A392183 - OEIS

A392183

Consider the square spiral in the first quadrant, with its cells numbered starting at 0, as in A392181. 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, 14, 19, 20, 21, 24, 30, 35, 36, 39, 41, 43, 45, 47, 55, 56, 57, 65, 68, 72, 81, 83, 85, 87, 89, 91, 93, 100, 105, 109, 110, 111, 127, 130, 132, 136, 145, 149, 151, 153, 155, 157, 158, 159, 161, 167, 171, 175, 181, 182, 183, 184, 186, 187, 189, 201, 203, 204

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

There is a subtle point about the definition. Because the players take turns in placing a knight, the spiral is not filled in consecutively. To obtain the sequence, one must first 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.

LINKS

Michael S. Branicky, Table of n, a(n) for n = 1..50000

Michael S. Branicky, Python program for OEIS A392182 and A392183

Michael S. Branicky, The first 10^4 filled cells of the spiral

Michael S. Branicky, The first 10^6 filled cells of the spiral

Michael S. Branicky, The first 4*10^6 filled cells of the spiral

Michael S. Branicky, The first 64*10^6 filled cells of the spiral

N. J. A. Sloane, The playing field: The square spiral in the first quadrant, with initial square labeled 0.

N. J. A. Sloane, Squares 0 to 100 of the spiral. [Black circle = Black knight, red circle = Red knight, black slash = attacked by a Black knight, red slash = attacked by a Red knight.]

PROG

(Python) # see linked program

CROSSREFS

Cf. A392177-A392182.

Sequence in context: A279938 A280331 A079274 * A282421 A282684 A024863

Adjacent sequences: A392180 A392181 A392182 * A392184 A392185 A392186

KEYWORD

nonn

AUTHOR

Michael S. Branicky and N. J. A. Sloane, Feb 14 2026

STATUS

approved