various news items Sep 15 2007

[N. J. A. Sloane]

still to process.
Return-Path: <philip.lallouet at wanadoo.fr>
X-Ids: 166
X-ME-UUID: 20070915234315721.119787000085 at mwinf1a01.orange.fr
From: Philippe LALLOUET <philip.lallouet at wanadoo.fr>
Reply-To: Philippe LALLOUET <philip.lallouet at wanadoo.fr>
To: Seqfan <seqfan at ext.jussieu.fr>
Message-ID: <4170819.433991189899795047.JavaMail.www at wwinf1a31>
Subject: Comment on A091910
MIME-Version: 1.0
Content-Type: multipart/alternative; 
	boundary="----=_Part_32099_30132754.1189899795029"
X-Originating-IP: [83.195.71.160]
X-Wum-Nature: EMAIL-NATURE
X-WUM-FROM: |~|
X-WUM-TO: |~|
X-WUM-REPLYTO: |~|
Date: Sun, 16 Sep 2007 01:43:15 +0200 (CEST)
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.166]); Sun, 16 Sep 2007 01:43:16 +0200 (CEST)
X-Virus-Scanned: ClamAV 0.88.7/4281/Sat Sep 15 18:07:24 2007 on shiva.jussieu.fr
X-Virus-Status: Clean
X-j-chkmail-Score: MSGID : 46EC6E14.000 on shiva.jussieu.fr : j-chkmail score : X : 0/50 1 0.400 -> 1
X-Miltered: at shiva.jussieu.fr with ID 46EC6E14.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)!

------=_Part_32099_30132754.1189899795029
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 7bit




Hugo Pfoertner has published In 2004 in OEIS the sequence A091910.: 1,3,4,10,11,21,20,36,36,55,56,78,79,103,103,136,135
I have found the following sequence whose terms are the last ones of each row of the triangle read by row: 
1,2,3,6,5,4,7,8,9,10,15,14,13,12,11 (natural numbers written from left to right on even raws and from right to left on the odd raws.
The sequence is : 1,3,4,10,11,21,22,36,37,55,56,78,79,105,106,136,137,171,172
whose terms are given by the formulas  a(n) = n*(n+1)/2 if n is odd ,else  a(n)=(n-1)*n/2 +1 
This sequence shows a very close but not perfect similitude with 1091910; It's difficult not to think to a connection between these two sequences.
May the imperfection in this similitude be the sign of some error? I am enable to check.
Regards
Philippe LALLOUET



oer
------=_Part_32099_30132754.1189899795029
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: 7bit

<BR><BR>
<P>Hugo Pfoertner has published In 2004 in OEIS the sequence A091910.: 1,3,4,10,11,21,20,36,36,55,56,78,79,103,103,136,135</P>
<P>I have found the following sequence whose terms are the last ones of each row of the triangle read by row: </P>
<P>1,2,3,6,5,4,7,8,9,10,15,14,13,12,11 (natural numbers written from left to right on even raws and from right to left on the odd raws.</P>
<P>The sequence is : 1,3,4,10,11,21,22,36,37,55,56,78,79,105,106,136,137,171,172</P>
<P>whose terms are given by the formulas  a(n) = n*(n+1)/2 if n is odd ,else  a(n)=(n-1)*n/2 +1 </P>
<P>This sequence shows a very close but not perfect similitude with 1091910; It's difficult not to think to a connection between these two sequences.</P>
<P>May the imperfection in this similitude be the sign of some error? I am enable to check.</P>
<P>Regards</P>
<P>Philippe LALLOUET</P>
<P> </P>
<P><BR><BR>oer<BR></P>
------=_Part_32099_30132754.1189899795029--






Dear Seqfans, it would be nice to have a b-file for A023052.
Apparently G. N. Gusev has computed it to 10^50 - does nayone know him?
Neil




Does anyone know if the seq fan web site is working again - and
if so what is the URL?

Neil




This was posted to the number theory list - could
and see if it is a new sequence?   Neil


What bounds are known for the size of the largest subset of {1,2,...,N} s
uch
that no two distinct elements differ by a perfect square? 

(end)