A396616 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 Red knight.

1, 3, 4, 6, 12, 16, 23, 25, 27, 32, 36, 39, 45, 50, 52, 65, 66, 67, 71, 73, 77, 82, 88, 90, 92, 96, 98, 99, 112, 117, 118, 119, 120, 121, 122, 123, 140, 142, 144, 146, 148, 153, 154, 158, 159, 161, 164, 166, 175, 179, 181, 185, 186, 187, 188, 189, 190, 191, 192, 193

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 Red knights that are encountered as one walks along the spiral.

See A396615 for images of the spiral.

Links

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

Crossrefs

Cf. A396617, A396615 (the Black knights), A392177, A392178, A392182, A392183.

Sequence in context: A044843 A293593 A024373 * A111159 A210523 A109069

Adjacent sequences: A396613 A396614 A396615 * A396617 A396618 A396619

Keyword

nonn

Author

Scott R. Shannon, May 31 2026

Status

approved