Perrin pseudoprime

Given the Perrin sequence, $a_{0}=3$ , $a_{1}=0$ , $a_{2}=2$ and $a_{n}=a_{n-3}+a_{n-2}$ for $n>2$ , if $n$ is not prime yet $n|a_{n}$ , that number is then called a Perrin pseudoprime. The first few Perrin pseudoprimes are 271441, 904631, 16532714, 24658561, 27422714, 27664033, 46672291 (listed in A013998 of Sloane’s OEIS).

By itself this is not a good enough test of primality. Further requiring that $a_{n}\equiv 0\mod n$ and $a_{-n}\equiv 1\mod n$ improves the test but not enough to be preferable to actually factoring out the number. The first few strong Perrin pseudoprimes are 27664033, 46672291, 102690901, 130944133, 517697641 (listed in A018187 of Sloane’s OEIS).

Unlike Perrin pseudoprimes, most other pseudoprimes (http://planetmath.org/PseudoprimeP) are because of a congruence relation to a given base.

Title	Perrin pseudoprime
Canonical name	PerrinPseudoprime
Date of creation	2013-03-22 16:11:33
Last modified on	2013-03-22 16:11:33
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	5
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 11B39
Defines	strong Perrin pseudoprime