[seqfan] Re: What is a "Q unit fraction"?

Neil Sloane njasloane at gmail.com
Fri Dec 28 04:45:47 CET 2018 

David , you are right - thanks - fixed!
Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Thu, Dec 27, 2018 at 8:44 PM David Wilson <davidwwilson at comcast.net>
wrote:

> The offset of A016017 is inconsistent with the examples.
>
> > -----Original Message-----
> > From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil
> > Sloane
> > Sent: Wednesday, December 26, 2018 2:10 PM
> > To: Sequence Fanatics Discussion list
> > Subject: [seqfan] Re: What is a "Q unit fraction"?
> >
> > As a result of emails from Ray C. and Peter M., A016013 is now declared
> > "dead", an erroneous version of A016017.
> >
> > So the matter is closed.  Thanks to everyone who helped.
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Wed, Dec 26, 2018 at 10:46 AM Peter Munn
> > <techsubs at pearceneptune.co.uk>
> > wrote:
> >
> > > I meant A016017 in my final paragraph, not A016007.
> > >
> > > On Wed, December 26, 2018 11:39 am, Peter Munn wrote:
> > > > Now we have Bob's reply, I will attempt to draw some conclusions from
> > my
> > > > own delving using the history function in OEIS.
> > > >
> > > > I get the data for A016013 to be exactly the result of prefixing "2"
> and
> > > > appending "1, 2" to the version #1 data for A016017 (Smallest k such
> that
> > > > 1/k can be written as a sum of exactly 2 unit fractions in n ways).
> It is
> > > > difficult to imagine how two such information-rich sequences could
> run
> > > > identically for twenty terms and then diverge as dramatically as "1,
> 2"
> > > > and "1048576, 2097152" except by arbitrary concoction. So I concur
> with
> > > > Neil's Dec 24 2018 comment in A016013 that its last two published
> terms
> > > > seem to be wrong.
> > > >
> > > > The names of the following related sequences were amended by Vladeta
> > > > Jovovic at a time consistent with the phrase "over a decade ago" from
> > > > Bob's reply: A015995, A015996, A015999, A016001 - A016003, A016005 -
> > > > A016009, A016012, A016018, A016020 and A016025. Many of these
> > amendments
> > > > were very similar to changing the name of A016013 to the name of
> > A016017.
> > > >
> > > > From the evidence to hand, my own prime suspects for (1) the origin
> of
> > Q:
> > > > human mistranscription of a curlily handwritten 2 and (2) the data: a
> > > > variant of A016007, with spurious appending of "1,2" due to human or
> > > > computer mistranscription, perhaps originating from offset data or
> > > initial
> > > > terms of another sequence.
> > > >
> > > > Best Regards,
> > > >
> > > > Peter
> > > >
> > > > On Wed, December 26, 2018 5:00 am, Neil Sloane wrote:
> > > >> Bob, Thanks for that reply! (The "History" tab for A016013 doesn't
> show
> > > >> that anything has ever been removed from the entry.)
> > > >>
> > > >> Even if you don't remember the details of our email exchange over a
> > > >> decade
> > > >> ago, do you remember what the outcome was?  The fact that it has not
> > > >> changed (except in trivial ways) since you submitted it in 1999 (or
> > > >> earlier) suggests that my level of confusion about it hasn't
> changed a
> > > >> whole lot in 20 years!
> > > >>
> > > >> Looking at the author lines for sequences around that one, here is
> what
> > > >> I
> > > >> see:
> > > >>
> > > >> %A A016000 _Simon Plouffe_
> > > >> %A A016001 _Robert G. Wilson v_
> > > >> %A A016002 _Robert G. Wilson v_
> > > >> %A A016003 _Robert G. Wilson v_
> > > >> %A A016004 _Simon Plouffe_
> > > >> %A A016005 _Robert G. Wilson v_
> > > >> %A A016006 _Robert G. Wilson v_
> > > >> %A A016007 _Robert G. Wilson v_
> > > >> %A A016008 _Robert G. Wilson v_
> > > >> %A A016009 _Robert G. Wilson v_
> > > >> %A A016010 _Simon Plouffe_
> > > >> %A A016011 _Simon Plouffe_
> > > >> %A A016012 _Robert G. Wilson v_
> > > >> %A A016013 _Robert G. Wilson v_, Dec 11 1999
> > > >> %A A016014 _Robert G. Wilson v_
> > > >> %A A016015 _Simon Plouffe_
> > > >> %A A016016 _Robert G. Wilson v_
> > > >> %A A016017 _Robert G. Wilson v_
> > > >> %A A016018 _Robert G. Wilson v_
> > > >> %A A016019 _Simon Plouffe_
> > > >> %A A016020 _Robert G. Wilson v_
> > > >> %A A016021 _David W. Wilson_, Jun 07 2000
> > > >> %A A016022 _Simon Plouffe_
> > > >> %A A016023 _Simon Plouffe_
> > > >> %A A016024 _Simon Plouffe_
> > > >> %A A016025 _Robert G. Wilson v_
> > > >> %A A016026 _Robert G. Wilson v_
> > > >> %A A016027 _Robert G. Wilson v_
> > > >> %A A016028 _Robert G. Wilson v_
> > > >> %A A016029 _Robert G. Wilson v_
> > > >> %A A016030 _Simon Plouffe_
> > > >> %A A016031 _N. J. A. Sloane_, _Robert G. Wilson v_
> > > >> %A A016032 _Robert G. Wilson v_
> > > >> %A A016033 _Simon Plouffe_
> > > >> %A A016034 _Robert G. Wilson v_
> > > >> %A A016035 _Robert G. Wilson v_
> > > >> %A A016036 _Wolfdieter Lang_
> > > >> %A A016037 _Robert G. Wilson v_
> > > >> %A A016038 _Robert G. Wilson v_
> > > >> %A A016039 _Simon Plouffe_
> > > >> %A A016040 _Robert G. Wilson v_
> > > >> %A A016041 _Robert G. Wilson v_
> > > >> %A A016042 _Simon Plouffe_
> > > >> %A A016043 _Robert G. Wilson v_
> > > >> %A A016044 _Simon Plouffe_
> > > >> %A A016045 _Robert G. Wilson v_
> > > >> %A A016046 _Robert G. Wilson v_
> > > >> ....
> > > >>
> > > >>
> > > >> It is only 20 to 25 years ago when this happened (it could have been
> > > >> submitted any time from 1996 to 1999),
> > > >> but we have both looked at a lot of sequences since then!  It is
> just
> > > >> possible I have the original submission ( which would have been
> through
> > > >> email) buried somewhere in my files on this computer.
> > > >>
> > > >> Well, in any case,  Merry Christmas!
> > > >>
> > > >> Best regards
> > > >> Neil
> > > >>
> > > >> Neil J. A. Sloane, President, OEIS Foundation.
> > > >> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > > >> Also Visiting Scientist, Math. Dept., Rutgers University,
> Piscataway,
> > > >> NJ.
> > > >> Phone: 732 828 6098; home page: http://NeilSloane.com
> > > >> Email: njasloane at gmail.com
> > > >>
> > > >>
> > > >>
> > > >> On Tue, Dec 25, 2018 at 10:35 PM <rgwv at rgwv.com> wrote:
> > > >>
> > > >>> Dear Neil,
> > > >>>
> > > >>>         You asked me this over a decade ago to which I answered
> you. I
> > > >>> no
> > > >>> longer have that information.
> > > >>>
> > > >>>         Also I believe that there was a reference which has been
> > > >>> removed.
> > > >>>
> > > >>>         That's the best I can do presently.
> > > >>>
> > > >>> Respectfully yours, Bob.
> > > >>>
> > > >>> -----Original Message-----
> > > >>> From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of Neil
> > Sloane
> > > >>> Sent: Saturday, 22 December, 2018 3:18 PM
> > > >>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >>> Subject: [seqfan] Re: What is a "Q unit fraction"?
> > > >>>
> > > >>> I will ask Bob Wilson directly
> > > >>>
> > > >>> In the mean time I added "obsc" (to A016013).
> > > >>>
> > > >>> Q is pretty certainly a numerical value (or range), since A016017
> is %N
> > > >>> A016017 Smallest k such that 1/k can be written as a sum of
> exactly 2
> > > >>> unit
> > > >>> fractions in n ways.
> > > >>> and - also from Bob Wilson  - there is:
> > > >>> %N A018892 Number of ways to write 1/n as a sum of exactly 2 unit
> > > >>> fractions.
> > > >>>
> > > >>> Best regards
> > > >>> Neil
> > > >>>
> > > >>> Neil J. A. Sloane, President, OEIS Foundation.
> > > >>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > > >>> Also Visiting Scientist, Math. Dept., Rutgers University,
> Piscataway,
> > > >>> NJ.
> > > >>> Phone: 732 828 6098; home page: http://NeilSloane.com
> > > >>> Email: njasloane at gmail.com
> > > >>>
> > > >>>
> > > >>>
> > > >>> On Sat, Dec 22, 2018 at 2:46 PM Alex Meiburg
> > <timeroot.alex at gmail.com>
> > > >>> wrote:
> > > >>>
> > > >>> > Two guesses. First option: this is a "q-analog" of a unit
> fraction.
> > > >>> > There are "q-analogs" of a variety of quantities, but I don't
> > > >>> > understand them very well and I think you'd have to specify q?
> > Maybe
> > > >>> > it ends up being independent of q here, though.
> > > >>> >
> > > >>> > Second option: you're misparsing the description, and instead of
> > > >>> > decomposing into "Q unit fractions", it's decomposing into plain
> old
> > > >>> > unit fractions, of which there are Q. Q is some variable that
> hasn't
> > > >>> > been properly explained.
> > > >>> >
> > > >>> > Actually, I'd bet on the second one, given that they say
> "exactly Q"
> > > >>> > unit fractions, which really suggests that Q is a quantity of
> unit
> > > >>> fractions.
> > > >>> >
> > > >>> > On Sat, Dec 22, 2018, 11:30 AM Sean A. Irvine <sairvin at gmail.com
> > > >>> wrote:
> > > >>> >
> > > >>> > > A016013 Number of ways to write 1/n as a sum of exactly Q unit
> > > >>> fractions.
> > > >>> > >
> > > >>> > > Not a lot of information to go on here.
> > > >>> > >
> > > >>> > > Sean.
> > > >>> > >
> > > >>> > > --
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> > > >
> > > >
> > > >
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