Perrin sequence

Construct a recurrence relation with initial terms a0=3, a1=0, a2=2 and an=an-3+an-2 for n>2. The first few terms of the sequenceMathworldPlanetmath 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 sequenceMathworldPlanetmath, 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 n|an, then n is a prime numberMathworldPlanetmath, at least among the first hundred thousand integers or so. However, the square of 521 passes this test.

The nth Perrin number asymptotically matches the nth power of the plastic constant.


Title Perrin sequence
Canonical name PerrinSequence
Date of creation 2013-03-22 16:05:19
Last modified on 2013-03-22 16:05:19
Owner Mravinci (12996)
Last modified by Mravinci (12996)
Numerical id 5
Author Mravinci (12996)
Entry type Definition
Classification msc 11B39
Defines Perrin number