A395649 Consider the square spiral with its cells numbered starting at 0. Three players, Red, Green and Blue, take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of a different color. a(n) = k if the n-th cell has been occupied at the k-th turn, a(n) = 0 otherwise.

1, 2, 3, 4, 5, 6, 0, 0, 0, 0, 7, 10, 0, 0, 0, 0, 0, 0, 13, 0, 9, 0, 0, 16, 8, 19, 0, 0, 11, 0, 22, 0, 0, 0, 25, 14, 12, 0, 0, 0, 15, 28, 17, 18, 31, 0, 34, 20, 37, 23, 26, 0, 40, 0, 0, 0, 21, 24, 27, 43, 29, 30, 32, 0, 35, 38, 41, 0, 46, 0, 33, 36, 0, 0, 0, 0

Offset

0,2

Comments

Each positive integer appears once.

Links

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

Rémy Sigrist, Table of n, a(n) for n = 0..10000, as in the b-file, but now the color of a(n) matches the color of the knight in cell n.

Rémy Sigrist, PARI program

Formula

a(A395645(k)) = 3*k-2.

a(A395646(k)) = 3*k-1.

a(A395647(k)) = 3*k.

a(A395648(k)) = 0.

Example

The first terms alongside the square spiral are:
    47---0---0---0---0---0--48---0--58---0--45
     |                                       |
     0  35---0--32--30--29--43--27--24--21  55
     |   |                               |   |
    50  38  12--14--25---0---0---0--22   0  42
     |   |   |                       |   |   |
     0  41   0   0---0---0---0---0   0   0   0
     |   |   |   |               |   |   |   |
    53   0   0   0   5---4---3  10  11   0  39
     |   |   |   |   |       |   |   |   |   |
     0  46   0  13   6   1---2   7   0  40  44
     |   |   |   |   |           |   |   |   |
     0   0  15   0   0---0---0---0   0   0   0
     |   |   |   |                   |   |   |
     0  33  28   9---0---0--16---8--19  26  52
     |   |   |                           |   |
     0  36  17--18--31---0--34--20--37--23  49
     |   |                                   |
     0   0---0---0---0---0---0---0---0---0---0
     |
    51--56--54---0--57--61--59--64--62--67--65

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A392177, A395486, A395506, A395645, A395646, A395647, A395648.

Sequence in context: A332782 A266449 A265536 * A037849 A037885 A347729

Adjacent sequences: A395646 A395647 A395648 * A395650 A395652 A395653

Keyword

nonn

Author

Rémy Sigrist, May 03 2026

Status

approved