt(2)) with x=sqrt(2)+sqrt(3).

Original entry on oeis.org

3, 6, 1, 9, 12, 2, 15, 18, 4, 22, 25, 5, 28, 31, 7, 34, 37, 8, 40, 44, 47, 10, 50, 53, 11, 56, 59, 13, 62, 66, 14, 69, 72, 16, 75, 78, 17, 81, 84, 19, 88, 91, 94, 20, 97, 100, 21, 103, 106, 23, 110, 113, 24, 116, 119, 26, 122, 125, 27, 128, 132, 29, 135, 138, 141, 30, 144
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 13 2005

Keywords

Links

Crossrefs

Cf. A108591, A110117, A110118.
Cf. A135611 (sqrt(2)+sqrt(3)).

Formula

a(A110117(n)) = A110118(n) and a(A110118(n)) = A110117(n).

A138252 Beatty sequence of the number t satisfying 1/s + 1/t = 1, where s is the positive root of x^3 - x^2 - 1.

Original entry on oeis.org

3, 6, 9, 12, 15, 18, 22, 25, 28, 31, 34, 37, 40, 44, 47, 50, 53, 56, 59, 62, 66, 69, 72, 75, 78, 81, 84, 88, 91, 94, 97, 100, 103, 107, 110, 113, 116, 119, 122, 125, 129, 132, 135, 138, 141, 144, 147, 151, 154, 157, 160, 163, 166, 169, 173, 176, 179, 182, 185, 188
Offset: 1

Views

Author

Clark Kimberling, Mar 09 2008

Keywords

Comments

Complement of A138251.
First differs from A110117 at 34th term.

Crossrefs

Cf. A110117, A138252, A138253.

Formula

a(n)=Floor(t*n).

Extensions

Typo in data corrected by D. S. McNeil, Aug 17 2010

A014248 a(n) = b(n) - c(n) where b(n) = [ n*(sqrt(2)+sqrt(3)) ] and c(n) is the n-th number not in sequence b( ).

Original entry on oeis.org

2, 4, 5, 7, 8, 10, 12, 14, 15, 17, 18, 20, 21, 24, 26, 27, 29, 30, 32, 33, 36, 37, 39, 40, 42, 43, 45, 47, 49, 51, 52, 54, 55, 57, 59, 61, 62, 64, 65, 67, 68, 71, 72, 74, 76, 77, 79, 81, 83, 84, 86, 87, 89, 90, 93, 94, 96, 97, 99, 101, 102, 105, 106, 108, 109, 111
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A110117, A110118.

Programs

  • Magma
    [Floor(n*(Sqrt(2)+Sqrt(3))) - Floor(n*(Sqrt(2)+Sqrt(6)+2)/4): n in [1..70]]; // G. C. Greubel, Jun 19 2019
  • Mathematica
    Table[Floor[n*(Sqrt[2]+Sqrt[3])] - Floor[n*(Sqrt[2]+Sqrt[6]+2)/4], {n, 1, 70}] (* G. C. Greubel, Jun 19 2019 *)
  • PARI
    vector(70, n,(n*(sqrt(2)+sqrt(3)))\1 -(n*(sqrt(2)+sqrt(6)+2)/4)\1) \\ G. C. Greubel, Jun 19 2019
  • Sage
    [floor(n*(sqrt(2)+sqrt(3))) - floor(n*(sqrt(2)+sqrt(6)+2)/4) for n in (1..70)] # G. C. Greubel, Jun 19 2019

Formula

a(n) = A110117(n) - A110118(n). - Sean A. Irvine, Oct 17 2018

A172324 a(n) = floor(n*(sqrt(7)+sqrt(5))).

Original entry on oeis.org

0, 4, 9, 14, 19, 24, 29, 34, 39, 43, 48, 53, 58, 63, 68, 73, 78, 82, 87, 92, 97, 102, 107, 112, 117, 122, 126, 131, 136, 141, 146, 151, 156, 161, 165, 170, 175, 180, 185, 190, 195, 200, 205, 209, 214, 219, 224, 229, 234, 239, 244, 248, 253, 258, 263, 268, 273
Offset: 0

Views

Author

Vincenzo Librandi, Feb 01 2010

Keywords

Comments

a(n) = integer part of n*(sqrt(7)+sqrt(5)), where the constant is the largest root of x^4 -24*x^2 +4.

Links

Crossrefs

Cf. A110117, A172323-A172332, A172334, A172336-A172338.

Programs

  • Magma
    [Floor(n*(Sqrt(7)+Sqrt(5))): n in [0..60]];
  • Mathematica
    With[{c = Sqrt[7] + Sqrt[5]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)

A172325 Floor(n*(sqrt(7)+sqrt(3))).

Original entry on oeis.org

0, 4, 8, 13, 17, 21, 26, 30, 35, 39, 43, 48, 52, 56, 61, 65, 70, 74, 78, 83, 87, 91, 96, 100, 105, 109, 113, 118, 122, 126, 131, 135, 140, 144, 148, 153, 157, 161, 166, 170, 175, 179, 183, 188, 192, 197, 201, 205, 210, 214, 218
Offset: 0

Views

Author

Vincenzo Librandi, Feb 01 2010

Keywords

Comments

Also integer part of n*4.3778021186..., where the constant is the largest root of x^4 -20*x^2 +16.

Links

Crossrefs

Cf. A110117, A172323-A172332, A172334, A172336-A172338.

Programs

  • Magma
    [Floor(n*(Sqrt(7)+Sqrt(3))): n in [0..60]];
  • Mathematica
    With[{c = Sqrt[7] + Sqrt[3]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)

A172326 a(n) = floor(n*(sqrt(7) + sqrt(2))).

Original entry on oeis.org

0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202
Offset: 0

Views

Author

Vincenzo Librandi, Feb 01 2010

Keywords

Comments

Also integer part of n*4.0599648734..., where the constant is the largest root of x^4 - 18*x^2 + 25.

Links

Crossrefs

Cf. A110117, A172323-A172332, A172334, A172336-A172338.

Programs

  • Magma
    [Floor(n*(Sqrt(7)+Sqrt(2))): n in [0..60]];
  • Maple
    a:=n->floor(n*(sqrt(7)+sqrt(2))): seq(a(n),n=0..60); # Muniru A Asiru, Sep 28 2018
  • Mathematica
    With[{c = Sqrt[7] + Sqrt[2]}, Floor[c Range[0, 60]]]  (* Harvey P. Dale, Mar 23 2011 *)
  • PARI
    vector(60, n, n--; floor(n*(sqrt(7)+sqrt(2)))) \\ G. C. Greubel, Sep 28 2018

A172327 Floor(n*(sqrt(11)+sqrt(5))).

Original entry on oeis.org

0, 5, 11, 16, 22, 27, 33, 38, 44, 49, 55, 61, 66, 72, 77, 83, 88, 94, 99, 105, 111, 116, 122, 127, 133, 138, 144, 149, 155, 161, 166, 172, 177, 183, 188, 194, 199, 205, 211, 216, 222, 227, 233, 238, 244, 249, 255, 260, 266, 272, 277
Offset: 0

Views

Author

Vincenzo Librandi, Feb 01 2010

Keywords

Comments

Also integer part of n*5.5526927678..., where the constant is the largest root of x^4 -32*x^2 +36.

Links

Crossrefs

Cf. A110117, A172323-A172332, A172334, A172336-A172338.

Programs

  • Magma
    [Floor(n*(Sqrt(11)+Sqrt(5))): n in [0..60]];
  • Mathematica
    With[{c = Sqrt[11] + Sqrt[5]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)

A172328 a(n) = floor(n*(sqrt(11)+sqrt(3))).

Original entry on oeis.org

0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 201, 206, 212, 217, 222, 227, 232, 237, 242, 247, 252
Offset: 0

Views

Author

Vincenzo Librandi, Feb 01 2010

Keywords

Comments

Also integer part of n*5.0486755979..., where the constant is the largest root of x^4 -28*x^2 +64.

Links

Crossrefs

Cf. A110117, A172323-A172332, A172334, A172336-A172338.

Programs

  • Magma
    [Floor(n*(Sqrt(11)+Sqrt(3))): n in [0..60]];
  • Mathematica
    With[{c = Sqrt[11] + Sqrt[3]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)

A172329 a(n) = floor(n*(sqrt(11) + sqrt(2))).

Original entry on oeis.org

0, 4, 9, 14, 18, 23, 28, 33, 37, 42, 47, 52, 56, 61, 66, 70, 75, 80, 85, 89, 94, 99, 104, 108, 113, 118, 123, 127, 132, 137, 141, 146, 151, 156, 160, 165, 170, 175, 179, 184, 189, 193, 198, 203, 208, 212, 217, 222, 227, 231, 236
Offset: 0

Views

Author

Vincenzo Librandi, Feb 01 2010

Keywords

Comments

Also integer part of n*4.7308383527..., where the constant is the largest root of x^4 - 26*x^2 + 81.

Links

Crossrefs

Cf. A110117, A172323-A172332, A172334, A172336-A172338.

Programs

  • Magma
    [Floor(n*(Sqrt(11)+Sqrt(2))): n in [0..60]];
  • Maple
    a:=n->floor(n*(sqrt(11)+sqrt(2))): seq(a(n),n=0..60); # Muniru A Asiru, Sep 28 2018
  • Mathematica
    With[{c=Sqrt[11]+Sqrt[2]},Table[Floor[c n], {n,0,50}]]  (* Harvey P. Dale, Mar 12 2011 *)
  • PARI
    vector(60, n, n--; floor(n*(sqrt(11)+sqrt(2)))) \\ G. C. Greubel, Sep 28 2018

A172330 Floor(n*(sqrt(13)+sqrt(11))).

Original entry on oeis.org

0, 6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 76, 83, 89, 96, 103, 110, 117, 124, 131, 138, 145, 152, 159, 166, 173, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 263, 269, 276, 283, 290, 297, 304, 311, 318, 325, 332, 339, 346
Offset: 0

Views

Author

Vincenzo Librandi, Feb 01 2010

Keywords

Comments

Also integer part of n*6.9221760658..., where the constant is the largest root of x^4 -48*x^2 +4.

Links

Crossrefs

Cf. A110117, A172323-A172332, A172334, A172336-A172338.

Programs

  • Magma
    [Floor(n*(Sqrt(13)+Sqrt(11))): n in [0..60]];
  • Mathematica
    With[{c = Sqrt[13] + Sqrt[11]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)
Previous Showing 11-20 of 23 results. Next

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

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