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:
, where
It is also noted that if n is a prime number, then , [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.


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October 19, 2010 at 5:42 pm
pluprofedgar
cool. I have never heard of the Perrin sequence before nor did I know the fact about
. Is the proof easy to show that? Do you know?
October 20, 2010 at 6:44 am
risesa
I see in some JSTOR articles that this has been proven as far back as 1876. However, I have yet to see the actual proof, which probably means it’s not so easy to show. http://www.jstor.org/pss/2008548