It’s strange: you can learn something, use it daily for years, and never notice the underlying patterns. Until I read a post on Paleoglot this morning, I hadn’t realised how regular six of the Japanese numerals are.
The rule to double is: i → u, o → a. (Keep in mind that h and f represent the same morpheme in Japanese.)
The pattern has disappeared from the basic forms of the numbers between Old and Modern Japanese, but it’s still represented perfectly in the counter forms listed above.