a sequence that needs extending

[Dean Hickerson]

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