[seqfan] Re: Divisibility sequences in OEIS.

franktaw at netscape.net franktaw at netscape.net
Sat Dec 12 01:36:47 CET 2009

What is a divisibility sequence?  Just glancing at examples doesn't 
tell me.

There is no definition for divisibility sequence in either Mathworld or 
Wikipedia.  (Wikipedia does have an entry for Elliptic Divisibility 
Sequence.)  Does this term (without the elliptic) occur in the 
mathematical literature anywhere?  (A087612 has a reference to a paper 
it claims is titled "Primes in Divisibility Sequences"; but tracking 
down the link, I find it is actually titled "Primes in Elliptic 
Divisibility Sequences".)

I can't support adding a new keyword for this concept without more 
widespread recognition in the mathematical community than appears to 

I would suggest the following:

(1) Write a short description of what a divisibility sequence is, and 
the properties entailed thereby, and put it somewhere it can be 
referenced.  (One possibility is to send it to Neil and have him put it 
the directory for the OEIS.)

(2) Perform your suggested survey of the OEIS, putting in appropriate 
comments, and links to the document described in (1).  Possibly also 
add an entry to the OEIS index, and reference the sequences you find.

(3) Write up a paper describing the concept, proving the associated 
properties and listing divisibility sequences in the OEIS, and get it 

(4) By this point, the OEIS will probably have gone Wiki, and the 
introduction of a new keyword will be a somewhat different issue than 
it is now.  That would be the time suggest a new keyword, in any event.

If this concept has been described in the literature, step 1 can be 
modified to finding or creating an on-line reference if possible, with 
a link to it being added in step 2; step 3 can then be skipped.  A 
print reference would also be useful.

Franklin T. Adams-Watters

-----Original Message-----
From: Richard Guy <rkg at cpsc.ucalgary.ca>


Here is the preface to a file:

This is a list, in OEIS numerical order, of
divisibility sequences...

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