[seqfan] Re: Sequences with nice graphs / "Entanglement permutations"

[Neil Sloane]

Just to respond to a couple of Antti's questions:


> I guess it's OK from now on to include in the links-section of the
sequences that appear in that list a link like:

<a href="http://oeis.org/wiki/Index_to_OEIS:_Section_Gra#graphs_plots">Index
entries for sequences with interesting graphs or plots</a>

???

Absolutely! Good idea - because otherwise one has no idea whether
a graph is interesting.

You could even say:
<a href="http://oeis.org/wiki/Index_to_OEIS:_Section_Gra#graphs_plots">Index
entries for sequences with interesting graphs or plots</a> [mentions this
sequence]



> (BTW, I'm not anymore entirely happy with that word "entangling",
maybe "interweaving" would have been better? )

if you mean an ababababa... alternation, "interleaving" is the usual term

> BTW, I'm not submitting these by myself, because my mental backburner
is still full with dozens of _other_ interesting sequences...

They sound like they should be in the OEIS, so if
you can send them in, that would be worth doing. You may have
done most of the real work already!

Best regards

Neil


On Fri, Jan 24, 2014 at 6:08 PM, Antti Karttunen
<antti.karttunen at gmail.com>wrote:

> > Message: 3
> > Date: Tue, 21 Jan 2014 16:57:30 -0500
> > From: Neil Sloane <njasloane at gmail.com>
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>, Paul
> >         Tek <paul.tek at mail.be>
> > Subject: [seqfan] Sequences with nice graphs
> > Message-ID:
> >         <CAAOnSgRkpp-QkRP10_-az=qXHnaUrGou=
> 4O32x0mqQ4DAeoJjg at mail.gmail.com>
> > Content-Type: text/plain; charset=ISO-8859-1
> >
> > Paul Tek's User Page on the OEIS wiki has a short
> > list of sequences that have interesting graphs.
> > For example:
> > lacework: A003987
> >
> > Stimulated by this, I've created a subsection of
> > the Index to the OEIS to list such sequences.
> > This is in Section Gra of the Index, under
> > graphs (or plots), sequences with interesting
> >
> > I used Paul's list and added a handful of others.
> >
> > Anyone who has watched Tony Noe's OEIS Movie will
> > know that there are many sequences with lovely graphs.
> > The best way to look at the frames of the movie is here:
> > http://www.sspectra.com/math/MovieFrames/
> >
> > The purpose of this posting is to invite people
> > to expand these entries in the Index.
> >
> > Of course, whether you think a graph
> > looks like a waterfall or a hurricane is a matter of taste - but
> > that's OK!
> >
> > This is all part of the plan to emphasize the visual aspects of
> > the OEIS.
> >
> > Neil
> >
>
>
> I added two from my own list (which I admit has some bias to the seqs
> submitted by myself, as I recall those ones the best):
> http://oeis.org/wiki/User:Antti_Karttunen#My_favourite_graphs
>
> with these two new "visually descriptive subheadings":
>
> fractal froth: A135141
>  and
> waves: A218789
>
> to
> http://oeis.org/wiki/Index_to_OEIS:_Section_Gra#graphs_plots
>
> I guess it's OK from now on to include in the links-section of the
> sequences that appear in that list a link like:
>
> <a href="http://oeis.org/wiki/Index_to_OEIS:_Section_Gra#graphs_plots
> ">Index
> entries for sequences with interesting graphs or plots</a>
>
> ???
>
> -------
>
> As what comes to A135141 by Katarzyna Matylla, (see
> http://oeis.org/A135141/graph )
> I found its beautiful graph from the still-frame of the OEIS-movie.
> (I mean, the one which Youtube will show for example in its "side-video"
> lists).
>
> Inspired by it, I submitted its inverse permutation A227413 last July,
> as well as later, several generalized cases, i.e. "entanglement
> permutations", see:
>
> http://oeis.org/search?q=A135141&sort=&language=&go=Search
>
> where one divides a set of natural numbers to two complementary
> subsets, in two different ways, and then "entangles" them, in some
> cases requiring extra +1 or -1 fiddling with indices, as to make the
> resulting sequences permutations of nonnegative integers/natural
> numbers.
> (BTW, I'm not anymore entirely happy with that word "entangling",
> maybe "interweaving" would have been better? )
>
> First, I was hesitating as whether to submit any of those at all, as I
> considered them just as further noise into the system, but then I
> realized that we obtain also some "old friends", for example, when
> entangling the even/odd pair with evil/odious pair (A001969/A000069)
> we get Gray code and its inverse: A003188/A006068.
>
> Also, when entangling even/odd pair with the complementary pair
> A048724/A065621 (which are actually just evil and odious numbers
> further permuted) I bumped into "Blue code": http://oeis.org/A193231
> which itself is a very nice sequence.
>
>
> So, for Katarzyna's A135141, those two pairs of complementary sets are
> primes/composites and even/odd numbers, and the latter occur as one of
> the pairs in all examples I have submitted so far. But of course one
> does not need to delimit oneself to that. E.g. what comes if one
> "entangles" pair primes/composites with pair composites/primes, in a
> similar way?
> Is it already in OEIS? (Should result a self-inverse permutation).
>
> Also, as what comes to possibly graphically interesting variants, I
> suggest permutations pairs like A135141/A227413 but instead of
> primes/composites, use complementary pairs like the following,
> obtained with various sieving processes:
>
> A000959/A050505 (Lucky/Unlucky numbers),
> A003309/A192607 (Ludic/Nonludic numbers),
> A014580/A091242 (Irreducible/Reducible GF(2)[X] polynomials, evaluated at
> X=2),
> etc.
>
> Also, one could entangle these, not just with even/odd numbers pair,
> but also with each other. What will result? (I mean, will they look
> radically different from http://oeis.org/A135141/graph or are they
> also "fractal froth" ?)
>
> BTW, I'm not submitting these by myself, because my mental backburner
> is still full with dozens of _other_ interesting sequences...
>
>
> Yours,
>
> Antti Karttunen
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

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