n such that there is one sequence of length n having equal sum and product

[N. J. A. Sloane]

This was sent to the Number Theory List,
and at Victor Miller's suggestion I'm posting
it here too
NJAS
>From victor at idaccr.org  Wed Apr  6 21:37:40 2005
>Delivered-To: njas at research.att.com
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>To: Neil Sloane <njas at research.att.com>
>Subject: Should this be on Seqfan?
>From: victor at idaccr.org (Victor S. Miller)
>Date: Wed, 06 Apr 2005 21:36:49 -0400
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>--=-=-=
>
>This was submitted to the Number Theory list.  I think that it should
>also be on seqfan.  Do you agree?
>
>Victor
>
>
>
>--=-=-=
>Content-Type: message/rfc822
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>Message-ID: <425485E7.9000002 at marmet.ca>
>Date: Wed, 06 Apr 2005 20:59:19 -0400
>From: Louis Marmet <louis at marmet.ca>
>Subject: n such that there is one sequence of length n having equal sum and
> product
>Lines: 22
>MIME-Version: 1.0
>
>I am interested in the series of "numbers n such that there is just one 
>sequence of length n having equal sum and product".  According to the 
>"On-Line Encyclopedia of Integer sequences", only 8 terms are known {2, 
>3, 4, 6, 24, 114, 174, 444}.
>See: 
>http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A033179
>A reference to R. K. Guy's book 'Unsolved Problems in Number Theory' 
>(Section D24) is given and I wonder how far this series has been tested 
>(I don't have the book).  I can only suppose there is no proof that the 
>series is finite (or infinite).
>
>  I tested it up to 3634884924 but haven't found any other terms to the 
>series.  I am writing a web page explaining how I searched these numbers 
>(page not finished yet...and  I am still checking my algorithm too... 
>http://www.marmet.ca/louis/sumprod/index.html)
>
>Any information would be appreciated,
>
>Thanks,
>
>Louis Marmet
>
>
>--=-=-=
>
>
>
>-- 
>Victor S. Miller     | " ... Meanwhile, those of us who can compute can hardly
>victor at idaccr.org    | be expected to keep writing papers saying 'I can do the
>CCR, Princeton, NJ   | following useless calculation in 2 seconds', and indeed
>    08540 USA        | what editor would publish them?"  -- Oliver Atkin
>
>--=-=-=--
>