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

1,2

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.

Links

Table of n, a(n) for n=1..62.

Prog

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

Crossrefs

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

Sequence in context: A195497 A316588 A323810 * A195336 A196773 A197824

Adjacent sequences: A342943 A342944 A342945 * A342947 A342948 A342949

Keyword

nonn,fini

Author

Andrew Smith, Mar 30 2021

Status

approved