Derived from Koslov, Evasiveness Conjecture; Fwd: SEQ FROM Jonathan Vos Post

[N. J. A. Sloane]

so I rejected it!
 %N A000001 The number of vertices for which the Evasiveness
Return-Path: <njas at research.att.com>
X-Ids: 164
Date: Mon, 3 Mar 2008 07:46:40 -0500
From: "N. J. A. Sloane" <njas at research.att.com>
Message-Id: <200803031246.m23CkeMK013471 at prim.research.att.com>
X-Mailer: mailx (AT&T/BSD) 9.9 2008-02-12
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
To: blekraj at yahoo.com, jvospost3 at gmail.com, seqfan at ext.jussieu.fr
Subject: Re: emirp formed by concatenating primitive Pythagorean triples
Cc: njas at research.att.com
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.164]); Mon, 03 Mar 2008 13:46:42 +0100 (CET)
X-Virus-Scanned: ClamAV 0.92/6092/Mon Mar  3 06:04:26 2008 on shiva.jussieu.fr
X-Virus-Status: Clean
X-Miltered: at jchkmail.jussieu.fr with ID 47CBF331.013 by Joe's j-chkmail (http : // j-chkmail dot ensmp dot fr)!
X-j-chkmail-Enveloppe: 47CBF331.013/192.20.225.112/mail-dark.research.att.com/mail-yellow.research.att.com/<njas at research.att.com>
X-j-chkmail-Score: MSGID : 47CBF331.013 on jchkmail.jussieu.fr : j-chkmail score : XX : R=. U=. O=. B=0.395 -> S=0.395
X-j-chkmail-Status: Unsure
Me: you are correct!
 Best regards
 			 Neil
Return-Path: <njas at research.att.com>
X-Ids: 168
Date: Mon, 3 Mar 2008 07:50:51 -0500
From: "N. J. A. Sloane" <njas at research.att.com>
Message-Id: <200803031250.m23Cop7Y013484 at prim.research.att.com>
X-Mailer: mailx (AT&T/BSD) 9.9 2008-02-12
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
To: jvospost3 at gmail.com, maxale at gmail.com
Subject: Re: Derived from Koslov, Evasiveness Conjecture; Fwd: SEQ FROM Jonathan Vos Post
Cc: seqfan at ext.jussieu.fr
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.168]); Mon, 03 Mar 2008 13:50:57 +0100 (CET)
X-Virus-Scanned: ClamAV 0.92/6092/Mon Mar  3 06:04:26 2008 on shiva.jussieu.fr
X-Virus-Status: Clean
X-Miltered: at jchkmail.jussieu.fr with ID 47CBF42E.006 by Joe's j-chkmail (http : // j-chkmail dot ensmp dot fr)!
X-j-chkmail-Enveloppe: 47CBF42E.006/192.20.225.112/mail-dark.research.att.com/mail-yellow.research.att.com/<njas at research.att.com>
X-j-chkmail-Score: MSGID : 47CBF42E.006 on jchkmail.jussieu.fr : j-chkmail score : X : R=. U=. O=. B=0.250 -> S=0.250
X-j-chkmail-Status: Ham
 Best regards
 			 Neil
Return-Path: <hv at zen.crypt.org>
X-Ids: 166
Message-Id: <200803031703.m23H3mxm024488 at zen.crypt.org>
To: seqfan at ext.jussieu.fr
cc: hv at crypt.org
From: hv at crypt.org
Subject: square-free ternary numbers
Date: Mon, 03 Mar 2008 17:03:48 +0000
Sender: hv at zen.crypt.org
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.166]); Mon, 03 Mar 2008 18:04:22 +0100 (CET)
X-Virus-Scanned: ClamAV 0.92/6092/Mon Mar  3 06:04:26 2008 on shiva.jussieu.fr
X-Virus-Status: Clean
X-Miltered: at jchkmail.jussieu.fr with ID 47CC2F95.002 by Joe's j-chkmail (http : // j-chkmail dot ensmp dot fr)!
X-j-chkmail-Enveloppe: 47CC2F95.002/217.146.123.119/upuaut.novacaster.com/zen.crypt.org/<hv at zen.crypt.org>
X-j-chkmail-Score: MSGID : 47CC2F95.002 on jchkmail.jussieu.fr : j-chkmail score : . : R=. U=. O=. B=0.104 -> S=0.104
X-j-chkmail-Status: Ham
squarefree string, it is "critical", in the sense that disallowing any
  3, 8, 9, 18, 20, 20, 21, 38, 39, 42, 42, 42, 44, 44, 45, 78, 79, 80, 81, 86,
  86, 86, 86, 86, 87, 90, 90, 90, 92, 92, 93, 158
  n=40 => 174; n=80 => 350.
  6, 38, 55, 224, 292, 335, 378, 1216, 1320, 1601, 1703, 1805, 2009, 2110,
  2210, 6374, 6613, 6851, 7085, 8275, 8508, 8741, 8974, 9207
  n=40 => 41499; n=80 => 206743.
Return-Path: <rsc at swtch.com>
X-Ids: 166
To: hv at crypt.org
CC: seqfan at ext.jussieu.fr
Subject: Re: square-free ternary numbers
From: "Russ Cox" <rsc at swtch.com>
Date: Mon, 3 Mar 2008 17:37:16 -0500
In-Reply-To: <200803031703.m23H3mxm024488 at zen.crypt.org>
MIME-Version: 1.0
Content-Type: text/plain; charset="US-ASCII"
Content-Transfer-Encoding: 7bit
Message-Id: <20080303223756.828A71E8C22 at holo.morphisms.net>
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.166]); Mon, 03 Mar 2008 23:37:21 +0100 (CET)
X-Virus-Scanned: ClamAV 0.92/6097/Mon Mar  3 21:58:29 2008 on shiva.jussieu.fr
X-Virus-Status: Clean
X-Miltered: at jchkmail.jussieu.fr with ID 47CC7DA0.002 by Joe's j-chkmail (http : // j-chkmail dot ensmp dot fr)!
X-j-chkmail-Enveloppe: 47CC7DA0.002/216.254.78.15/holo.morphisms.net/holo.morphisms.net/<rsc at swtch.com>
X-j-chkmail-Score: MSGID : 47CC7DA0.002 on jchkmail.jussieu.fr : j-chkmail score : XX : R=. U=. O=. B=0.294 -> S=0.294
X-j-chkmail-Status: Unsure

> Of particular interest is the pair (010, 212). I cannot be certain that
> this yields an infinite string, since I am relying only on observation of

You might be interested in 

Narad Rampersad, ``A note on avoidable words in ternary strings''
http://arxiv.org/abs/math/0307363v1

The fact that you can build an infinite square-free
string without 010 and 212 follows from the construction
used in Theorem 2.  (The construction actually avoids 101 and 202.)

> Alternatively expressed: it appears that any infinite squarefree string that
> avoids the substrings 010 and 212 must necessarily contain every other
> allowable substring, of any length.

The paper has nothing to say about this question, though.

Russ