A396615 Consider the spiral of numbers in the upper half-plane with its cells numbered as in A396617, but starting at 0. Two players, Black and Red, take turns. When it is Black's turn, he places a knight at the smallest unoccupied cell not attacked by an existing Red knight, and when it is Red's turn, she places a knight at the smallest unoccupied cell not attacked by an existing Black knight. Sequence lists squares occupied by a Black knight.

0, 2, 5, 7, 13, 17, 18, 24, 31, 33, 35, 38, 40, 44, 46, 51, 55, 59, 60, 61, 72, 76, 78, 84, 86, 89, 94, 100, 102, 105, 106, 107, 109, 111, 113, 127, 128, 129, 133, 135, 137, 138, 152, 156, 160, 162, 168, 170, 171, 172, 173, 174, 176, 180, 197, 199, 201, 203, 205, 206

Offset

0,2

Comments

Note that spiral is not filled in consecutively so, to obtain the sequence, one must fill in the whole spiral and then return to the start and record the Black knights that are encountered as one walks along the spiral.

Links

Scott R. Shannon, Table of n, a(n) for n = 0..10000

Scott R. Shannon, Image of the first 1000 filled cells. Zoom in to see the spiral numbers and the small grey lines indicating the spiral's path. White cells indicate no knight is placed there.

Scott R. Shannon, Image of the first 1000000 filled cells.

Crossrefs

Cf. A396617, A396616 (the Red knights), A392177, A392178, A392182, A392183.

Sequence in context: A293762 A161889 A275284 * A261123 A336451 A249330

Adjacent sequences: A396612 A396613 A396614 * A396616 A396617 A396618

Keyword

nonn

Author

Scott R. Shannon, May 31 2026

Status

approved