A396465 Consider the square spiral in a single quadrant with its cells numbered starting at 0. Three players take turns and place black knights(K), cyan antelopes(A), and red ferzes(F), respectively, at the smallest unoccupied cell not attacked by an existing pieces of a different color. Sequence lists unoccupied squares.

6, 8, 14, 16, 21, 23, 24, 27, 31, 33, 35, 37, 40, 42, 44, 45, 47, 52, 53, 54, 60, 62, 67, 69, 71, 73, 75, 77, 79, 81, 88, 92, 94, 95, 103, 104, 106, 114, 116, 119, 120, 122, 124, 128, 129, 131, 133, 138, 140, 142, 148, 150, 151, 153, 155, 157, 159, 161, 162, 163, 167, 172, 174, 183, 187, 188, 189, 190, 191, 192, 193, 195, 196, 203

Offset

1,1

Comments

A variant of A392177 with three players with different fairy chess pieces.

Links

Sander G. Huisman, Table of n, a(n) for n = 1..10000

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

Sander G. Huisman, Image of the first 10^5 grid positions.

Sander G. Huisman, Image of the first 10^6 grid positions.

Sander G. Huisman, Image of the first 10^7 grid positions.

Sander G. Huisman, Image of the first 10^8 grid positions.

Example

The grid is as follows:
  0  1  8  9  24 25
  3  2  7  10 23 26
  4  5  6  11 22 27
  15 14 13 12 21 .
  16 17 18 19 20 .
  .  .  .  .  .  .
And gets occupied as follows:
  K A . A . K
  K F K K . A
  F K . A K .
  A . F K . A
  . F K F A K
  . A . F . F
Where the . means that the position remains unoccupied.

Crossrefs

Cf. A392182, A392183. Pieces given by: A396461, A396462, A396463.

Sequence in context: A332820 A359827 A315884 * A178950 A047451 A194399

Adjacent sequences: A396462 A396463 A396464 * A396466 A396467 A396468

Keyword

nonn,new

Author

Sander G. Huisman, May 26 2026

Status

approved