The return of dupe hunting, pt. 1

[Andrew Plewe]

start, some statistics on the longest and shortest sequences:
	-Andrew Plewe-
Return-Path: <jvospost3 at gmail.com>
X-Ids: 166
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
        d=gmail.com; s=beta;
        h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition;
        bh=8DoY6mFW6ZrSVsoJ0wBLR/mPZ6BKWaEpN1VPT6ZyfVQ=;
        b=XxndHFrGRnl4N6WPLyLiTWY8Zmq5v60mAWxYQePrl4J8kys0ykRg6mwcc7bqLf2tLqqwW34ZcG5dbvhHxI2kowVY/xMftwNxcTQDmcU/N/kkVkmHSMsZjly0DCVJrQ6JWZmNXxvBo00jTt45GvdNySuoSPq5ZN/PowO6QczOKuI=
DomainKey-Signature: a=rsa-sha1; c=nofws;
        d=gmail.com; s=beta;
        h=received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition;
        b=qHQPreIZyHC3xzanrd6eVwIPMzkTfTEiRb5a8M1iFsGcXJHFzrLYQdS4E9D+zaMUewL7bvxpl8fvyWnILqiyzp3GRt6ai8/CCA62uh3+BbixXlohpJw6iAn9wuhvhyeBJDTuaQ6MhPyRwZF0IrLvyD95i33LHEDGuj3UX7NN64U=
Message-ID: <5542af940709210255o62cf65a4p406dd463cff78c01 at mail.gmail.com>
Date: Fri, 21 Sep 2007 02:55:20 -0700
From: "Jonathan Post" <jvospost3 at gmail.com>
To: "Sequence Fans" <seqfan at ext.jussieu.fr>,
   "jonathan post" <jvospost2 at yahoo.com>,
   "Erich Friedman" <erich.friedman at stetson.edu>,
   "Larry Reeves" <larryr at acm.org>
Subject: Why isn't 0 in A034710?
MIME-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
Content-Disposition: inline
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.166]); Fri, 21 Sep 2007 11:55:22 +0200 (CEST)
X-Virus-Scanned: ClamAV 0.88.7/4356/Fri Sep 21 09:19:47 2007 on shiva.jussieu.fr
X-Virus-Status: Clean
X-j-chkmail-Score: MSGID : 46F39509.000 on shiva.jussieu.fr : j-chkmail score : X : 0/50 1 0.524 -> 1
X-Miltered: at shiva.jussieu.fr with ID 46F39509.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)!

Why isn't 0 in A034710  Numbers for which the sum of digits equals the
product of digits?  That is, why not correct A034710 to 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 22, 123, 132, 213, 231, 312, 321, 1124, ... with offset
0,3?  0 would also thus be in A061672 Smallest number formed by a set
of digits whose product = sum of the digits?

As a formula, why not state the verbal title with crossrefs as:

A034710 = {n such that A007953(n) = A007954(n)}

A007954  does properly begin with 0, i.e. with offset 0,3.

-- Jonathan Vos Post