A393450 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 king at the smallest unoccupied cell not attacked by an existing Red king, and when it is Red's turn, she places a king at the smallest unoccupied cell not attacked by an existing Black king. Sequence lists squares occupied by a Black king.

0, 2, 5, 6, 11, 12, 13, 18, 19, 20, 21, 28, 29, 30, 31, 32, 39, 40, 41, 42, 43, 44, 53, 54, 55, 56, 57, 58, 59, 68, 69, 70, 71, 72, 73, 74, 75, 86, 87, 88, 89, 90, 91, 92, 93, 94, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159

Offset

0,2

Comments

Similar to A392177 and A392178, but placing kings instead of knights.

Links

Jonas Karlsson, Table of n, a(n) for n = 0..19999 (terms 0..9999 from Michael S. Branicky)

Michael S. Branicky, Python program for OEIS A393450 and A393451

Jonas Karlsson, Illustration of first 3200 squares of the spiral

Prog

(Python) # see linked program

Crossrefs

Cf. A393451 (Red kings). See also A308884, A274641, A392177, A392178 (knights).

For kings of a single color, see A307188.

For queens, see A273059, A395348, and A395349.

Sequence in context: A376762 A206332 A269966 * A026344 A284488 A322047

Adjacent sequences: A393447 A393448 A393449 * A393451 A393452 A393453

Keyword

nonn

Author

Jonas Karlsson and N. J. A. Sloane, Apr 20 2026

Status

approved