Enumeration formulas using partitions

Christian G. Bower bowerc at usa.net
Thu May 8 02:09:31 CEST 2008

sequence to another. It is not the algorithm used, but the mapping itself.
so it is just another expression (or algorithm) for the same transform.
Return-Path: <maxale at gmail.com>
X-Ids: 168
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
        d=gmail.com; s=gamma;
DomainKey-Signature: a=rsa-sha1; c=nofws;
        d=gmail.com; s=gamma;
Message-ID: <d3dac270805080036r7f067a63pf05d539815edfde9 at mail.gmail.com>
Date: Thu, 8 May 2008 00:36:36 -0700
From: "Max Alekseyev" <maxale at gmail.com>
To: koh <zbi74583 at boat.zero.ad.jp>
Subject: Re: RE : Edited A137606
Cc: seqfan at ext.jussieu.fr
In-Reply-To: <20080430070547.zbi74583 at boat.zero.ad.jp>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 7bit
Content-Disposition: inline
References: <20080430070547.zbi74583 at boat.zero.ad.jp>
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr []); Thu, 08 May 2008 09:36:38 +0200 (CEST)
X-Virus-Scanned: ClamAV 0.92/7059/Thu May  8 07:03:47 2008 on shiva.jussieu.fr
X-Virus-Status: Clean
X-Miltered: at jchkmail.jussieu.fr with ID 4822AD85.009 by Joe's j-chkmail (http : // j-chkmail dot ensmp dot fr)!
X-j-chkmail-Enveloppe: 4822AD85.009/<maxale at gmail.com>
X-j-chkmail-Score: MSGID : 4822AD85.009 on jchkmail.jussieu.fr : j-chkmail score : X : R=. U=. O=# B=0.216 -> S=0.254
X-j-chkmail-Status: Unsure

2008/4/30 koh <zbi74583 at boat.zero.ad.jp>:

>    I found some property of the sequence.
>    The terms are not 2 Mod 3.
>                  not 1 Mod 4.
>                  not 3 Mod 5
>                  not 4 Mod 7
>                  not 6 Mod 11
>                  not 9 Mod 17
>    Is it correct?
>    I don't understand well the reason.

You probably meant that there are no terms equal 2 mod 3, except the
term 2; there are no terms equal 1 modulo 4, except the term 1; there
are no terms equal 3 mod 5, except the term 3 etc.
This corrected statement is true. The reason is that the sequence
A137606 admits an alternative close-form definition:

A137606 contains 1 and numbers m>1 such that either d=m-1 and m is
even, or d=2(m-1), where d is the multiplicative order of -2 modulo

 From this definition it follows that for m>1 the number p=2m-1 must be
prime since there exists an element with the multiplicative order p-1
modulo p: namely, this element is 2 or -2 (depending on the above
former/latter case).

if  m=2 Mod 3 then 2m-1 is divisible by 3, implying that 2m-1=3 and m=2;
if m=3 Mod 5 then 2m-1 is divisible by 5, implying that 2m-1=5 and m=3;
etc. etc.

I will send an update to A137606 soon.


Dear Seqfans,  I think the idea of a wiki about the OEIS
is a terrible one.  It would inevitably produce two
versions of sequences, and it would make my job even harder
than it is now.

One argument that was mentioned was that there one
could give discussions of ambiguous terms (such as
proper divisor).  But that can be handled by entries
in the Index.  I'm adding an entry for 
divisor, proper

More information about the SeqFan mailing list