[seqfan] Re: What is a "Q unit fraction"?
Peter Munn
techsubs at pearceneptune.co.uk
Wed Dec 26 12:39:13 CET 2018
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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