[seqfan] Re: Getting an integer sequence for a specific song

Antti Karttunen antti.karttunen at gmail.com
Wed Jun 19 10:38:09 CEST 2019

On 6/18/19, Gordon Charlton <gordonrcharlton at gmail.com> wrote:
> Link to notes for a talk I am preparing on this subject.
> https://www.dropbox.com/s/f060yaybdpj9dk0/endless%20rivers%20talk.pdf
> Featured sequences - Collatz, Kolakoski, Fibonacci & lexicographical list of
> permutations.


How about adding the A-number links and mentioning OEIS in general,
for further inspiration?

The "vertical binary reading" of Fibonacci numbers is the thing I
encountered in 1998, see https://oeis.org/A036286 (maybe the binary
pattern was mentioned somewhere in Wolfram's papers or on Weinstein's
World of Mathematics site, although the NKS-book wasn't published
until 2002).

Note that the lexicographical list of permutations is actually
slightly harder to generate than simple A060117 / A060118 ("linear
time algorithm") that I use for example in my green music box, where
the conversion from a factorial expansion to permutation is actually
done in a single cycle with pure combinational logic. (No timewise
need for that, but it was a nice thing to do!)

Change ringing is a much explored field for finding permutation walk
algorithms, and I guess there would be potential for further
developing them (also for infinite variants).
"Plain Bob" must be plainest of them, but see the links:
(Beware of exotic terminology, quite different from those of group

For infinite variants, I started playing with the idea here:
That link to my page has been dead for a long time, but fortunately,
the Internet Archive saves:

Then, in the same directory, see:
and links to papers
J. H. Conway, N. J. A. Sloane and A. R. Wilks, Gray Codes for
Reflection Groups, Graphs and Combinatorics, 5 (1989), pp. 315-325.
F. Ruskey and Carla Savage, Hamilton Cycles which Extend Transposition
Matchings in Cayley Graphs of Sn, SIAM Journal on Discrete
Mathematics, 6 (1993) 152-166.

(for anybody wanting to jump into that rabbit's hole!)

> Target audience - experimental musicians with programming skills.

Do you know what platforms they are using? Overtone, for example?

Best regards,


> Note I do
> not consider myself a mathematician. If you happen to notice any errors of
> terminology in the text, please let me know off-list. Thank you.
> Gordon
> Sent from my iPad
> On 17 Jun 2019, at 11:44, aleksisto <aleksisto at gmail.com> wrote:
>>> I think it's the opposite direction, turning sequences (and other
>>> mathematical structures) to songs that's much more fertile field in
>>> the long run.
>> Using Parsons code(https://en.wikipedia.org/wiki/Parsons_code) you can
>> search for any melody in the pi digits sequence, for instance.
>> aleksisto
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>> Seqfan Mailing list - http://list.seqfan.eu/
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