a sequence that needs extending

[Rob Pratt]

On Fri, 25 Jul 2003, Dean Hickerson wrote:

> Neil wrote:
>
> > The reference is from 1994; i don't know if there
> > has been any progress since then
> > (although Dean Hickerson may know - he is cited several times
> > in the chapter where it appears).
> >
> > It would be nice to have some more terms.
>
> I thought that I'd submitted this sequence a few years ago, but apparently
> not.
>
> I don't think any more terms are known for sure, but a few years ago I
> improved the lower bound for a(8) from 22 to 23:
>
>     - - 1 - - 3 6 7
>     - - 0 6 7 - - -
>     6 7 - - - - - -
>     - 1 - 3 - - - 5
>     - 0 - - - 2 5 -
>     3 - - - 5 - - -
>     1 - - - 2 - - 4
>     0 - - 2 - - 4 -
>
> Also, someone proved that  a(n) = o(n^2),  answering Problem 3 on page 97
> of the Stein/Szabo book.  (I've asked Stein for a reference to the paper
> that proves that.)
>
> Dean Hickerson
> dean at math.ucdavis.edu

a(6) = 14 (the known lower bound is optimal)

Still working on n >= 7...

Rob Pratt
Department of Operations Research
The University of North Carolina at Chapel Hill

rpratt at email.unc.edu

http://www.unc.edu/~rpratt/