[seqfan] Re: Breaking news on partition numbers.

[Alexander P-sky]

FYI - there is already discussion at mathoverflow which is following
the trail of this seqfan thread

http://mathoverflow.net/questions/53205/computability-of-oeis-a034891-partitions-of-n-into-prime-parts-1-included

ARP
--------- Forwarded message ----------
From: Charles Greathouse <charles.greathouse at case.edu>
Date: Tue, 25 Jan 2011 13:50:05 -0500
Subject: [seqfan] Re: Breaking news on partition numbers.
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> I cannot, however, see how much more can be read from this picture
> and certainly not something worth calling "model" of any sort,
> though I am happy to be proven wrong here.

Of course this is what I'm looking for: something to prove your (and
my) intuition wrong.  It's not an isolated event, either: there are a
great many sequences submitted without any apparent motivating
factors.  If there is an interesting sequence that is submitted
without explanation, my concern is that someone might happen upon that
sequence later (remember, it is by assumption interesting) and *not*
learn anything about it because the author left off that explanation.

I believe in Neil's old rule of thumb here: a sequence should take at
least an hour to create, between research, referencing, calculating,
and writing.*  If you can't be bothered to spend that much time, the
sequence might not be interesting enough for inclusion (but rather as
a comment to an existing sequence, perhaps).

* This is not a complaint against those who submit many sequences at a
time, like R. H. Hardin; presumably a great deal of time is spent
preparing his sequences which are then submitted in batches.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On 1/25/11,  wrote:
> * Charles Greathouse <charles.greathouse at case.edu> [Jan 25. 2011 10:03]:
>> Can you explain why those sequences are interesting?
>>
>> http://www.polprimos.com/imagenespub/polpa3dt.jpg
>> is a fine illustration of A000041, but I don't immediately see the
>> value of these sequences.
>>
>
> As far as I can see this is an illustration of the fact that
> the partitions of n can be split into
> A) partitions of n-1 with the part 1 appended
> B) partitions without the part 1
>
> This shows that the numbers of partitions without part 1
> are the differences of the numbers of partitions,
> a nice "proof without words".
>
> I cannot, however, see how much more can be read from this picture
> and certainly not something worth calling "model" of any sort,
> though I am happy to be proven wrong here.
>
> Until this happens I'll remain the usual grumpy German,
> also known as Sauer Kraut.
>
> cheers,   jj
>
>> [...]