[seqfan]Suite de Perrin

[Jeffrey Shallit]

> From seqfan-request at ext.jussieu.fr  Sun May 17 11:45:59 1998
> From: Michel Tixier <tixier at dyadel.net>
> 
>             2) As regards the sequence A013988 (suite de Perrin)
>             a(0) = 3 , a(1) = 0 , a(n) = a(n-2) + a(n-3)
>             2 divide a(2) = 2
>             3 divide a(3) = 3
>             5 divide a(5) = 5
>             7 divide a(7) = 7
>            11 divide a(11) = 22
>            13 divide a(13) = 39
>             ........
> 
>          "   n prime divide a(n) " it's a conjecture or a theorem ?
> 
>             Can anyone give me any information about this?
> 
>                         Michel

It's discussed in my book with Eric Bach, _Algorithmic Number
Theory_, exercise 9.24, page 305.  In the solution you can find
many references.

Note that the result states "if n is prime, then n divides a(n)".  The
converse is not true.

Jeffrey Shallit