OFFSET
0,22
LINKS
Michael S. Branicky, Table of n, a(n) for n = 0..50000
PROG
(Python)
from itertools import count, islice
def square_spiral(): # generator of square spiral coordinates
i, j, di, dj, L = 0, 0, 1, 0, 1
yield i, j
while True:
for s in range(2):
for k in range(L):
i, j = i+di, j+dj
yield i, j
di, dj = -dj, di
L += 1
def agen(): # 0, 1 = Black, Red
p, g = {0: set(), 1: set()}, {0: square_spiral(), 1: square_spiral()}
K = {(0, 0), (2, 1), (1, 2), (-1, 2), (-2, 1), (-2, -1), (-1, -2), (1, -2), (2, -1)}
m, n, diffs = [-1, -1], -1, 0
pi = {0: set(), 1: set()}
while True:
for turn in (0, 1):
for k in count(m[turn]+1):
loc = next(g[turn])
if all((loc[0]+i, loc[1]+j) not in p[1-turn] for i, j in K):
m[turn] = k
p[turn].add(loc)
pi[turn].add(k)
break
for n in range(n+1, min(m)+1):
diffs += (1 if n in pi[0] else -1 if n in pi[1] else 0)
yield diffs
print(list(islice(agen(), 84))) # Michael S. Branicky, Feb 07 2026
CROSSREFS
KEYWORD
sign,look
AUTHOR
N. J. A. Sloane, Feb 07 2026
STATUS
approved
