If p is prime, then p|P(p), where P(p) is a member of the Perrin sequence 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, ... (OEIS A001608). A Perrin pseudoprime is a composite number n such that n|P(n). Several "unrestricted" Perrin pseudoprimes are known, the smallest of which are 271441, 904631, 16532714, 24658561, ... (OEIS A013998).

Perrin sequence | pseudoprime

Raoul Perrin