A342947 Squares visited by the black knight when a white knight and a black knight are moving on a diagonally numbered board, always to the lowest available unvisited square; white moves first.

1, 9, 4, 3, 13, 7, 5, 10, 26, 18, 11, 30, 37, 48, 22, 31, 38, 46, 58, 49, 41, 52, 27, 33, 40, 51, 60, 70, 57, 67, 81, 93, 106, 123, 79, 68, 82, 71, 61, 74, 64, 36, 65, 78, 118, 77, 88, 100, 85, 97, 110, 124, 139, 155, 172, 193, 138, 154, 212, 232, 256, 191, 213

Offset: 1

Author

Andrew Smith, Mar 30 2021

Keywords

• nonn
• fini

Comments

Board is numbered as follows:

1 2 4 7 11 16 .

3 5 8 12 17 .

6 9 13 18 .

10 14 19 .

15 20 .

21 .

.

Both knights start on square 1, white moves to the lowest unvisited square (8), black then moves to the lowest unvisited square (9) and so on...

This sequence is finite, on the black knight's 5503rd step, square 3828 is visited, after which there are no unvisited squares within one knight move.

Crossrefs

Cf. A338288, A338289, A338290, A342946, A342948.

Programs

Python

# see program in A342948
A342947_lst = A342948_lst[::2] # Michael S. Branicky, Mar 30 2021