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 1-4 of 4 results.

A110117 a(n) = floor(n * (sqrt(2) + sqrt(3))).

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, 106, 110, 113, 116, 119, 122, 125, 128, 132, 135, 138, 141, 144, 147, 151, 154, 157, 160, 163, 166, 169, 173, 176, 179, 182, 185, 188
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 13 2005

Keywords

Comments

Beatty sequence for sqrt(2)+sqrt(3); complement of A110118;
sqrt(2)+sqrt(3) = 3.14626... = A135611, a weak but interesting Pi approximation.

Links

Crossrefs

Cf. A110119, A135611.

Programs

  • Mathematica
    Table[Floor[n*(Sqrt[2] + Sqrt[3])], {n, 1, 50}] (* G. C. Greubel, Jul 02 2017 *)
  • PARI
    for(n=1,50, print1(floor(n*(sqrt(2) + sqrt(3))), ", ")) \\ G. C. Greubel, Jul 02 2017

Extensions

Typo in Link section fixed by Reinhard Zumkeller, Feb 15 2010

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).

A138251 Beatty sequence of the positive root of x^3 - x^2 - 1.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102
Offset: 1

Views

Author

Clark Kimberling, Mar 09 2008

Keywords

Comments

First differs from A110118 at 73rd term.

Crossrefs

Cf. A092526, A110118, A138253.

Formula

a(n)=Floor(r*n), where r=1.46557123187676...; see A092526 for more decimal places.

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
Showing 1-4 of 4 results.

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

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