A397055 Consider the Hilbert curve with its cells numbered starting at 0. Two players take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of the other player; a(n) = k if the n-th cell has been occupied at the k-th turn, a(n) = 0 otherwise.

1, 2, 3, 4, 6, 5, 8, 7, 0, 0, 9, 0, 0, 0, 0, 11, 10, 13, 0, 12, 15, 14, 16, 18, 0, 17, 20, 0, 0, 0, 0, 19, 21, 23, 0, 0, 25, 22, 24, 0, 0, 27, 26, 28, 29, 0, 30, 31, 33, 32, 0, 35, 0, 34, 0, 0, 0, 0, 37, 36, 38, 39, 0, 40, 0, 41, 42, 0, 0, 0, 0, 43, 45, 44, 47

Offset

0,2

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Formula

a(A397052(k)) = 2*k - 1.

a(A397053(k)) = 2*k.

a(A397054(k)) = 0.

Example

The first terms alongside the Hilbert curve are:
    40---0  32--33--31  29--28--26
         |   |       |   |       |
    38--39   0--35  30---0   0--27
     |           |           |
    36   0---0   0  23---0   0--24
     |   |   |   |   |   |       |
    37---0   0--34  21   0--25--22
                     |
     5---8   0---9  19   0---0--20
     |   |   |   |   |   |       |
     6   7---0   0   0---0   0--17
     |           |           |
     4---3   0---0  13---0  18--16
         |   |       |   |       |
     1---2   0--11--10  12--15--14

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A392177, A397052, A397053, A397054.

Sequence in context: A395364 A256988 A104650 * A083179 A391106 A123503

Adjacent sequences: A397052 A397053 A397054 * A397056 A397057 A397058

Keyword

nonn

Author

Rémy Sigrist, Jun 18 2026

Status

approved