Duplicate hunting

Tue Apr 10 20:17:42 CEST 2007

sequence in particular occurs 23 times, there are many that appear more than
	-Andrew Plewe-
From: franktaw at netscape.net [mailto:franktaw at netscape.net]
Sent: Tuesday, April 10, 2007 7:10 AM
To: seqfan at ext.jussieu.fr
Subject: Re: Duplicate hunting
From: aplewe at sbcglobal.net
   My mind is taking a bit of a break from other math pursuits, so I've
sequences to see if they actually have the same definition. I'd be
 ...
 -Andrew Plewe-
Return-Path: <franktaw at netscape.net>
X-Ids: 168
To: seqfan at ext.jussieu.fr
Content-Transfer-Encoding: 7bit
Subject: Re: Duplicate hunting
Date: Tue, 10 Apr 2007 18:58:35 -0400
X-MB-Message-Source: WebUI
In-Reply-To: <200704101817.l3AIHkqP069744 at shiva.jussieu.fr>
X-MB-Message-Type: User
MIME-Version: 1.0
From: franktaw at netscape.net
Content-Type: text/plain; charset="us-ascii"; format=flowed
X-Mailer: AIM WebMail 25045
Message-Id: <8C949DAE79B3AF0-1B68-41CE at mblk-r12.sysops.aol.com>
X-AOL-IP: 152.163.211.203
X-Spam-Flag: NO
X-Greylist: Sender IP whitelisted, not delayed by milter-greylist-2.0.2 (shiva.jussieu.fr [134.157.0.168]); Wed, 11 Apr 2007 00:58:42 +0200 (CEST)
X-Virus-Scanned: ClamAV 0.88.7/3064/Tue Apr 10 18:25:23 2007 on shiva.jussieu.fr
X-Virus-Status: Clean
X-j-chkmail-Score: MSGID : 461C16A2.000 on shiva.jussieu.fr : j-chkmail score : X : 0/50 1 0.603 -> 1
X-Miltered: at shiva.jussieu.fr with ID 461C16A2.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)!

Wow.  I had no idea.

I'm going to have to defer to Dr. Sloane on what he wants to do with 
these, especially the inverses of the cyclotomic polynomials.  One 
possibility is to add b-files for them.  Some observations:

The cases shown here clearly are all different sequences.

The sequences for inverses of cyclotomic polynomials all have the 
"sign" keyword, even if (as for the first group) the terms in the 
database are all non-negative.  This is counter to the keyword 
definition.

Most of these sequences (shown below) will differ at fairly low 
indices.  For example, the first difference between A043860 (base 4 
runs = 2 mod 9) and A043869 (base 4 runs = 2 mod 10) is an 11-digit 
base 4 number (10101010101_4 vs. 11000000000_4), which occurs at index 
407.  On the other hand, A043595 (base 4 runs = 4) and A043871 (base 4 
runs = 4 mod 10) first differ at an index a bit more than 243243.

Franklin T. Adams-Watters

-----Original Message-----
From: aplewe at sbcglobal.net

   I was wondering about those; there are many more duplicates that fit 
into
your three categories than duplicates that have the same definition. One
sequence in particular occurs 23 times, there are many that appear more 
than
4 times. Would it be best to submit those to the list? Here are the top 
10
duplicates, the number of times they occur regardless of definition,
comments on any obvious groupings, and the other A-numbers that match:

A016176 23 (Inverse of nth cyclotomic polynomial)
A014922 A014988 A015076 A015120 A015142 A015186 A015208 A015252 A015406
A015450 A015516 A015538 A015648 A015670 A015736 A015802 A015846 A015912
A015978 A016000 A016110 A016132

A016258 18 (Inverse of nth cyclotomic polynomial)
A015088 A015166 A015270 A015322 A015348 A015400 A015426 A015478 A015660
A015712 A015790 A015816 A015946 A015972 A016050 A016128 A016180

A016221 10 (Inverse of nth cyclotomic polynomial)
A015157 A015213 A015325 A015493 A015661 A015717 A015885 A015997 A016053

A016236 10 (Inverse of nth cyclotomic polynomial)
A015420 A015522 A015658 A015726 A015760 A015828 A015862 A015930 A016168

A043869 9 (Number n such that the number of runs in Base 4, various
properties)
A043593 A043827 A043830 A043834 A043839 A043845 A043852 A043860

A043818 9 (Number n such that the number of runs in Base 3, various
properties)
A043583 A043773 A043779 A043783 A043788 A043794 A043801 A043809

A043870 9 (Number n such that the number of runs in Base 4, various
properties)
A043594 A043825 A043831 A043835 A043840 A043846 A043853 A043861

A043819 8 (Number n such that the number of runs in Base 3, various
properties)
A043776 A043784 A043789 A043584 A043795 A043802 A043810

A016156 8 (Inverse of nth cyclotomic polynomial)
A015586 A015700 A015852 A015928 A015966 A016042 A016080

A043871 8 (Number n such that the number of runs in Base 4, various
properties)
A043595 A043828 A043836 A043841 A043847 A043854 A043862

Most of the duplicates are like these. There's another group that I'm
tracking where the sequences might be the same, but I either don't know
enough about the math involved to tell or it's probable that they 
differ at
higher terms. I can pass those along to the list as I find them if 
that's
the appropriate thing to do.

    -Andrew Plewe-

-----Original Message-----
From: franktaw at netscape.net [mailto:franktaw at netscape.net]
Sent: Tuesday, April 10, 2007 7:10 AM
To: seqfan at ext.jussieu.fr
Subject: Re: Duplicate hunting

The ones where the definition is not the same are also of interest.
There are three possibilities:

1) Although the definitions are different, the actual sequences (out to
infinity) are the same.  In this case, these are duplicates, and should
be merged.
2) The sequences differ at some term beyond what is included in the
database.  In this case, at least one - preferably both - should have a
comment indicating where they differ.
3) We can't tell if the sequences are different or not.  In this case,
they should reference each other with some sort of comment indicating
that the equality of the sequences is unknown.

Franklin T. Adams-Watters

-----Original Message-----
From: aplewe at sbcglobal.net

   My mind is taking a bit of a break from other math pursuits, so I've
decided in the down-time to find duplicate sequences in the OEIS. I
have a text file of about 1500 sequences that match lexically (same
values, same ordering) that I'm using, then manually comparing the
sequences to see if they actually have the same definition. I'd be
happy to share this file with anyone who'd like to participate, email
me off-list and I'll send it along (approx. 280k text file). Anyways,
here are a few that I've found this evening by working from the last
line of the file upwards. If it's preferable, I'll send future
duplicates to Neil directly or a designated editor/editors to keep
traffic down on the email list.
 ...

 -Andrew Plewe-

________________________________________________________________________
Check Out the new free AIM(R) Mail -- 2 GB of storage and 
industry-leading spam and email virus protection.