You asked a question, I gave an answer. I’m not sure where you get “condescending” there. I was assuming you had read an academic text, so I was hoping that you might have seen those patterns before.

You would look at the data for gaps, as my answer explained. You could use logic to predict some gaps, but not all gaps would be predictable. Mendeleev was able to use logic and patterns in the periodic table to predict the existence of germanium and other elements, which data confirmed, but you could not logically derive the existence of protons, electrons and neutrons without the later experimentations of say, JJ Thompson and Rutherford.

You can’t just feed the sum of human knowledge into a computer and expect it to know everything. You can’t predict “unknown unknowns” with logic.