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Construct a recurrence relation with initial terms  ,  ,  and
 for  . The first few terms of the sequence defined by this recurrence relation are: 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367 (listed in A001608 of Sloane's OEIS). This is the Perrin sequence, sometimes called the Ondrej Such sequence. Its generating function is
A number in the Perrin sequence is called a Perrin number.
It has been observed that if  , then  is a prime number, at least among the first hundred thousand integers or so. However, the square of 521 passes this test.
The  th Perrin number asymptotically matches the  th power of the plastic constant.
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- W. W. Adams and D. Shanks, ``Strong primality tests that are not sufficient" Math. Comp. 39, pp. 255 - 300 (1982)
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