A396186 Consider the square spiral with its cells numbered starting at 0, as in A308884 and A274641. Two players, Black and Red, take turns. When it is Black's turn, he places a knight at the first cell in the spiral that is beyond the last Red knight and is not attacked by any Red knight, and when it is Red's turn, she places a knight at the first cell that is beyond the last Black knight and is not not attacked by any Black knight. Sequence lists squares occupied by Red knights.

1, 3, 6, 12, 25, 35, 37, 41, 45, 48, 51, 55, 59, 62, 64, 68, 70, 72, 77, 81, 90, 92, 95, 114, 117, 121, 125, 137, 143, 146, 149, 151, 153, 155, 158, 161, 168, 170, 175, 179, 181, 185, 190, 192, 194, 196, 200, 204, 206, 208, 210, 214, 219, 233, 238, 240, 244, 247, 260, 276, 283, 287, 289, 293, 295, 299, 311, 317, 321, 323, 326, 329

Offset

0,2

Comments

Similar to A392178, except that now the Black and Red knights must alternate along the spiral. In A392178 it was possible to have two successive knights of the same color, but here that is forbidden.

References

Ingmar Eissfeldt, Email to N. J. A. Sloane, May 15 2026.

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..19999

Michael S. Branicky, Python program for OEIS A396185, A396186 and A396187

Crossrefs

Cf. A274641, A308884, A392177, A392178, A396185, A396187.

Sequence in context: A102254 A278666 A007239 * A088970 A068425 A329355

Adjacent sequences: A396183 A396184 A396185 * A396187 A396188 A396189

Keyword

nonn

Author

N. J. A. Sloane, May 31 2026, based on an email from Ingmar Eissfeldt, May 15 2026.

Status

approved