games born on day n

[John Conway]

On Thu, 22 Nov 2001, Richard Guy wrote:

> Dean is quite right, and there should be two sequences.
>
> All games are `born again' each day after their birthday.
>
> David Wolfe, Dan Calistrate & Marc Paulhus have
> shown that (all) the games born on day  n  form a
> distributive lattice.  A paper will appear in
> More Games of No Chance, the proceedings of the
> 2000 Workshop at eMiSaRI.

   Since the more interesting sequence is the inclusive

one, I was careful to use the phrase "born by day n"
                                           ^^
in ONAG (for the misere games problem).  Just what problem

does the following refer to?   JHC.


> Newborn games:  1  3  18  1452  ...
>
> Games:          1  4  22  1474  ...
>
> The number of levels in the lattice (another
> recordable sequence?)
>
>                 1  3   9    45   2949   ...
>
> is one more than twice the (total) number
> of games born on the previous day.
>
> Best,   R.
>
> On Wed, 21 Nov 2001, Dean Hickerson wrote:
>
> > > Will some fanster put this into the approved
> > > shape for Neil ?  Thanks!
> >
> > I'll do it in a few days if noone does it first.  (I don't have my
> > references handy at the moment.)
> >
> > > The following is the sequence of numbers of games
> > > born on days 0, 1, 2, 3.
> >
> > That should probably be "on or before".  E.g. the 4 games on day 1 include
> > the one from day 0 and 3 new ones.  Perhaps the sequence (1 3 18 1452) that
> > counts the new ones on day n should also be included.
> >
> > > 1 4 22 1474
> >
> > For what it's worth, Robert Li and I also counted 1474 games on day 3 when
> > we were grad students at Berkeley in 1974.  We were working without a
> > computer, and made no attempt to count the day 4 games.
> >
> > Dean Hickerson
> > dean at math.ucdavis.edu
>
>