[SeqFan] Re: Sequence relating to Pell numbers; a new technique

[Antti Karttunen]

creigh at o2online.de wrote:

> I'm glad you mentioned this. I am aware of 2)- for ex.,
>
>it was important (at least for me) to confirm that 
>a way had been found to generate infinitely many 
>sequences of the form:
>http://www.research.att.com/projects/OEIS?Anum=A097947
>Of course, I did not begin the long procedure of submitting  
>these sequences to OEIS.  
>  
>

If you discover an interesting family of sequences
of _enumerably infinite_ cardinality, I suggest that
you create a square array, where the said sequences
appears as rows and are sorted by some "natural"
order. The ordering technique depends on how
many "free parameters" there are that define each
sequence.
Then submit also a few sequences from the beginning
of that array, and depending on the naturalness of your
ordering, these are usually also the most important
sequences in that family.

Here is a bit complicated example where I have
used this idea:
http://www.research.att.com/projects/OEIS?Anum=A089840
which involves also filtering out the duplicate sequences.

Note that I can now refer to the kth sequence
occurring in that array just as A089840[k]
without an immediate need to submit it to the OEIS.


See http://www.research.att.com/projects/OEIS?Anum=A065625
for another table where the breadth-first traversal of
the Stern-Brocot tree is used as the underlying ordering
algorithm. Good if you need to iterate over the rationals
or ordered pairs of coprime integers.


Yours,

Antti Karttunen