A323750 Triangle read by rows: T(m,n) is the label of the ending square of an (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; 1 <= n < m. Each move is to the lowest-numbered unvisited square.

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

2,1

Links

Jud McCranie, Table of n, a(n) for n = 2..19901

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

Example

Triangle begins:
  n\k|      1      2     3     4     5     6     7     8    9
  ---+-------------------------------------------------------
   2 |   2084
   3 |   7081   4698
   4 |  10847   8399  1164
   5 |  25963   6760  2269  6500
   6 |  22421  28273 18946 18643  1202
   7 | 202891  10059  6425  6662  3039  1383
   8 | 142679  43325  3744 33725  1460  4639  1952
   9 | 252953  23684 63577  6040 10841 41836 10017  6338
  10 | 188501 104413 26546 26967 52736  9145  6580 25799 1869
A chess knight (a (2,1)-leaper) makes 2016 moves before it reaches the square labeled 2084 and has no moves available (see A316667).

Crossrefs

Cf. A306197, A323471 (first column), A323749, A343179 (main diagonal).

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

Sequence in context: A323714 A343179 A385003 * A323471 A251225 A306421

Adjacent sequences: A323747 A323748 A323749 * A323751 A323752 A323753

Keyword

nonn,tabl

Author

Jud McCranie, Jan 26 2019

Extensions

Offset changed by Pontus von Brömssen, Dec 15 2025

Status

approved