A396295 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 (Glinski) queen at the smallest unoccupied cell not attacked by an existing Red queen, and when it is Red's turn, she places a queen at the smallest unoccupied cell not attacked by an existing Black queen. Sequence lists cells occupied by Red queens.

19, 23, 47, 57, 61, 62, 68, 128, 129, 131, 137, 162, 173, 179, 205, 217, 223, 227, 284, 293, 327, 331, 332, 337, 338, 344, 345, 372, 382, 388, 397, 403, 406, 411, 465, 470, 471, 473, 476, 477, 540, 548, 557, 613, 622, 631, 633, 637, 640, 647, 686, 694, 723, 729, 732, 801, 807, 813, 817, 821, 823, 824, 826, 898, 904, 907, 910, 1020

Offset

0,1

Comments

These are Glinski queens, as in hexagonal chess (see A396292).

There is a subtle point about the definition. Because the players take turns placing a queen, 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 queens that are encountered as one walks along the spiral.

Links

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

Jonas Karlsson, The first 20000 queens in the spiral, 10000 of each color

Jonas Karlsson, The first 200000 queens in the spiral

Jonas Karlsson, The first two million queens in the spiral

Crossrefs

Cf. A395362, A395365-A395367, A396292, A396294, A396296.

Sequence in context: A039292 A043115 A043895 * A288614 A033214 A107185

Adjacent sequences: A396292 A396293 A396294 * A396296 A396297 A396298

Keyword

nonn

Author

Jonas Karlsson and N. J. A. Sloane, May 22 2026

Status

approved