[seqfan] Re: defn of A032452 transients in modified Poulet

Neil Sloane njasloane at gmail.com
Sat May 9 05:34:11 CEST 2020

```Amiram,  That is brilliant!!!!  Bravo!

Let's wait a bit to see what Richard Mather says, but I think you solved
the problem.

Tomorrow, could you edit the sequence?  Make the corrections, give the
correct definition, and so on (and send me an email so I can look at it)

Also, could you submit the same sequence, but with the order (phi, phi,
sigma)* ?

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.
Email: njasloane at gmail.com

On Fri, May 8, 2020 at 11:01 PM Ami Eldar <amiram.eldar at gmail.com> wrote:

> Here is my guess for interpreting A032452:
> When I break the data into rows, such that each row is terminated with 1, I
> get:
> 1
> 1
> 2, 3, 2, 1
> 2, 3, 2, 1
> 4, 7, 6, 2, 3, 2, 1
> 2, 3, 2, 1
> 6, 12, 4, 2, 3, 2, 1
> 4, 7, 6, 2, 3, 2, 1
> 6, 12, 4, 2, 3, 2, 1
> 4, 7, 6, 2, 3, 2, 1
> 10, 18, 6, 2, 3, 2, 1
> 4, 7, 6, 2, 3, 2, 1
> 12, 28, 12, 4, 7, 6, 2, 3, 2, 1
> 6, 12, 4, 2, 3, 2, 1
>
> This is similar to what I get when I iterate sigma, then twice phi for n =
> 1, 2, 3, ... until I get 1:
> 1
> 2, 3, 2, 1
> 3, 4, 2, 1
> 4, 7, 6, 2, 3, 2, 1
> 5, 6, 2, 1
> 6, 12, 4, 2, 3, 2, 1
> 7, 8, 4, 2, 3, 2, 1
> 8, 15, 8, 4, 7, 6, 2, 3, 2, 1
> 9, 13, 12, 4, 7, 6, 2, 3, 2, 1
> 10, 18, 6, 2, 3, 2, 1
> 11, 12, 4, 2, 3, 2, 1
> 12, 28, 12, 4, 7, 6, 2, 3, 2, 1
> 13, 14, 6, 2, 3, 2, 1
>
> So my guess is that this sequence is an irregular table with a few
> copy-paste errors.
>
> Best,
> Amiram
>
> On Fri, May 8, 2020 at 8:41 PM Neil Sloane <njasloane at gmail.com> wrote:
>
> > Richard
> >
> > I tried assuming that "sigma" mean the aliquot sigma, sum of divisors <
> n,
> > but I still do not understand A032452.
> >
> > Since phi(6) = phi(4) = 2, it follows that phi(phi(7))=2, phi(phi(8))=2
> so
> > whatever the offset and no matter which version of sigma we use, we
> should
> >   get a(7)=a(8).  But her sequence
> > starts 1,1,2,3,2,1,2,3,2,1,4,7,6,2,3,2,1,2,3,2,.. and there are no two
> > equal consecutive entries.
> > So maybe this is NOT the length of the transient.
> >
> > Here is the original submission, which she submitted via an html "form",
> > which was processed by my cgi-bin shell program on our external machine,
> > which then composed an email to me and was sent through the firewall to
> my
> > local machine:
> >
> > From njas at akpublic.research.att.com  Tue Apr  7 07:57:08 1998
> > To: njas at research.att.com
> > Date: Tue, 7 Apr 1998 07:56:31 -0400 (EDT)
> > From: "N. J. A. Sloane" <njas at research.att.com>
> > Subject: SEQ FROM Ursula Gagelmann
> > Reply-to: gagelmann at altavista.net
> >
> > %I A000001
> > %S A000001
> >
> >
> 1,1,2,3,2,1,2,3,2,1,4,7,6,2,3,2,1,2,3,2,1,6,12,4,2,3,2,1,4,7,6,2,3,2,1,6,12,4,2,3,2,1,4,7,6,2,3,2,1,10,18,6,2,3,2,1,4,7,6,2,3,2,1,12,28,12,4,7,6,2,3,2,1,6,12,4,2,3,2,1
> > %N A000001 iterates phi,phi,sigma,phi,phi,sigma,...
> > %D A000001 Alaoglu & Erdös:  A conjecture...  Bull Amer Math Soc 50
> (1944),
> > 881-882
> > %D A000001
> > %D A000001
> > %H A000001
> > %H A000001
> > %H A000001
> > %F A000001
> > %C A000001
> > %Y A000001
> > %A A000001 Ursula Gagelmann (gagelmann at altavista.net)
> > %O A000001 0
> > %K A000001 ,nonn,
> >
> >
> > So this is still a mystery.
> >
> > It is quite possible she is still living in Germany - could you try
> > contacting her?
> >
> >
> > <https://www.dr-gagelmann-schriesheim.de/>
> > Dr. med. Ursula Gagelmann (Psychologist) in 69198 ...
> > en.doctena.de › Dr_med_Ursula_Gagelmann-343245 › Pr...
> > <
> >
> https://en.doctena.de/doctor/Dr_med_Ursula_Gagelmann-343245/Praxis_Frau_Dr_med_Ursula_Gagelmann-297597
> > >
> > Schedule an appointment online with Dr. med. Ursula Gagelmann,
> > Psychologist. Also phone number, opening hours, education, awards,
> > recommandations and ...
> >
> > Dr. med. Ursula Gagelmann (Ärztin) in Schriesheim | jameda
> > www.jameda.de › aerzte › uebersicht
> > <
> >
> https://www.jameda.de/schriesheim/aerzte/psychosom-med-u-psychotherapeuten/dr-ursula-gagelmann/uebersicht/80335796_1/
> > >
> > <
> >
> > >
> >
> >    1.
> >    <
> >
> > >
> >    2.
> >    <
> >
> > >
> >
> > <
> >
> > >
> > Dr. med. Ursula Gagelmann (Ärztin) in Weinheimer Str. 1 B, 69198
> > Schriesheim ✓ Das sagen Nutzer über Dr. Gagelmann ✓ Finden Sie mehr zu
> Dr.
> > Gagelmann!
> >  Rating: 4.7 - ‎6 votes
> >
> > Bewertung & Infos Frau Dr. med. Ursula Gagelmann
> > www.weisse-liste.de › ... › Arztsuche
> > <
> >
> https://www.weisse-liste.de/de/arzt/arztsuche/ergebnisliste/profil/;jsessionid=ED4E57815896E75A677F1C98CCD58901?distance=2622&id=1159941&type=medic
> > >
> > <
> >
> > >
> >
> >    1.
> >    <
> >
> > >
> >
> > <
> >
> > >
> > Alle Infos zur Praxis von Frau Dr. med. Ursula GagelmannSpezialist für
> > Psychotherapeutische Medizin. Bewertungen ansehen oder Ärztin selbst
> > bewerten.
> >
> >
> >
> > 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.
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Fri, May 8, 2020 at 1:16 PM Neil Sloane <njasloane at gmail.com> wrote:
> >
> > > Richard,
> > > I found the original submissions from Ursula Gagelmann from 1998.
> > > For A032450 there was a formula that I have now added to the entry (I
> see
> > > you also added a comment - presumably saying the same thing, I did not
> > have
> > > time to check).
> > >
> > > For A032452 unfortunately there is nothing more than what I put in the
> > > entry for the sequence (except the submission date, which I have now
> > > She definitely says the offset is 0. However, that does not mean
> anything
> > > since  0 was the default offset and she did not change it in any of her
> > > half-dozen submissions at that time.  Perhaps she did not understand
> the
> > > significance of the offset.
> > > So it is very likely the offset in A032452 should be 1 not 0.
> > >
> > > 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.
> > > Email: njasloane at gmail.com
> > >
> > >
> > >
> > > On Fri, May 8, 2020 at 11:32 AM Richard J. Mathar <
> mathar at mpia-hd.mpg.de
> > >
> > > wrote:
> > >
> > >> It would be nice to have a definition of a(n) in terms of n in A032452
> > >> (modified Poulet sequences).
> > >> Starting at n, we have the sequences
> > >> [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
> > >> [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
> > >> [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
> > >> [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
> > >> [5, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
> > >> [6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
> > >> [7, 6, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
> > >> [8, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
> > >> [9, 6, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
> > >> [10, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...]
> > >> [11, 10, 4, 7, 6, 2, 3, 2, 1, 1, 1,...]
> > >> [12, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...]
> > >> [13, 12, 4, 7, 6, 2, 3, 2, 1, 1, 1,...]
> > >> ...
> > >> if we iterate twice phi(.) and once sigma(.) on the elements in these
> > >> sequences.
> > >> I suspect that a(n) is somehow a cumulation of periods or their
> > >> transients,
> > >> similar to A032450, but cannot find how that might actually be
> realized
> > >> in A032452.
> > >>
> > >> --
> > >> Seqfan Mailing list - http://list.seqfan.eu/
> > >>
> > >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
```