A binary orientable sequence of span 
is a finite binary sequence whose
windows of 
consecutive symbols, read in either direction, are all distinct. Thus no window is
a palindrome and no two windows are reversals of each other. For a periodic binary
orientable sequence, windows are counted within a single period, including those
crossing its boundary (Mitchell and Wild 2022).
Mitchell (2026) determined the maximum aperiodic lengths for spans 4 through 16 as 8, 14, 26, 48, 108, 210, 444, 882, 1878, 3752, 7764, 15534, 31810. The maximum periods for spans 5 through 16 are 6, 16, 36, 92, 194, 426, 860, 1856, 3728, 7738, 15504, 31776. There is no periodic binary orientable sequence of span 4. Mitchell (2026) reports AI assistance with the search programs and mathematical checking.
