A395647 - OEIS

A395647

Consider the square spiral with its cells numbered starting at 0. Three players, Red, Green and Blue, take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of a different color. Sequence lists squares occupied by a Blue knight.

%I #16 May 19 2026 14:20:34

%S 2,5,20,36,40,43,56,57,58,61,70,71,86,88,90,94,110,112,114,129,130,

%T 131,135,140,142,144,152,153,157,159,181,182,183,184,188,189,191,204,

%U 208,209,234,235,236,238,240,244,245,246,248,266,267,272,274,276,278,298

%N Consider the square spiral with its cells numbered starting at 0. Three players, Red, Green and Blue, take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of a different color. Sequence lists squares occupied by a Blue knight.

%H Rémy Sigrist, <a href="/A395647/b395647.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael S. Branicky, <a href="/A395645/a395645.py.txt">Python program for OEIS A395645, A395646 and A395647</a>

%H Michael S. Branicky, <a href="/A395645/a395645_2.png">First 10^8 cells (with |x|, |y| <= 5000)</a>

%H Brady Haran, Jonas Karlsson, and N. J. A. Sloane, <a href="https://youtu.be/UiX4CFIiegM">Red & Black Knights (extraordinary result)</a>; <a href="https://youtu.be/VgmDuBCayPw">Amazing Chessboard Patterns (extra)</a>, YouTube Numberphile videos, May 2026

%H Rémy Sigrist, <a href="/A395645/a395645_1.png">The center of the spiral (with |x|, |y| <= 50)</a>

%H Rémy Sigrist, <a href="/A395645/a395645.png">The center of the spiral (with |x|, |y| <= 500)</a>

%H Rémy Sigrist, <a href="/A395647/a395647.gp.txt">PARI program</a>

%o (PARI) \\ See Links section.

%o (Python) # See Links section.

%Y Cf. A392177, A395645, A395646, A395648, A395649.

%K nonn

%O 1,1

%A _Rémy Sigrist_, May 02 2026