[seqfan] Re: Median nth least factors in prime factorisations of the integers

[Peter Munn]

Thankyou, Neil for clarifying why there was a problem.

Though I have come across the use of "most" like that, I was not aware it
was such a standard terminology.  But nor would I have written "strictly
more than half" as the mathematician in me is unhappy with applying such
terminology to an infinite set.  I am a mathematician at heart if not by
experience!  I was aiming to use a less precise term that would concisely
give the general idea and I could go on to define - perhaps had I used "a
majority of" I would have avoided this pitfall?

Best Regards,
Peter

> Peter, You should be aware than in mathematics, when one says that
> "most" things have a certain property, it means "all except a finite
> number".
>
> In your submissions A284411 and A281889 you used "most" to mean
> "strictly more than half". This is too different from the standard
> usage, so I have
> changed the definitions to make it clear what you meant.
>
> You can't redefine a standard terminology to be anything you want!
>
>
> 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 Fri, Mar 31, 2017 at 2:38 PM, Peter Munn
> <techsubs at pearceneptune.co.uk> wrote:
>> Dear Seq Fans,
>>
>> This concerns my first significant piece of mathematical work since my
>> BSc
>> 40 years ago!  Note I suggest checking of A281889(4).
>>
>> Best Regards,
>>   Peter Munn
>>
>> Background
>> ==========
>>
>> I've been looking at prime factorisations with factors listed least
>> first
>> and examining how "quickly" the values "typically" grow from factor to
>> factor. (More detail on https://oeis.org/wiki/User:Peter_Munn)
>>
>> I have now proposed sequences of medians for both n-th least prime
>> factor
>> value in prime power factorisations (A284411) and n-th least listed
>> factor
>> in the simpler prime factorisation with a straight product of prime
>> numbers (A281889), but with definitions that emphasise their
>> distinctness.
>>
>> In the first case, my calculation of terms 2 and 3 led via Google to the
>> 4th term in the form of an advert for De Koninck's _Those Fascinating
>> Numbers_.  So I'm happy with A284411.  But I have yet to find the terms
>> of
>> A281889 (3, 7, 433, 9257821) elsewhere, and so...
>>
>> My calculation check suggestion
>> ===============================
>>
>> I have checked my calculation method against empirical counts, and
>> looked
>> at rounding errors, but I see scope for an error in complexity I added
>> in
>> order to calculate A281889(4) on a limited platform.  So I would
>> appreciate an independent calculation, whether or not based on the
>> formulae I give in A281890 and A281891 which underpin the sequence.
>>
>> Many thanks if you can help,
>>
>> Peter
>>
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>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>
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