A342946 Squares visited by the white 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, 8, 6, 2, 12, 16, 24, 19, 15, 34, 14, 21, 43, 20, 25, 17, 39, 29, 23, 32, 42, 35, 45, 53, 28, 54, 63, 73, 84, 50, 59, 47, 56, 69, 80, 92, 108, 95, 83, 72, 62, 75, 44, 55, 89, 101, 86, 98, 111, 125, 140, 94, 107, 121, 173, 156, 137, 122, 174, 157, 141, 126

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 white knight's 292nd step, square 406 is visited, after which there are no unvisited squares within one knight move.

Crossrefs

Cf. A338288, A338289, A338290, A342947, A342948.

Programs

Python

# see program in A342948
A342946_lst = [1] + A342948_lst[1::2] # Michael S. Branicky, Mar 30 2021