A306197 Triangle read by rows: T(m,n) is 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; 1 <= n < m. Each move is to the lowest-numbered unvisited square.

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

2,1

Comments

Are all terms finite?

Links

Table of n, a(n) for n=2..47.

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

Example

Triangle begins:
  m\n|      1      2     3     4     5     6     7     8     9
  ---+--------------------------------------------------------
   2 |   3199
   3 |   9173   7416
   4 |  16270  12669  4238
   5 |  36667  10947  4851 15027
   6 |  34407  36777 28411 29623  5832
   7 | 237635  17075 14329 17064  8669  9152
   8 | 191876  65307 10536 50425  7243 17187  9730
   9 | 307545  45627 82813 16948 24847 66622 23741 24678
  10 | 259181 147061 48250 43525 78711 19501 18600 59821 15410
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).

Crossrefs

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

Sequence in context: A250386 A069401 A225056 * A211840 A235786 A235781

Adjacent sequences: A306194 A306195 A306196 * A306198 A306199 A306200

Keyword

nonn,tabl

Author

Jud McCranie, Jan 28 2019

Extensions

Offset changed by Pontus von Brömssen, Dec 14 2025

Status

approved