A Strange Permutation Substring Sequence: Introducing OEIS A359012

I’ve been exploring a new integer sequence on the OEIS, A359012, and turned it into a small experiment in “data‑driven number theory”. This post briefly introduces the sequence and shares links to the live dataset and code. What is A359012? A359012 tracks integers (k) that reappear inside permutation numbers (xPy) when (k) is formed by concatenating the digits of (x) and (y). More concretely: Take natural numbers (x) and (y). Form (k) by writing the digits of (x) followed by the digits of (y). Compute (xPy), the number of permutations of (x) objects taken (y) at a time. If the decimal expansion of (xPy) contains (k) as a contiguous substring, then (k) belongs to A359012. The first few terms (with one witness each) look like this: k x y xPy (permutations) 318 31 8 318073392000 557 55 7 1022755734000 692 69 2 4692 729 72 9 30885807297945600 2226 222 6 111822261510960 In each case, (k) appears as a substring of the decimal representation of (xPy). A few empirical facts Using a brute‑force