Perrin number

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The Perrin numbers are defined by the recurrence relation

The first few numbers of the sequence are: 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, ...

Properties

A special property of the sequence of Perrin numbers is, that if is a prime number, then divides . The converse is false, because there exist composite numbers which divide . Those numbers are called Perrin pseudoprimes. The first few Perrin pseudoprimes are: 271441, 904631, 16532714, 24658561, 27422714, ...