I think the rule is: as long as there is a sequence of at least 3 adjacent 1-bits, you can replace them with 2 1-bits (1 on each side). The new 1-bit can of cou

I think the rule is: as long as there is a sequence of at least 3 adjacent 1-bits, you can replace them with 2 1-bits (1 on each side). The new 1-bit can of course merge into an existing run. This only fails to decrease the needed work for the N/3 and N/5 cases here, which form small regular patterns. For larger regular patterns, or for irregular patterns (2^odd-1), chances are that there will be at least some simplification (unless the pattern is mostly zeros in which case it isn't needed anyway).