A395647 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. Sequence lists squares occupied by a Blue knight.

2, 5, 20, 36, 40, 43, 56, 57, 58, 61, 70, 71, 86, 88, 90, 94, 110, 112, 114, 129, 130, 131, 135, 140, 142, 144, 152, 153, 157, 159, 181, 182, 183, 184, 188, 189, 191, 204, 208, 209, 234, 235, 236, 238, 240, 244, 245, 246, 248, 266, 267, 272, 274, 276, 278, 298

Offset

1,1

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Michael S. Branicky, Python program for OEIS A395645, A395646 and A395647

Michael S. Branicky, First 10^8 cells (with |x|, |y| <= 5000)

Brady Haran, Jonas Karlsson, and N. J. A. Sloane, Red & Black Knights (extraordinary result); Amazing Chessboard Patterns (extra), YouTube Numberphile videos, May 2026

Rémy Sigrist, The center of the spiral (with |x|, |y| <= 50)

Rémy Sigrist, The center of the spiral (with |x|, |y| <= 500)

Rémy Sigrist, PARI program

Prog

(PARI) \\ See Links section.
(Python) # See Links section.

Crossrefs

Cf. A392177, A395645, A395646, A395648, A395649.

Sequence in context: A247131 A192164 A244087 * A396118 A361134 A056726

Adjacent sequences: A395644 A395645 A395646 * A395648 A395649 A395650

Keyword

nonn

Author

Rémy Sigrist, May 02 2026

Status

approved