Unusual uses of OEIS sequences on GitHub

[Bob Lyons]

Currently trending on Hacker News:

https://www.jeremykun.com/shortform/2026-04-13-0700/

Bob

[Jeremy Kun]

And I just joined the mailing list, too, mostly to lurk.

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[Jon Awbrey]

See also —

https://oeis.org/wiki/Riffs_and_Rotes

aside from the recursive grace note like patterns
i once saw these structures as forming a basis
for a type of fourier analysis of waveforms

jon

[M F Hasler]

That was already posted on this list 5 weeks ago ( 13th of April ... )

[Bob Lyons]

By me? 😀

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[Allan Wechsler]

No, Bob, it was Victor Miller who pointed out that article by Jeremy Kun back in April.

The topic is essentially unavoidable: no institution with OEIS's mission could avoid either this criticism (including whimsical, arguably nonmathematical content) or the opposite one (excluding arguably relevant content). I'm personally pleased that OEIS has chosen to err on the inclusive side, even though that means that some goofy content sneaks in. But I'm sure there some who can argue the other side with equal justice.

-- Allan

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[David Radcliffe]

Jeremy Kun said that he couldn't imagine a melody decided by the Inventory Sequence sounds very good.

I wouldn't call it a beautiful melody, but it is at least musically interesting. I created a piano roll visualization of this sequence and uploaded it to YouTube. https://www.youtube.com/watch?v=z9t0KYD4xEI

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[Jeremy Kun]

I hope my article isn't taken as a criticism, per se. I find a lot of joy in the quirky corners of OEIS, and I hope, if nothing else, my little vignettes bring positive attention to the community.

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[Antti Karttunen]

On Wed, May 20, 2026 at 10:01 PM Allan Wechsler <acw...@gmail.com> wrote:

No, Bob, it was Victor Miller who pointed out that article by Jeremy Kun back in April.

Yes, and I immediately responded to that in quite a grouchy tone, as I was reading too much criticism on Jeremy's article.

The topic is essentially unavoidable: no institution with OEIS's mission could avoid either this criticism (including whimsical, arguably nonmathematical content) or the opposite one (excluding arguably relevant content). I'm personally pleased that OEIS has chosen to err on the inclusive side, even though that means that some goofy content sneaks in. But I'm sure there some who can argue the other side with equal justice.

Well, (almost) all the sequences mentioned by Jeremy in https://www.jeremykun.com/shortform/2026-04-13-0700/ 

are mathematically valid and many even very relevant in various fields of mathematics. On the other hand, it probably takes SeqFanatics to really appreciate something like Recaman's sequence or the Inventory sequence as mathematical constructs.

Now, what I sensed instead as a hidden undertone in Jeremy's piece was that whether some "music theory" or another _allows_ employing those sequences for generating music. But, for example, de Bruijn sequence (A000695), Thue-Morse sequence (A010060), and Dress’s/Gould's sequence (A001316) are intimately related to base-2 expansion, so at least I can see that somebody might find them useful in this context. (Although I think that A007814 would be even more useful.)

The Hacker News thread (unless there are several) mentioned was this: https://news.ycombinator.com/item?id=48179172

The first commenter is a bit confused there. If one uses a certain definite sequence (not randomly selected) for generating music, it's _not_ an aleatoric composition (regardless of how much it might sound like "random garbage" to somebody else's ears. But please, no more digits of π). I recommend instead to start investigating this topic from https://en.wikipedia.org/wiki/Algorithmic_composition and then follow also to some of the "See also" links at the bottom.

The third commenter "jerf" makes interesting suggestions after his criticism:

--- (quote start) 

I would, however, be intrigued to see an example of someone mapping some mathematical object to music in some less trivial way that could actually reveal something interesting. Doesn't have to use tones. Maybe something that maps certain characteristics of something to the intensity of overtones or something. Or map something into an interesting polyrhythmic percussion line that somehow reflects something about the underlying sequence or mathematical object. Maybe there's something really interesting out there like this, but I expect it takes more than just shoving a sequence of numbers into the obvious integer mapping to conventional 12-tone pitches.

Perhaps the closest thing I've seen to this are the many videos on YouTube that map pitches to the order of operations of a sorting algorithm. Though I question if the audio brings anything new to the party that the visuals hadn't already brought.

--- (quote end)

Best regards,

Antti

-- Allan

On Wed, May 20, 2026 at 12:04 PM Bob Lyons <bobly...@gmail.com> wrote:

By me? 😀

On May 20, 2026, at 10:45 AM, M F Hasler <mha...@dsi972.fr> wrote:

That was already posted on this list 5 weeks ago ( 13th of April ... )

On Tue, May 19, 2026 at 9:59 PM Bob Lyons <bobly...@gmail.com> wrote:

Currently trending on Hacker News:

https://www.jeremykun.com/shortform/2026-04-13-0700/

Bob

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[Jeremy Kun]

> Now, what I sensed instead as a hidden undertone in Jeremy's piece was that whether some "music theory" or another _allows_ employing those sequences for generating music

I think it was simpler: someone deliberately chose it, and so there must be a reason behind it. If it was just the Fibonacci sequence, then I can see it being a sort of "golden rectangles are everywhere" reasoning that isn't all that deep. But with these more exotic sequences, I figured they must have tried using them and made something that seemed useful.

Maybe I should have just emailed the author :)

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[Ruud H.G. van Tol]

On 2026-05-20 03:59, Bob Lyons wrote:

> Currently trending on Hacker News:
> https://www.jeremykun.com/shortform/2026-04-13-0700/

Sierpinski in 16 bytes, with audio:
https://hellmood.111mb.de//wake_up_16b_writeup.html

-- Ruud

[Joerg Arndt]

Attached an old demo of mine for the Apple ][ (6502 CPU).
44 Bytes, but mildly cheating, using JSR to set pixels,
the layout of the video RAM was somewhat nontrivial.
Volume warning: sound is mostly noise.

The "Variations" near end change the sound created IIRC.
The two NOPs are space to allow for those variations.

Best regards,  jj

[brad klee]

Thanks! We've got video covered but needed some sheet music.

Noise is perfect, but I don't know if Harm.On.ica's pass through
filter is accurate or not? It doesn't really matter.

The hellmood article was also an interesting read, and I thought
that tongue or hang drum might be a skin choice if you want to
sell more pretty sounds.

Here's what Harm.On.ica figured out:

"Vervollständigungssequenz zum HCE-Supertile"
https://www.youtube.com/watch?v=8kj-39sEAys
(Watch at your own risk! Lego content warning.)

This is still short of being a sequence. It gets to 0 choices,
sort of. What's interesting is that it's forcing more surrounds
than the eight-tile model I derived it from.

Earlier I wanted to make time-dependent count sequences for the
hat tiling if a deterministic growth law could be found, but fell
short on knob twiddling to try and cancel branching choices.

If AI is good at knob twiddling, maybe there's new hope? There's
definitely new hope from the three-tile model, because its strong
forcing property is well-tuned to growth rules. I'd wager that at
least a Socolar-style probabilistic construction is possible, but
with all the branching we've already seen, maybe something fully
deterministic more like T&C is what I would hope for.

Do we have a non-proprietary online encyclopedia for combinatorial
hints? This is the first artifact I've personally found using Chat
GPT thinking or similar that seems to be newish consequential and
have a futurist outlook.



Cheers,




--Brad

On Saturday, May 23rd, 2026 at 3:58 AM, Joerg Arndt <joerg...@th-nuernberg.de> wrote:

> Attached an old demo of mine for the Apple ][ (6502 CPU).

...
> > https://hellmood.111mb.de//wake_up_16b_writeup.html
> > -- Ruud