[seqfan] Re: A new sequence in Dutch magazine "Pythagoras"

Arie Bos arie.0.bos at gmail.com
Fri Dec 2 11:25:16 CET 2016


"Andere rijen" is "Other sequences", but it appears to be only one other sequence, the others were flawed.

Given two fractions a_1/b_1 and a_2/b_2 with period p_1 and p_2, what is the maximal period of a_1/b_1 * a_2/b_2?
If you make a table with all combinations of (p_1,p_2) you get (see table in page 29 of http://www.pyth.eu/jaargangen/Pyth55-5.pdf)
    1     2      3      4        5        6        7
1  9  18    27    36     45      54      63
2      198  54  396    90    594    126
3          2997  108  135  5994   189
4                39996  180  3564   252  
5                         499995 270    315
Column-wise, this becomes  9, 18, 198, 27, 54, 2997, 36, 396, 108, 39996, …

Hope I made no mistakes.
Arie Bos


> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil
> Sloane
> Sent: 2 December, 2016 7:43
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: A new sequence in Dutch magazine "Pythagoras"
> 
> By the way,  what about the other new sequences in the same Pythagoras
> article? See "Andere Rijen" - can someone explain what they are?  (And then
> they too should be added to the OEIS.) (Here is the link again:
> http://www.pyth.eu/jaargangen/Pyth55-6.pdf  See page 21)
> 
> 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
> 
> 
> On Fri, Dec 2, 2016 at 1:35 AM, Neil Sloane <njasloane at gmail.com> wrote:
> 
> > I didn't want to leave this up in the air, so I created the entry for it:
> > see A278586.  Feel free to improve it.
> >
> > 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 <(732)%20828-6098>; home page:
> > http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Thu, Dec 1, 2016 at 11:10 PM, Robert G. Wilson v <rgwv at rgwv.com>
> wrote:
> >
> >> f[n_] := Length@ NestWhileList[# - Ceiling[#/n] &, n^2, # > 1 &];
> >> Array[f, 65]
> >>
> >> -----Original Message-----
> >> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Jon
> >> Schoenfield
> >> Sent: Thursday, December 01, 2016 7:41 PM
> >> To: Sequence Fanatics Discussion list
> >> Subject: [seqfan] Re: A new sequence in Dutch magazine "Pythagoras"
> >>
> >> The following Magma code gives the same set of terms as those listed
> >> for Pim Spelier's sequence on p. 20 of Pythagoras:
> >>
> >> a:=[];
> >> for n in [1..26] do
> >>    k:=n^2;
> >>    count:=0;
> >>    while k gt 0 do
> >>       count+:=1;
> >>       k-:=Ceiling(k/n);
> >>    end while;
> >>    a[n]:=count;
> >> end for;
> >> a;
> >>
> >> -- Jon
> >>
> >> ----- Original Message -----
> >> From: "Neil Sloane" <njasloane at gmail.com>
> >> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> >> Sent: Thursday, December 01, 2016 2:00 PM
> >> Subject: [seqfan] A new sequence in Dutch magazine "Pythagoras"
> >>
> >>
> >> > Dear Sequence Fans, In the June 2016 issue of Pythagoras on pages
> >> > 20 and 21 there is a new sequence from Pim Spelier.
> >> >
> >> > See http://www.pyth.eu/jaargangen/Pyth55-6.pdf
> >> >
> >> > It looks like Pythagoras had a competition to find the best
> >> > sequence not in the OEIS, and this was the winner.  I think we
> >> > should add it to the OEIS, but my Dutch is not good enough to give
> >> > a clear definition.
> >> >
> >> > Maybe someone who speaks Dutch would be willing to submit the
> >> > sequence
> >> (if
> >> > so, please tell me the A-number).
> >> >
> >> > Thanks to Omar Pol who found the magazine (there is also an article
> >> about
> >> > the toothpick sequence A139250).
> >> >
> >> > --
> >> > Seqfan Mailing list - http://list.seqfan.eu/
> >> >
> >> >
> >>
> >>
> >> --
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >>
> >> --
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
> 
> --
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