[seqfan] Re: No progress on the classic "Football pools" problem in 52 years

[Tomasz Ordowski]

Note that 2k+1 divides 3^k if and only if k = (3^n-1)/2 for n = 0,1,2,...
https://oeis.org/A003462


śr., 23 cze 2021 o 19:14 Benoît Jubin <benoit.jubin at gmail.com> napisał(a):

> It looks like A004044(0) = 1 !
> In that case, the trivial lower bound is attained.  Actually, in the known
> cases where 3^n/(2n+1) is an integer, then that lower bound is attained.
> This means that there is a solution with no overlaps.  If this is true in
> general, this is probably well-known by people knowing Hamming codes (of
> which I am not).  Or did I misinterpret the problem ?
> Best regards,
> Benoît
>
> On Mon, Jun 21, 2021 at 6:52 AM Neil Sloane <njasloane at gmail.com> wrote:
>
> > I grew up in a country where many people played the football pools every
> > week (trying to guess the winners of next week's games: you know
> Manchester
> > United is going to beat Arsenal, but there are 13 games to predict).
> >
> > The classical problem translates into finding the smallest covering code
> in
> > {0,1,2}^n with covering radius 1.  The sequence (A004044) begins
> > 1,3,5,9,27, but even after 52 years, a(6) is still not known.  Tonight I
> > came across a lot of references, which I have added to A004044.  a(6) is
> > known to be 71, 72, or 73.
> > If you can solve it, you might not make any money, but you will probably
> > get your name in the science section of the newspaper.
> >
> > Good publicity for the OEIS too!
> >
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> > --
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> >
>
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