A395366 Walk along the hexagonal spiral, with its cells numbered starting at 0, as in A395362. Two players, Black and Red, take turns. When it is Black's turn, he places a knight at the smallest unoccupied cell not attacked by an existing Red knight, and when it is Red's turn, she places a knight at the smallest unoccupied cell not attacked by an existing Black knight. Sequence lists cells occupied by Red knights.

1, 3, 5, 8, 12, 16, 24, 30, 36, 40, 48, 52, 56, 63, 70, 74, 77, 80, 83, 86, 87, 90, 91, 96, 101, 102, 103, 108, 113, 114, 115, 120, 125, 126, 132, 134, 146, 148, 152, 156, 160, 162, 169, 183, 184, 185, 189, 195, 199, 200, 201, 205, 211, 215, 216, 218, 224, 225, 226, 232, 236, 242, 243, 244, 248, 250, 251, 253, 254, 256, 261, 262, 268

Offset

0,2

Comments

These are Glinski knights, as in hexagonal chess (see A395362).

There is a subtle point about the definition. Because the players take turns in placing a knight, the spiral is not filled in consecutively. To obtain the sequence, one must first fill in the whole spiral, and then return to the start, and record the Red knights that are encountered as one walks along the spiral.

Links

Jonas Karlsson, Table of n, a(n) for n = 0..19999

Jonas Karlsson, 12 shells of the completed spiral, containing 100 black and 100 red knights

Jonas Karlsson, 48 shells of the completed spiral, containing 1600 black and 1600 red knights

Crossrefs

This has the same relationship to A395362 as A392178 has to A308885.

See A395365 for the cells with Black knights, and A395367 for the unoccupied cells.

Sequence in context: A094913 A265060 A320849 * A255981 A020678 A310034

Adjacent sequences: A395363 A395364 A395365 * A395367 A395368 A395369

Keyword

nonn

Author

Jonas Karlsson and N. J. A. Sloane, May 18 2026

Status

approved