Is it possible to identify the mechanism or algotithm that generates numbers having a list of matches and a list of mismatches

Dear stackoverflow community,

I thank in advance for your comments.

This example is fictional:
Let's assume that universities do not assign matriculation numbers continuously but pseudo-randomly. Furthermore, let's assume that these matriculation numbers have 7 digits (and thus 7^7 possible outcomes).

I have a list of (pseudo-randomly generated) a hundred thousand of matriculations numbers that are not assigned yet.
In addition, I can collect, say, 100 (or more?) numbers that actually are assinged and put them into another list.
I need a pseudo-randomly generated list of matriculation numbers that are assigned, e.g. to invite students to a survey using randomized sampling.

Now a list of assigned numbers (matches) and unassigned numbers (mismatches), is there any way to identify the mechanism or algorithm that assinges the numbers to students? And if there is no way to reproduce it, is there any possibility to minimize the prediction of mismatches (in order to increase efficiency)?

Thank you and best wishes!