more on A119028 and Re: Identical-digit blocks in decimal representation of partition numbers

[Jonathan Post]

Yes, I can see this -- and it is as visually pretty as it is abstractly so.
Makes me want to see more...

On 8/10/06, Joseph Biberstine <jrbibers at indiana.edu> wrote:
>
>        You're too kind.  I wish I could take credit for the sequence, but
> I
> really just followed the breadcrumbs in response to Tanya Khovanova.
>        Your interest inspires me to share a message from a dialogue I had
> with
> Robert G. Wilson v last month.  This natural generalization of the
> sequence seems to have a beautiful graphical interpretation.
> Unfortunately the awkward code I have won't allow me to generate more
> terms efficiently, so we only see what I suppose is the tip of a most
> pleasant iceberg.
>
> -JRB
>
> Jonathan Post wrote:
> He recently gave us the rather pretty:
> > A119028 <http://www.research.att.com/%7Enjas/sequences/A119028>
> >       Numbers that have 3 different *partitions* into 3 parts with the
> same
> product.
>
> -------- Original Message --------
> Subject: Re: Proposed joint submittal.
> Date: Fri, 28 Jul 2006 01:54:00 -0400
> From: Joseph Biberstine <jrbibers at indiana.edu>
> To: rgwv at rgwv.com
>
> tanya[n_, p_] := Max[Length /@ Split[Sort[Times @@@ Partition[Last /@
> Flatten[FindInstance[a + b + c == n && a >= b >= c > 0, {a, b, c},
> Integers, PartitionsP[n]]], p]]]];
> Table[tanya[k + p, p], {p, 2, 8}, {k, 2, 34}] //MatrixForm
>
>        Which comes out looking like this (hopefully your mail client can
> handle):
>
> 1 1 2 2 1 2 4 2 3 3 2 3 4 4 3 3 3 4 4 4 4 4 4 4 4 2 4 4 4 4 5 4 4
> 1 1 1 1 1 1 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
> 1 1 1 1 2 1 1 2 2 1 2 1 1 1 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2 2
> 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 2 2 2 2 1 1 1 2 1 1 1 1
> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1
> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
>
>        Pretty, huh?  Looks like some neat chaotic curtain
> effect.  Attached is
> a graphical interpretation.
>
> JRB
>
>
>
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