Find the next two numbers in the sequence

This question appeared in my math competition and I managed to solve it, and I will give a hint if this becomes too hard.

  • $\begingroup$ Amazingly funny to attempt!!!! $\endgroup$ – user65573 Feb 22 at 1:53

It is:

OEIS A005150

The next two numbers are:

31131211131221, 13211311123113112211

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