One possible answer is:
9 10 11 12 4 5 6 7 8 4 9 5 10 6 11 7 12 8
The structure hints at a general method (which might not have been apparent from the original example, but nevertheless follows the same idea). Using numbers m to n, n needs to be (at least) 3m.
If you’re interested I developed this into a sequence which has now been published on the OEIS (Online Encyclopedia of Integer Sequences): https://oeis.org/A338804