Tricky Google interview question

Question

A friend of mine is interviewing for a job. One of the interview questions got me thinking, just wanted some feedback.

There are 2 non-negative integers: i and j. Gi

Answer 1

This is the relevant entry at OEIS.

It seems to be possible to obtain the ordered sequence by generating the first few terms, say

1 2 4 5

and then, starting from the second term, multiplying by 4 and 5 to get the next two

1 2 4 5 8 10

1 2 4 5 8 10 16 20

1 2 4 5 8 10 16 20 25

and so on...

Intuitively, this seems correct, but of course a proof is missing.