[seqfan] Re: Sowing integers

[Maximilian Hasler]

Dear Eric & SeqFans,

"working on this" is exaggerated -- unfortunately I don't have the time,
not even to think whether (or why) there cannot be some smaller "loop"
in the orbit of some numbers such that the initial position would
never be reproduced.
But since you asked me, I looked at it and found this an interesting idea.
I quickly wrote a PARI 1-liner (so cryptic that it segfaults on PARI
versions prior to 2.4.4 due to a Vecsmall()++ bug)
which calculates the "looping values":

b(n)={my(o=n=Vecsmall(Str(n)),c,p=Mod(0,#n));until(!p &
o==n,c++;for(i=1,n[lift(p)+1]-n[lift(p)+1]=48,n[lift(p++)+1]++));c}

It gives:
S = [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 3, 6, 10, 12, 4, 8, 18, 6, 4, 3,
6, 10, 12, 4, 8, 18, 6, 11, 3, 2, 10, 12, 4, 8, 18, 3, 11,
20, 6, 10, 12, 4, 8, 18, 6, 11, 20, 18, 10, 12, 2, 8, 18, 6, 11, 4,
18, 28, 12, 4, 8, 18, 3, 11, 20, 6, 28, 5, 4, 8, 18, 2, 11, 20,
18, 28, 5, 10, 8, 18, 6, 11, 20, 18, 28, 5, 10, 12, 18, ...]

which seems to coincide with the S on your page (après correction ;-)

Regards,
Maximilian


On Tue, Sep 11, 2012 at 7:20 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
> Hello SeqFans,
> The sowing technique performed below could recall the Oware game.
> (...)
> http://www.cetteadressecomportecinquantesignes.com/AwalENG.htm
>
> In French:
> http://www.cetteadressecomportecinquantesignes.com/Awale.htm
>
> Maximilian Hasler is already working on this -- I hope this will be of interest for the rest of the list.
> Best,
> É.