[seqfan] Re: [math-fun] Divisibility sequences in OEIS.

[rwg at sdf.lonestar.org]

NJAS> Here is the preface to a file:
>
> This is a list, in OEIS numerical order, of
> divisibility sequences.

I confess to having looked up only a few of the 60-odd sequences, but it
may come as news to some that there are elliptic divisibility sequences
of polynomials.  E.g.
s[1]:s[2]:1,s[3]:-1,s[4]:x,s[n+4] :=(s[n+3]*s[n+1] + s[n+2]^2)/s[n]
gives
1 1
2 1
3 - 1
4 x
5 x + 1
   2
6 x  - x - 1
      3
7 - (x  + x + 1)
8 - x (3 x + 2)
   5    4      2
9 x  - x  + 3 x  + 3 x + 1
               5    4      3      2
10 - (x + 1) (x  - x  + 3 x  + 2 x  - 2 x - 1)
       7      6      5      4      3      2
11 - (x  - 2 x  + 3 x  + 9 x  + 5 x  + 3 x  + 3 x + 1)
         2            6      4      3      2
12 - x (x  - x - 1) (x  + 2 x  + 5 x  + 9 x  + 9 x + 3)
 . . .
where s[<prime>] is irreducible, etc.
--rwg