218933
i did some math to try to generalize this property, the illusion of multiple periodicity -- my metric was amortized, normalized edit distance between successive periods of a shorter length than the actual binary sequence. if we discard sequences with runs of longer than 2 digits, this sequence (10100101) and 11011010 are the only sequences of 8 digits or less that have an amortized, normalized edit distance of 1/4 of less for a smaller period (5 in both cases). there are some 9- and 10-digit sequences that also fit the bill:
110101010 (7)
110110010 (6)
110110100 (6)
1101100100 (7)
1101101100 (7)
tho ofc the 6-period ones aren't coprime with the actual sequence length of 9. and ofc this info depends on me having done everything right
choice of "mode" seems important; these are listed in the "brightest" mode which may not be what you want to establish an initial sense of a different period
110101010 (7)
110110010 (6)
110110100 (6)
1101100100 (7)
1101101100 (7)
tho ofc the 6-period ones aren't coprime with the actual sequence length of 9. and ofc this info depends on me having done everything right
choice of "mode" seems important; these are listed in the "brightest" mode which may not be what you want to establish an initial sense of a different period
