The Perrin sequence follows \(P(n) = P(n-2) + P(n-3)\) from seeds 3, 0, 2 — skipping the immediately previous term. It runs 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, 51.
Its fame rests on a striking divisibility pattern: if \(n\) is prime, then \(n\) divides \(P(n)\). The converse — whether a composite \(n\) can divide \(P(n)\) — was open for over a century until 1982, when the first Perrin pseudoprime (271441) was found. The growth rate of the sequence is the plastic number ≈ 1.3247, the smallest possible Pisot number, with its own cult following in architecture via Dom Hans van der Laan.