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

Ami Eldar amiram.eldar at gmail.com
Fri May 8 21:01:43 CEST 2020

```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
>
> %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/
>
```