[seqfan] Re: What is a "Q unit fraction"?
Peter Munn
techsubs at pearceneptune.co.uk
Wed Dec 26 14:37:44 CET 2018
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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>>> >
>>>
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>>
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>>
>
>
>
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