2, 3, 3, 9, 9, ?

3, 7, 3, 3, 7, 9, ?

determine the two missing numbers and find the rule,

Bonus. how far can each sequence go? Can you find a longer sequence of numbers that follow the same rule?

Using the rule in my first answer, the first sequence stops with the single missing digit of 9 (233999), and the second sequence can go one longer: 37337999.

The second part of the bonus question looks harder.