Another old Foxtrot comic for you today…

Obviously Jason makes a reference to the Fibonacci sequence, as mentioned in the strip. But what sequence is Marcus alluding to in the last panel? Fortunately, Wolfram MathWorld has the answer for us.

Marcus is referring to what is known as the Perrin Sequence. The Perrin Sequence is defined by the recurrence relation:

$P(n) = P(n-2)+P(n-3)$ $for$ $n > 2$, where

$P(0)=3, P(1)=0, P(2)=2$

It is also noted that if n is a prime number, then $n|P(n)$, [n divides P(n)]. For example, 19 is prime, P(19) = 209 and 209/19 = 11.

There have been many posts about prime numbers in other student blogs, and there seems to be some application with them here in the Perrin Sequence. Also the recursion that we see in the Fibonacci sequence, which has popped up in several other posts as well, makes an appearance here.