OEIS comments on method of computation

[Victor Miller]

Should contributors of values to sequences (especially hard ones)
indicate what method they used to calculate the terms? Often a short
program is given which is just an exhaustion. This has no chance of
reproducing the results for the larger values. I realize that we're
not writing a paper here, but it would be good if at least an outline
for a method of computation is given. If there is a reference that
describes it, it should be indicated. If not there should be a short
description.

Victor

[Tomas Rokicki]

I think this would be great!  Best might be a link to a github repo.

Sometimes the method cannot be easily described, especially for

those not familiar with some "Project Euler" tricks (like the Lucy

Hedgehog algorithm).

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[Sean A. Irvine]

Hi Victor,

Ideally, yes. It's an important part of reproducibility.

The editors already do a very good job of requesting details on how values were obtained (or in reproducing the data with their own programs). We do encourage submitters to either upload programs or provide links to programs where that is appropriate.

There are situations where this is difficult to achieve, particularly where the data is coming from a published paper.  Difficulties here include that the paper might not have been written by the person making the submission (we have people scouring the literature for sequences to include); the values might depend on theoretical arguments only understood by a small number of people (i.e., difficult for our editors); or require access to obscure, specialized, proprietary or otherwise concealed software. 

There are also those who like to demonstrate prowess without revealing their methods, which seems to be a very long tradition in mathematics and I think part of the historical culture of the field. It's not something that I personally ascribe to, but I would hesitate to refuse a submission solely because the method has not been described or revealed.

Ultimately if we can reproduce initial terms of data we tend to accept the entire data of the sequence, because having it seems more beneficial than not. In my experience the number of values subsequently needing correction is comparatively low.

Sean.

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[Victor Miller]

Reproducibility is what I had in mind. Right now I’m having a discussion with the editor for A145789. This is one of many sequences contributed by Ron Hardin which have no indication of how they were computed. By my guess, confirmed by correspondence with him, he used BDDs (binary decision diagrams). Even that is not straightforward as it depends strongly on the method of constructing a Boolean function, and on the choice of variable order. A wrong choice there will blow up memory use. I have another approach which confirms the existing values and extends them. I gave a short two sentence description of that approach in the comments but the editor thinks it’s superfluous. I disagree for the reasons given in my original post.

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[Robert McKone]

Sarcasm:  Of course no one can know my secrets, after all, I operate on an intellectual plane so rarefied that ordinary verification simply cannot reach it.  The methods are too subtle, the computations too vast, and the insight too elevated for anyone else to follow.  If others cannot reproduce the results, that merely confirms the point.

Seriously:  This kind of secrecy is self-serving and dangerous.  When methods are concealed, when behind claims of extreme computational complexity or vagueness, it becomes easy for those to hide academic dishonesty, selective reporting, fabrication, or uncheckable extrapolation.

Step 1:  Establish credibility by publishing increasingly large values, offering just enough information for others to verify the early cases with effort, but never enough to fully reproduce the method.
Step 2:  Gradually introduce results that sit beyond practical recomputation, relying on scale and complexity as a shield against independent verification.
Step 3:  Let uncheckable claims harden into accepted facts, thereby cementing a place in history on results that can neither be disproven nor confirmed.

Results that no one else could ever verify can neither be disproven nor proven, allowing someone to “cement their place in history” on the basis of claims that sit beyond scrutiny.  I truly think this practice is bad for the OEIS.

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[Martin Fuller]

What are the guidelines when extending an existing sequence? Sometimes I add my program and sometimes I don't. Should I upload my programs more often?

Here are some examples where I could have included a program but did not:

A358882-A358885, A358302-A358303:

Python program, 60 lines, does not calculate A358302-3, nothing very clever, and only good for a few of the new terms.

C++ program, 250 lines, still not very clever, but faster and more memory efficient. Limited documentation and several messy details. I would feel bad asking someone else to read it.

A104429, A002047, A002848, A002849, A334250:

C++, 1800 lines, straightforward ideas but many, many nasty details to reduce memory. I think there is more future in the method described by Assarpour et al (A014552).

A326512:

C++, only 75 lines, some bit manipulation and some caching, no documentation at all.

A051567, A051757

C++, 300 lines, same as above.

If anyone is interested in these sequences, you can mail me :)

Martin Fuller

[M F Hasler]

As others, I absolutely second Victor's idea.

There are many good reasons for which it is important and useful to know how initial or additional terms were computed.

(In addition to those already mentioned:

- it might help detect/avoid wrong terms produced by AI hallucinations and/or incorrect programs,

- it will clarify which definition or formula was used, in cases where we have different definitions and/or formulas that are thought to be equivalent but maybe aren't.)

I also understand that sometimes the data is not the result of a simple program suitable for publication.

In those cases, it should be explained in a comment how the terms were found

(as Victor already suggested towards the end of his post).

I think the Editors should be allowed to request / require this information.

As others said, the result of any scientific publication should be reproducible,

and in other scientific publications it is also required for the authors to explain in detail how they obtained their results.

So this is a really standard requirement.

- Maximilian

On Sat, Jan 17, 2026 at 2:58 AM 'Martin Fuller' via SeqFan <seq...@googlegroups.com> wrote:

What are the guidelines when extending an existing sequence? Sometimes I add my program and sometimes I don't. Should I upload my programs more often?

Here are some examples where I could have included a program but did not:

A358882-A358885, A358302-A358303:

Python program, 60 lines, does not calculate A358302-3, nothing very clever, and only good for a few of the new terms.

C++ program, 250 lines, still not very clever, but faster and more memory efficient. Limited documentation and several messy details. I would feel bad asking someone else to read it.

A104429, A002047, A002848, A002849, A334250:

C++, 1800 lines, straightforward ideas but many, many nasty details to reduce memory. I think there is more future in the method described by Assarpour et al (A014552).

A326512:

C++, only 75 lines, some bit manipulation and some caching, no documentation at all.

A051567, A051757

C++, 300 lines, same as above.

If anyone is interested in these sequences, you can mail me :)

Martin Fuller

On Saturday, 17 January 2026 at 02:54:38 UTC r.p.m...@gmail.com wrote:

Sarcasm:  Of course no one can know my secrets, after all, I operate on an intellectual plane so rarefied that ordinary verification simply cannot reach it.  The methods are too subtle, the computations too vast, and the insight too elevated for anyone else to follow.  If others cannot reproduce the results, that merely confirms the point.

Seriously:  This kind of secrecy is self-serving and dangerous.  When methods are concealed, when behind claims of extreme computational complexity or vagueness, it becomes easy for those to hide academic dishonesty, selective reporting, fabrication, or uncheckable extrapolation.

Step 1:  Establish credibility by publishing increasingly large values, offering just enough information for others to verify the early cases with effort, but never enough to fully reproduce the method.
Step 2:  Gradually introduce results that sit beyond practical recomputation, relying on scale and complexity as a shield against independent verification.
Step 3:  Let uncheckable claims harden into accepted facts, thereby cementing a place in history on results that can neither be disproven nor confirmed.

Results that no one else could ever verify can neither be disproven nor proven, allowing someone to “cement their place in history” on the basis of claims that sit beyond scrutiny.  I truly think this practice is bad for the OEIS.

 

On Sat, 17 Jan 2026 at 13:53, Tomas Rokicki <rok...@gmail.com> wrote:

[Victor Miller]

I also might suggest that, if possible (especially for hard
sequences), that there be a way to give the time/storage used for some
of the hard calculations. If someone wants to reproduce the results
(and maybe improve them!) this would be helpful in evaluating their
own method. I'm not sure where this information should be placed (I
know that the b-file can be sort of a catch all for extra
information).

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[Harry Neel]

All Interested Parties:

As someone new with no verifiable credentials, and likely to be misunderstanding the issue(s) , how hard is it to inform those who submit potential sequences that if their sequences cannot be verified they will not be accepted for inclusion into the OEIS.

Unless others had provided their expertise, sequences that I submitted to OEIS would likely have never been approved. Afterall, how boring is it to follow someone's procedure of their setting up a particular 'sieve' followed by their use of an online 'prime number calculator,' and inputting that information into a spreadsheet (by hand), then ....... 

At the same time, if someone has an issue concerning how to verify their data, why would they want their sequence to be known in the first place.

Please forgive my ignorance, but if someone wants to have their sequence known, but not why or how its values are valid, perhaps one should ask , "Why?"

Clear Thinking To  All

Regards,

Neel

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[Robert McKone]

What I would add (though it is secondary to providing mathematics or code sufficient for reproduction) is that, when a sequence counts concrete mathematical objects, I believe it is often good practice to provide an accompanying A-file listing all objects for each n, within reasonable size limits.

As an example, when I extended A290689 (number of transitive rooted trees with n nodes), I also supplied the corresponding A-file:
https://oeis.org/A290689/a290689.txt
This allows anyone to independently verify the count with only modest effort.  If someone needs a specific rooted tree, it is already available.  If someone doubts a value such as a(21)-a(22), they can attempt to disprove it directly by examining the listed objects or by producing a counterexample.

(Now I do admit, I had not uploaded the code I wrote to get this, but this is something I will seek to fix if I can find it through my old computer.)

I also did this for A185178 a bit differently, when I was counting the number of distinct values of the permanent of an n X n (0,1)-matrix with exactly three 1's in each row and each column, when I extended this by a(9)-a(11).  I gave one example for each permanent:

https://oeis.org/A185178/a185178.txt

also the frequency count of each permanent:

https://oeis.org/A185178/a185178_1.txt

and then finally the code:

https://oeis.org/A185178/a185178.cpp.txt

The EXAMPLE section is valuable for illustrating small cases in a compact and readable way. However, if one can construct examples algorithmically, then (subject to reasonable file-size constraints) it is often feasible and useful to provide all examples, not just a selected subset.  Doing so shifts verification from trust in the contributor’s computation to direct inspection of the underlying data.

This approach does not replace the need for clear definitions, algorithms, or references, but it can significantly lower the barrier to independent verification, reuse, and error detection, especially for (but not limited to) combinatorial counting sequences.

The OEIS has earned its reputation as a uniquely high-quality reference precisely because it emphasises verifiability, transparency, and long-term reuse.  Where feasible, natively hosting auxiliary data such as complete object listings, frequency tables, or other such data, strengthens this role.  This preserves not just the claimed values, but the concrete mathematical evidence behind them.  This kind of material turns the OEIS from a catalogue of numbers into a durable repository of structured mathematical knowledge, and helps ensure that results remain checkable and useful long after the original computations, software environments, or authors are no longer available.

Fermat famously claimed a proof “too large for the margin”.  The OEIS works best when proofs, data, code, or examples actually exist.  No one can go back to the 1600s and ask Fermat what he really had in mind, and in 400 years no one will be able to ask us either, only what we leave behind will matter.

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[Jaap Spies]

Yes, I agree, especially the hard ones need a possibility to be checked.

In 2003 we had a kind of competition to expand sequences around the permanent of (0,1)-matrices. No one showed his programs.

Recently I expanded  https://oeis.org/A089475    and    https://oeis.org/A089476 with a(7). I decided to publish my methods in a github library: https://github.com/jaapspies/permanents-determinant to make it possible for every one to check the results and eventuele use it for their own purpose.

Sometimes I wonder where the results come from. In  https://oeis.org/A087983 we see a(8)=7980. I'm really curious how this number was calculated. Who checked it and how?

Regards,

Jaap Spies

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[Brendan]

I just verified all the values of https://oeis.org/A087983 .

The computation for A087983(8)=7980 took 5 core-hours. My method was to generate all 14,685,630,688 binary 8*8 matrices up to row and column permutation using the program genbg which comes with my package nauty. Then I applied a permanent function I made for some earlier project that implements the Ryser method using bit-picking.  That comes to about 800,000 permanents per second.

This raises another issue relevant to the present discussion.  It would be good in the case of difficult computations that replication was noted in the OEIS entry. I think I've never seen this, but it would add confidence that entries are correct especially in the cases where replication is difficult.  I boldly added my replication to the entry, which has some proposed edits open.

Cheers, Brendan.

  

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[Robert McKone]

A replication tag where people say that they expanded the sequence would be cool I think.  Not sure exactly how this could or should work, but I do see great value in it.

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[Brendan]

I just added "a(1)-a(8) verified by .." to the author section, assuming the editors accept it.  I think that is enough unless there is a more extensive addition to make. Brendan.

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[Neil Sloane]

> A replication tag where people say that they expanded the sequence would be cool I think.  Not sure exactly how this could or should work, but I do see great value in it.

This is normally indicated in the EXTENSIONS field, by saying something like "Entries up to a(25) confirmed by  ..."

Best regards

Neil 

Neil J. A. Sloane, Chairman, OEIS Foundation.

Also Visiting Scientist, Math. Dept., Rutgers University, 

Email: njas...@gmail.com

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[Sean A. Irvine]

There are over 800 sequences with extension lines using "verified", "confirmed", or "checked" (admittedly often in conjunction with providing new terms).

Given this is only useful for "hard" sequences, I think we already have the necessary mechanism.

Sean.

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[David desJardins]

Obviously it's good if people document their methods and if others confirm their computations. But I wouldn't want to see a formal requirement that every sequence (or even every "hard" sequence) be accompanied by documented code. I'd still rather have people share their results if not fully documented, than not share them at all.

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[Jaap Spies]

Thank you Brendan for your explanation. As I see in the history of https://oeis.org/A087983 in 2024 there was no discussion at all.

Maybe it is not always possible to publish the exact code, but acceptance should come beyond reasonable doubt.

As a personal note: I should have published my algorithm in 2003. I found a fast alternative for Ryser's algorithm, implemented it in a C-program and calculated some sequences in the OEIS. A lookalike is now known as Glynn's formula (2010). In my github repository https://github.com/jaapspies/permanents-determinant there is the Spies/Masschelein formula for use with rectangular matrices.

In general I think it is good to share code as much as possible.

Regards,

Jaap 

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[Michel Marcus]

I think you could try to write to the user that wrote extension  a(8) from Minfeng Wang, Oct 04 2024

Click in the user name, then login, then use e_mail user in tools box

If email user is not available, click in discussion tab of the user page and type your message there

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[Joerg Arndt]

When adding more terms I sometimes used the a pink-box comment to put
"all given terms recomputed" where this seemed reasonable
This way it is at least in the edit history.

Best,  jj

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