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

Fri May 8 23:53:58 CEST 2020

Richard,  I thought some more about this problem, without success.  I
created two sequences that might have matched hers , following your
suggestions, but as you noticed, they do not match hers.  See A334685 and
-6.

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, May 8, 2020 at 1:40 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/>
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> 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, 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 added)
>> 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.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> 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/
>>>
>>