# Two ordering problems

franktaw at netscape.net franktaw at netscape.net
Thu Aug 28 00:59:34 CEST 2008

```The property you need is similar to that for a Beatty sequence.  The
position
of the nth X (or Y) in the sequence will be floor(a*n+c) for some a and
c.

-----Original Message-----
From: David Wilson <dwilson at gambitcomm.com>

Max Alekseyev wrote:
> It appears that the sequence is good iff the number of Y (resp. X)
> symbols between any two neighboring X (resp. Y) symbols either equals
> an integer constant or varies between some two consecutive integer
> values.
> In the aforementioned sample sequence
> X,Y,X,Y,X,X,Y,X,Y,X,X,Y,...
> the distance between every two neighboring X's is 0 or 1 and the
> distance between every two neighboring Y's is 1 or 2.
>
> With this characterization in mind, it is easy to compute the number
> of good sequences of length n.
>
Your observation is certainly a property of good sequences, indeed the
distance between any two adjacent X's will always be k or k+1 for some
k
(similarly for adjacent Y's). This is necessary for a good sequence,
but
not sufficient. For example

X,Y,X,Y,X,Y,X,X,Y,X,X

is not good.

Dear Sequence Fans,

There are now three new web pages to use when sending in:

1.  A new sequence
2.  An addition to an existing sequence
3.  A b-file

See the old "Submit new seq. or comment" page for the links.
Please use the new pages rather than the old page!
This will make maintaining the OEIS a lot easier.

But these pages are new - let me know
if you find any bugs!

Thanks

Neil

```