Perrin SequenceYou are currentlybrowsing as guest. Click here to log in 

The Perrin Sequence is the integer sequence defined by
Taking $\beta$ and $\gamma$ to be the solutions with modulus less than 1, this gives

Since the $n^{th}$ term is roughly $\alpha^n,$ we can take log base ten and see that $log_{10}(\alpha)=0.1221234...$ and so $n^{th}$ term will have roughly $0.12n$ decimal digits.
The Perrin Sequence has the amazing property that it seems that n divides P(n) if and only if n is a prime number. This conjecture seems solid, certainly holding for n up to 10^5, but it fails for n=271441. This is a great example how patterns fail for large enough cases.
Here are the first few values ...



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