User blog comment:Ikosarakt1/Unusual number naming scheme/@comment-25418284-20140429200600

Good stuff. It sucks that every sequence is confined to starting with an up arrow due to the way binary numbers work.

Although it's significantly dirtier, you could just enumerate all the possible sequences by length and lexicographical order. So zeroarrowal = 3v3, onearrowal = 3^3, twoarrowal = 3vv3, threearrowal = 3v^3 ...