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

1,2

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

Links

Table of n, a(n) for n=1..63.

Prog

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

Crossrefs

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

Sequence in context: A236257 A019909 A324002 * A227324 A359441 A117018

Adjacent sequences: A342944 A342945 A342946 * A342948 A342949 A342950

Keyword

nonn,fini

Author

Andrew Smith, Mar 30 2021

Status

approved