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.

A323750 The label of the ending square of a (m,n)-leaper (a generalization of a chess knight) when 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

2084, 7081, 4698, 10847, 8399, 1164, 25963, 6760, 2269, 6500, 22421, 28273, 18946, 18643, 1202, 202891, 10059, 6425, 6662, 3039, 1383, 142679, 43325, 3744, 33725, 1460, 4639, 1952, 252953, 23684, 63577, 6040, 10841, 41836, 10017, 6338, 188501, 104413, 26546, 26967, 52736, 9145, 6580, 25799, 1869, 257479, 35652
Offset: 1

Views

Author

Jud McCranie, Jan 26 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.

Examples

			A chess knight (a (2,1)-leaper) makes 2016 moves before it reaches the square labeled 2084 and has no moves available (see A316667).

Links

Crossrefs

Cf. A323749, A316667, A317106, A317471, A317416, A323750, A317438, A317916.

A337254 Squares visited by a rook moving on a spirally numbered board always to the lowest available unvisited square with a move length of the current square (in decimal) + 1.

Original entry on oeis.org

1, 11, 13, 15, 17, 19, 21, 23, 25, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 227, 229, 231, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251
Offset: 1

Views

Author

Patrick Wienhöft, Aug 21 2020

Keywords

Comments

The rook may move over squares it has already visited, only the final square after a full move must not have been visited before.
As for A316667, the rook gets trapped as well. This happens after step 185 on square 118.
Rook movement on the square spiral is also considered in A336447 and A336413.
This is a variation of generalized knights, as in A323749, where here each move is a (x,0)-leaper but as opposed to A323749 the x changes depending on the current square rather than having a fixed size for each move.

Examples

			The rook starts on square a(1) = 1. Thus its available moves are of length len(1) + 1 = 2, possibly reaching squares 11, 15, 19 and 23. Since 11 is the smallest value, a(2) = 11. From there on, the next move must have length len(11) + 1 = 3, etc.

Links

Crossrefs

Cf. A316667, A323749, A336413, A336447.

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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