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 1-5 of 5 results.

A113807 Permutation of natural numbers generated by 7-rowed array shown below.

Original entry on oeis.org

1, 13, 2, 15, 12, 3, 27, 16, 11, 4, 29, 26, 17, 10, 5, 41, 30, 25, 18, 9, 6, 43, 40, 31, 24, 19, 8, 7, 55, 44, 39, 32, 23, 20, 14, 57, 54, 45, 38, 33, 22, 21, 69, 58, 53, 46, 37, 34, 28, 71, 68, 59, 52, 47, 36, 35, 83, 72, 67, 60, 51, 48, 42, 85, 82, 73, 66, 61, 50, 49
Offset: 1

Views

Author

Giovanni Teofilatto, Jan 22 2006

Keywords

Comments

For such arrays A_k see the k-family of 2k-periodic sequences P_k defined in a comment on A203571. There the k residue classes mod n have been defined. The present array is A_7 if the last class, starting with 7, is taken as first class [0] after adding a 0 in front. Then one obtains a permutation of the nonnegative integers. However, each complete residue class also includes its negative members. - Wolfdieter Lang, Feb 02 2012

Examples

			1 13 15 27 29 41 43 55 57 69 71 83 85 ... (A113801)
2 12 16 26 30 40 44 54 58 68 72 82 86 ... (A113802)
3 11 17 25 31 39 45 53 59 67 73 81 87 ... (A113803)
4 10 18 24 32 38 46 52 60 66 74 80 88 ... (A113804)
5  9 19 23 33 37 47 51 61 65 75 70 89 ... (A113805)
6  8 20 22 34 36 48 50 62 64 76 78 90 ... (A113806)
7 14 21 28 35 42 49 56 63 70 77 84 91 ... (A008589)

Crossrefs

Cf. A088520, A090243, A090298, A092260, A204453.

Extensions

A-numbers added for array rows by Wolfdieter Lang, Dec 15 2011
More terms from Ray Chandler, Dec 15 2011

A092260 Permutation of natural numbers generated by 6-rowed array shown below.

Original entry on oeis.org

1, 11, 2, 13, 10, 3, 23, 14, 9, 4, 25, 22, 15, 8, 5, 35, 26, 21, 16, 7, 6, 37, 34, 27, 20, 17, 12, 47, 38, 33, 28, 19, 18, 49, 46, 39, 32, 29, 24, 59, 50, 45, 40, 31, 30, 61, 58, 51, 44, 41, 36, 71, 62, 57, 52, 43, 42, 73, 70, 63, 56, 53, 48, 83, 74, 69, 64, 55, 54, 85, 82, 75
Offset: 1

Views

Author

Giovanni Teofilatto, Feb 19 2004

Keywords

Comments

1 11 13 23 25 35 37 47 49 59... (A091998)
2 10 14 22 26 34 38 46 50 58... (A091999)
3 9 15 21 27 33 39 45 51 57... (A016945)
4 8 16 20 28 32 40 44 52 56... (A092259)
5 7 17 19 29 31 41 43 53 55... (A092242)
6 12 18 24 30 36 42 48 54 60... (A008588, excluding initial term)
For such arrays A_k, here A_6, see a W. Lang comment on A113807, the A_7 case. However, to get the array A_6 one should take the last line as the first one and add a 0 in front (thus obtaining a permutation of the nonnegative integers). - Wolfdieter Lang, Feb 02 2012

Crossrefs

Cf. A088520, A090243, A090298, A113807.

Extensions

Edited and extended by Ray Chandler, Feb 21 2004

A090298 Permutation of natural numbers generated by 5-row array shown below.

Original entry on oeis.org

1, 9, 2, 11, 8, 3, 19, 12, 7, 4, 21, 18, 13, 6, 5, 29, 22, 17, 14, 10, 31, 28, 23, 16, 15, 39, 32, 27, 24, 20, 41, 38, 33, 26, 25, 49, 42, 37, 34, 30, 51, 48, 43, 36, 35, 59, 52, 47, 44, 40, 61, 58, 53, 46, 45, 69, 62, 57, 54, 50, 71, 68, 63, 56, 55, 79, 72, 67, 64, 60, 81, 78
Offset: 1

Views

Author

Giovanni Teofilatto, Jan 25 2004

Keywords

Comments

1 9 11 19 21 29 31 39... (A090771)
2 8 12 18 22 28 32 38... (A090772)
3 7 13 17 23 27 33 37... (A063226)
4 6 14 16 24 26 34 36... (A090773)
5 10 15 20 25 30 35 40... (A008587, excluding initial term)
-----------------------------------------------------------
For such arrays A_k, here A_5, see a W. Lang comment on A113807, the A_7 case. However, in order to obtain A_5 one should take the last row as the first one after adding a 0 in front (thus getting a permutation of the nonnegative integers). - Wolfdieter Lang, Feb 02 2012

Crossrefs

Cf. A088520, A090243, A092260, A113807.

Extensions

More terms from Ray Chandler, Feb 01 2004

A088520 Permutation of natural numbers generated by 3-rowed array shown below.

Original entry on oeis.org

1, 5, 2, 7, 4, 3, 11, 8, 6, 13, 10, 9, 17, 14, 12, 19, 16, 15, 23, 20, 18, 25, 22, 21, 29, 26, 24, 31, 28, 27, 35, 32, 30, 37, 34, 33, 41, 38, 36, 43, 40, 39, 47, 44, 42, 49, 46, 45, 53, 50, 48, 55, 52, 51, 59, 56, 54, 61, 58, 57, 65, 62, 60, 67, 64, 63, 71, 68, 66, 73, 70, 69
Offset: 1

Views

Author

Giovanni Teofilatto, Nov 14 2003

Keywords

Comments

1 5 7 11 13 17 19 23 25 29 31 35 37 41 43...
2 4 8 10 14 16 20 22 26 28 32 34 38 40 44...
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45...

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

Crossrefs

Cf. A090243, A090298, A092260, A113807.

Extensions

Corrected and extended by Ray Chandler, Nov 16 2003

A115302 Permutation of natural numbers generated by 3-rowed array shown below.

Original entry on oeis.org

1, 4, 2, 7, 5, 3, 10, 8, 6, 13, 11, 9, 16, 14, 12, 19, 17, 15, 22, 20, 18, 25, 23, 21, 28, 26, 24, 31, 29, 27, 34, 32, 30, 37, 35, 33, 40, 38, 36, 43, 41, 39, 46, 44, 42, 49, 47, 45, 52, 50, 48, 55, 53, 51, 58, 56, 54, 61, 59, 57, 64, 62, 60
Offset: 1

Views

Author

Giovanni Teofilatto, Mar 05 2006

Keywords

Comments

1 4 7 10 13 16 19 22 25...a(n)=3n+1 => A016777
2 5 8 11 14 17 20 23 26...a(n)=3n+2 => A016789
3 6 9 12 15 18 21 24 27...a(n)=3n => A008585
Reversing the direction of the diagonals gives A143097. - Jeremy Gardiner, Oct 14 2012.

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

Crossrefs

Cf. A088520, A090243, A090298, A143097.

Formula

For n > 1, a(n+5) = a(n) + 6, iff a(n+5)=1.
Showing 1-5 of 5 results.

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