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.

A323749 Triangle read by rows: T(n,m) (1 <= n < m) = number of moves of a (m,n)-leaper (a generalization of a chess knight) until it can no longer move, starting on a board with squares spirally numbered from 1. Each move is to the lowest-numbered unvisited square. T(n,m) = -1 if the path never terminates.

Original entry on oeis.org

2016, 3723, 4634, 13103, 2016, 1888, 14570, 7574, 1323, 4286, 26967, 3723, 2016, 4634, 1796, 101250, 12217, 4683, 9386, 1811, 3487, 158735, 13103, 5974, 2016, 2758, 1888, 3984, 132688, 33864, 3723, 8900, 6513, 4634, 4505, 7796, 220439, 14570, 36232, 7574, 2016, 1323, 9052, 4286, 5679, 144841, 52738, 19370, 6355, 6425
Offset: 1

Views

Author

Jud McCranie, Jan 26 2019

Keywords

Comments

The entries are the lower triangle of an array, for an (m,n)-leaper, where 1 <= n < m, ordered: (2,1), (3,1), (3,2), (4,1), (4,2), etc. Are all the paths finite? This appears to be an open question.

Examples

			A chess knight (a (2,1)-leaper) makes 2016 moves before it has no moves available (see A316667). Initial placement on square 1 counts as one move.

Links

Crossrefs

Cf. A316667, A323750, A317106, A317471, A317416, A323750, A317438, A317916.

Extensions

Edited by N. J. A. Sloane, Apr 30 2021

A343179 On a spirally numbered square grid, with labels starting at 1, this is the number of the last cell that an (n,n+1) leaper reaches before getting trapped, or -1 if it never gets trapped.

Original entry on oeis.org

2084, 4698, 1164, 6500, 1202, 1383, 1952, 6338, 1869, 3743, 5280, 3626, 4522, 14191, 8313, 23750, 10852, 5967, 6601, 16191, 24571, 33535, 20978, 21552, 10661, 36193, 51587, 69754, 17618, 33186, 36548, 33424, 19389, 19670, 21097, 50306, 25040, 51385, 50256
Offset: 1

Views

Author

N. J. A. Sloane, Apr 30 2021

Keywords

Comments

As in all these sequences (cf. A316667), the knight or leaper must always move to the lowest-numbered unvisited square.

References

  • Andrew Trevorrow, Posting to Math Fun Mailing List, Apr 29 2021.

Links

Crossrefs

Cf. A316667, A323469, A323471, A323750, A343178.

Extensions

More terms from Rémy Sigrist, Apr 30 2021

A306197 The label of the largest square that an (m,n)-leaper (a generalization of a chess knight) reaches before it can no longer move, starting on a board with squares spirally numbered, starting at 1. Each move is to the lowest-numbered unvisited square.

Original entry on oeis.org

3199, 9173, 7416, 16270, 12669, 4238, 36667, 10947, 4851, 15027, 34407, 36777, 28411, 29623, 5832, 237635, 17075, 14329, 17064, 8669, 9152, 191876, 65307, 10536, 50425, 7243, 17187, 9730, 307545, 45627, 82813, 16948, 24847, 66622, 23741, 24678, 259181, 147061, 48250, 43525, 78711, 19501, 18600, 59821, 15410, 334131
Offset: 1

Views

Author

Jud McCranie, Jan 28 2019

Keywords

Comments

The entries are the lower triangle of an array, for (m,n)-leaper, where 1 <= n < m, ordered: (2,1), (3,1), (3,2), (4,1), (4,2), etc. Are all terms finite?

Examples

			A chess knight (a (2,1)-leaper) reaches the square labeled 3199 before it reaches the square labeled 2084 and has no moves available (see A316667).

Links

Crossrefs

Cf. A316667, A323749, A323750, A317106, A317471, A317416, A323750, A317438, A317916.
Showing 1-3 of 3 results.

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

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