1,3

Comments from N. J. A. Sloane, Feb 06 2026 (Start)

An equivalent definition: Walk along the square spiral, with its cells numbered starting at 0, as in A308884 and A274641. Start with no knights. If the square you are at is not attacked by an existing knight, place a knight there, otherwise leave it empty. The sequence lists the squares where the knights are. See links for illustrations.

For the initial 26 or so layers of the spiral, Karlsson's illustration shows a regular structure. But other sequences of this type have been known to become chaotic after millions of terms. Could that happen here? (End)

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Jonas Karlsson, Illustration for the equivalent definition mentioned in the COMMENTS. [Blue dots indicate squares occupied by knights. Shows 26 layers of the spiral.]

N. J. A. Sloane, Illustration for the equivalent definition mentioned in the COMMENTS. [Shows 6 layers of the spiral. Circles contain a knight, squares with a slash are attacked by a knight.]

(Python) # uses code/imports in A308884

def A308885_gen(t=0): yield from (k for k, ak in enumerate(A308884_gen()) if ak == t)

print(list(islice(A308885_gen(), 61))) # Michael S. Branicky, Feb 05 2026

Cf. A308884-A308895, A392177, A392178.

Sequence in context: A041093 A154746 A042781 * A136886 A191423 A195686

Adjacent sequences: A308882 A308883 A308884 * A308886 A308887 A308888

N. J. A. Sloane, Jul 01 2019

approved