[riebfrgk] Concatenation of increasing binary numbers

Given a binary string the concatenation of a sorted sequence binary numbers (of varying bit width, but the most significant bit is 1), parse it into "guesses" as to what the original sequence was.

In particular, what is the longest parse, the sequence with the most elements?  (The shortest parse is trivially 1 element long.)

Sorted numerically or lexicographically?

MSB first, or LSB?

Application: broadcasting Mersenne primes exponents.  (Or indices).