A317471 -id:A317471 - cp's OEIS frontend

A317473 Numbers missing from A317471.

2845, 3060, 3072, 3082, 3270, 3284, 3288, 3290, 3293, 3303, 3307, 3308, 3328, 3463, 3469, 3470, 3471, 3472, 3515, 3518, 3519, 3521, 3522, 3526, 3527, 3537, 3540, 3541, 3542, 3552, 3564, 3640, 3645, 3708, 3709, 3715, 3720, 3722, 3730

Offset: 1

Daniël Karssen, Jul 29 2018

nonn

A317471 is finite, so this sequence is infinite.

See A317471 for further information.

Daniël Karssen, Table of n, a(n) for n = 1..42346

Cf. A317471.

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

Jud McCranie, Jan 26 2019

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.

			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.

Jud McCranie, Table of n, a(n) for n = 1..19900
N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

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

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

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

Jud McCranie, Jan 26 2019

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.

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

Jud McCranie, Table of n, a(n) for n = 1..19900
N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

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

A317470 Squares visited by a (2,3)-leaper on a spirally numbered board and moving to the lowest available unvisited square at each step, squares labelled >=0.

Original entry on oeis.org

0, 25, 2, 19, 14, 9, 4, 23, 18, 13, 6, 11, 22, 17, 8, 15, 10, 21, 38, 7, 12, 5, 24, 3, 20, 1, 16, 59, 28, 33, 92, 87, 26, 45, 40, 75, 70, 113, 46, 27, 32, 53, 58, 133, 30, 85, 48, 115, 42, 105, 36, 95, 186, 89, 136, 55, 94, 29, 60, 37, 96, 31, 52, 47, 84, 79, 124, 119, 172

Offset: 0

Daniël Karssen, Jul 29 2018

Board is numbered with the square spiral:
.
  16--15--14--13--12
   |               |
  17   4---3---2  11   .
   |   |       |   |
  18   5   0---1  10   .
   |   |           |
  19   6---7---8---9   .
   |
  20--21--22--23--24--25
.
The sequence is finite: at step 4633, square 4697 is visited, after which there are no unvisited squares within one move.

Daniël Karssen, Table of n, a(n) for n = 0..4633
Daniël Karssen, Figure showing the first 51 steps of the sequence
Daniël Karssen, Figure showing the complete sequence

Cf. A317471, A317472.

a(n) = A317471(n+1) - 1.

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

Jud McCranie, Jan 28 2019

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?

			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).

N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

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

cp's OEIS Frontend

A317473 Numbers missing from A317471.

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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.

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A317470 Squares visited by a (2,3)-leaper on a spirally numbered board and moving to the lowest available unvisited square at each step, squares labelled >=0.

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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.

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