querying multidimensional sequences in OEIS

[franktaw at netscape.net]

Exactly what factorization order?  For most numbers, the sequence of
prime power exponents is not a sequence of positive integers.  If 2
represents the sequence (1), what sequence does 3 represent?

If doesn't work any better to use prime power exponents to represent
sequences of non-negative integers.  If 2 is (1) and 3 is (0,1), what 
do
you use to represent (1,0)?

There are ways around these difficulties, but they are pretty 
artificial.

A066099 sorts, first of all, by the number being composed; I think any
reasonable standard candidate should do that.  Second, it is simple,
with a definition tied in to the binary numbers.  Third, it is similar 
to the
Mathematica ordering for partitions (subsort in reverse lexicographic
order), which is one of the two standards for partition ordering in the
OEIS.

(The equivalent of the other, the Abramowitz and Stegun ordering,
was not yet in the OEIS; I did submit it the other day with A-number
A124734.  It is, in any event, not as simple to define as A066099.)

In any event, based on Neil saying to go ahead and submit these
sequences, I  have submitted them with comments stating that
A066099 is the standard ordering.

Franklin T. Adams-Watters


-----Original Message-----
From: maxale at gmail.com

  On 11/3/06, franktaw at netscape.net <franktaw at netscape.net> wrote:

  > In the following, b(i), i = 1..k is the finite sequence. I'm 
starting
 > all these
 > sequences with the empty sequence, but I searched for them without
 > that first term. All are shown here in A066099 order.

 What is good about this order comparing, say, to the prime
 factorization order suggested by Marc?

 I would vote for having a standard way to represent such sequences in
 OEIS (well documented there, and maybe even having a dedicated
 keyword). ...
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