A000792

[Juan Arias de Reyna]

Dear Sq. fans,

Oeis make possible to have a name for any sequence by refereeing to its sequence number in Oeis. For example sequence A000792. But few will name Fibonacci numbers by its number A000045. Sometimes it is useful to have a name at this.

By my writings about the complexity of natural numbers ||n||, (sequence A005245), I frequently deal in my papers with A000792. I want to give a name to this sequence. 
I propose to call it "Moser numbers".

This sequence has appeared many times before. Among other A000792 is characterised as:

(a) A000792(n) is the largest value of x_1...x_k for x_1+...+x_k=n.

(b) The maximal size of a Abelian subgroup of the symmetric group S_n.

(c) The maximal number of maximal cliques possible in a graph with n vertices.

(d) The maximum number k with complexity ||k|| = n.

We want to emphasise the role of L. Moser on the study of this sequence:

(1) L. Moser. Problem 125 proposed by L. Moser and solved by L. Carlitz, Pi Mu Epsilon J. 3 (1961), 232--233.  

(2) R. Bercov & L. Moser, On abelian Permutation Groups, Canad. Math. Bull. 8 (1965), 627--630

(3) J. W. Moon & L. Moser, On cliques in graphs, Israel J. Math. 3 (1965), 23--28.

In (1) Moser asked the question of the maximal product associated to (a) above. He solved (b) in (2). He asked with Erdös the question about the maximum of cliques and gave a solution to this question in (3), different from other one from Erdös.

Without doubt, this sequence was known before 1961. I do not know the first mathematician dealing with it. And I ask to anyone who has a better proposal to give it. 

In any case what I propose is to modify in Oeis the name of this sequence to "Moser numbers". I do not know if this is an adequate proposal for Oeis. 

Thank you. 

Juan Arias de Reyna

[Neil Sloane]

Juan,  We don't normally add names to sequences in the OEIS, unless the name is in common use in the literature.  And A000792 is not even a "core" sequence.

But maybe we could make an exception in this case.  I am neutral.  Let's see what Sean says.

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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[Geoffrey Caveney]

I observe that there already exist the Moser-de Bruijn sequence (A000695 and A063010), an analog of Moser's worm constant (A247553), and the Moser-Newman sum sequence and its analog (A360737 and A005599).

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[Antti Karttunen]

On Thu, Jan 22, 2026 at 3:40 PM Geoffrey Caveney <geoffre...@gmail.com> wrote:

I observe that there already exist the Moser-de Bruijn sequence (A000695 and A063010), an analog of Moser's worm constant (A247553), and the Moser-Newman sum sequence and its analog (A360737 and A005599).

Hello all,

If I would vote a better name for A000792, it would be "After a(0) = 1, numbers of the form 3^k, 2*3^k, 4*3^k." (which is now the first comment. Or we could append it as an alt-definition to the name-field, after a semicolon).

In general, I dislike the way how most of the "higher mathematics" is peppered with the surnames of long dead people, and often not even much involved with the things their name was later used for. I understand that many live a materially poor life, so awarded even a posthumous acknowledgement of all the sweat and toil they expended to the sake of mathematics must feel consoling. But... sometimes it makes for hard reading, of the topic which is hard enough even without any jargon.

Best regards,

Antti

 

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[M F Hasler]

On Thu, Jan 22, 2026 at 3:40 PM Geoffrey Caveney <geoffre...@gmail.com> wrote:

I observe that there already exist the Moser-de Bruijn sequence (A000695 and A063010), an analog of Moser's worm constant (A247553), and the Moser-Newman sum sequence and its analog (A360737 and A005599).

Yes, lots of things are already named after Leo Moser, e.g. Moser spindle, Moser's circle problem, Moser's worm problem, Moser–de Bruijn sequence, Erdős–Moser equation, Lambek–Moser theorem, Steinhaus–Moser notation,

cf. https://en.wikipedia.org/wiki/Leo_Moser.

On Thu, Jan 22, 2026 at 10:22 AM Antti Karttunen <antti.k...@gmail.com> wrote:

If I would vote a better name for A000792, it would be "After a(0) = 1, numbers of the form 3^k, 2*3^k, 4*3^k." (which is now the first comment. Or we could append it as an alt-definition to the name-field, after a semicolon).

I agree that names should be the simplest and most easily understandable.

From that new title one can immediately "see" the terms of the sequence, so I'd approve that change.

(As usual, we should leave the original definition as the 1st comment

and here maybe also as first formula.)

 

In general, I dislike the way how most of the "higher mathematics" is peppered with the surnames of long dead people, (...) 

many live a materially poor life, so awarded even a posthumous acknowledgement of all the sweat and toil they expended 

Leo Moser probably doesn't need more posthumous acknowledgement. He was already quite famous during his lifetime. (According to a necrology, "the most popular of the lecturers of the MAA sponsored program", "he lectured at more than 100 American and Canadian universities", "held the Alberta Chess Championship for many years"...)

 

But... sometimes it makes for hard reading, of the topic which is hard enough even without any jargon.

Well, here  the idea was to make it easier to read, by saying Moser numbers instead of A792.

But in contrast to OP's take, I think it's not that bad to use short A-numbers to repeatedly refer to a sequence.

I wouldn't find it difficult to follow if an author used A45 to refer to the Fibonacci sequence (insofar more as it makes it unambiguous, in particular for the offset and initial terms, which are often somewhat ambiguous for sequences with common names: for some authors, the F-sequence is 1,1,2,3,... rather than 0,1,1,2,... etc.)

But actually, in most cases where they use A45, even in the OEIS, the contributors define F = A45 and go on using F rather than A45.

In the same way, nothing forbids to say "the Moser numbers M = A792" when you are working with these, and use M and or "Moser numbers" in the sequel.

I'm also very much frowning upon introducing new names that don't already exist in literature.

There are a few cases where names or terminology were invented by the author of a sequence, and then popularized on OEIS in more and more sequences referring to the first one, and then it looks as if that was standard terminology, although it is only used in the OEIS, and only by one single author.

- Maximilian

On Thu, Jan 22, 2026 at 4:40 AM Juan Arias de Reyna <ariasder...@gmail.com> wrote:

(...) I frequently deal in my papers with A000792. I want to give a name to this sequence. 

[Juan Arias de Reyna]

Dear all, 

In any case the sequence should not be   "After a(0) = 1, numbers of the form 3^k, 2*3^k, 4*3^k.", but 

 "After a(0)=1, numbers of the form 3^k, 2*3^k, 4*3^k sorted out."    or "After a(0)=a(1)=1 numbers of the form 2*3^k, 3*3^k, 4*3^k"

To me this is not a name for the sequence, but a description. 

The Fibonacci numbers in Oeis get his name and his description in the first line.

I agree that it is not usual to give in Oeis a name that is not in common use. In my next preprint I will call it Moser sequence, that is for which I proposed this to OEIS.  I am not with those that call Euler or Gauss the last category of bundle  that he concot.  But Moser was really involved in any characterisation of this sequence. 

Best regards, 

Juan Arias de Reyna

[jp allouche math]

Actually there already is at least one "Moser sequence", see https://mat.ufpb.br/jmbo/papers/11.pdf
(Page 5) (also p.~138 of the published version at https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.10015).
Oh actually it is already page 122 of the 2019 paper at
 https://projecteuclid.org/journals/topological-methods-in-nonlinear-analysis/volume-54/issue-1/A-weighted-Trudinger-Moser-type-inequality-and-its-applications-to/10.12775/TMNA.2019.027.pdf
Oops I stop searching, the same sequence was already alluded to in 2003, see p. 6 of
https://www.research-collection.ethz.ch/server/api/core/bitstreams/c4703ac8-552e-433a-9024-b1db5d0e7827/content

all the best
jean-paul

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[Antti Karttunen]

On Thu, Jan 22, 2026 at 5:57 PM M F Hasler <mha...@dsi972.fr> wrote:

...

I'm also very much frowning upon introducing new names that don't already exist in literature.

There are a few cases where names or terminology were invented by the author of a sequence, and then popularized on OEIS in more and more sequences referring to the first one, and then it looks as if that was standard terminology, although it is only used in the OEIS, and only by one single author.

I admit that I have done this, but what's so wrong with that? Especially if the name is descriptive, and sometimes even funny?

E.g., I finally chose "Primorial base exp-function" for my dear brainchild A276086, and later I have used it a zillion times in further sequences, often in their title saying, "... , where A276086 is the primorial base exp-function.", so people who are not interested about such things can avoid going down that rabbit hole, when they already see it from a distance once removed, when hovering their mouse over the link present in some other sequence. (Instead of having to remember or research what the heck that A276086 is).

And now even Gemini uses that name when I ask it about related problems, and gets the gist of it very well. And don't worry, that name will eventually appear also in "literature", when I will have finished my paper concerning it and related sequences.

Also, I added "Primorial inflation of n" to A108951, as it was already coined by Matthew Vandermast in related A181815. I think that is also very descriptive name, like is also "Primorial deflation" for its left inverses (it has at least two).

By the way, I have noticed that Gemini in Pro-mode can even analyze PARI-code provided in the sequences to see what they are about. 

Best,

Antti

- Maximilian

[Sean A. Irvine]

Hi Juan,

You have obviously put some thought into this, but after reading the other responses to your question I am leaning toward "no".

The "Name" in the OEIS is really the definition of the sequence. Sure there are exceptions for widely understood sequences (things that school kids might recognize, primes, Fibonacci, etc.), but usually the name is the definition.

In terms of a label for the sequence "A000792" is better than "Moser numbers" because it is unique and precise. When I try a Google search for "Moser numbers", I don't see anything that looks like this sequence.

As an encyclopedia the OEIS does try to reflect naming used in the literature, but it is not the right place to be specifying nomenclature (other editors will likely disagree with me on this), although we will sometimes select particular options among available nomenclature (cf. the Style sheet).

I am fine with adding a comment, "These numbers could be called "Moser numbers"" or, better, "These numbers are called "Moser numbers" in [citations]".

Sean.

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[Arthur O'Dwyer]

(Repeating mostly what Sean said)

Seems to me that it would be somewhat defensible for Juan to add a comment

> Juan Arias de Reyna suggests that these numbers be called "Moser numbers."

although that's obviously a very abusable pattern if it were to be encouraged in general. Much more defensible IMHO would be to add a comment like

> Juan Arias de Reyna, in "Complejidad de los números hipotéticos" (2027), suggests that these numbers be called "Moser numbers."

This latter, not accidentally, requires "putting your money where your mouth is" by first making the proposal outside the auspices of OEIS. But it's also better because it's more amenable to updates. If, ten years from now, the note reads,

> Arias de Reyna (2027) first suggested that these numbers be called "Moser numbers." This nomenclature is used in Arias de Reyna (2028, 2030, 2035), Jones (2029, 2030), Smith (2032), and Brown (2030, 2031, 2032).

then, well, it has justified itself. Or if in ten years the note hasn't changed, then... something else.

my $.02,

–Arthur

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[Juan Arias de Reyna]

Hello,

I agree with Sean and Arthur,  it is the time what will say if the name is adopted, and we shouldn't force this by adding a comment about my suggestion in Oeis. The names in Mathematics always has been a process where each mathematician makes their own free choice and a consensus is arriving.  A slow process that many times ends in the wrong name after all :)

About the comment  Jean-Paul Allouche,  this" Moser sequences" appear to be of functions and due to Jürgen Kurt Moser, another notable mathematician 

working on PDE. 

[jp allouche math]

Yes I know that this is a quite different "sequence" and "Moser" but 
then the name "Moser sequence" is ambiguous (out of context)
jean-paul

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[David desJardins]

Another idea for giving sequences easy-to-reference names would be to give “core” sequences an additional “C-number” starting with C001, as well an “A-number”. That would be a lot more recognizable than a 6-digit A-number. Are there more than 1000 core sequences?

  — David desJardins

[Allan Wechsler]

If I did this right (search for "keyword:core") there are 183 sequences currently marked "core".

-- Alland

On Thu, Jan 22, 2026 at 9:47 PM David desJardins <da...@desjardins.org> wrote:

Another idea for giving sequences easy-to-reference names would be to give “core” sequences an additional “C-number” starting with C001, as well an “A-number”. That would be a lot more recognizable than a 6-digit A-number. Are there more than 1000 core sequences?

  — David desJardins

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[Bob Lyons]

I see 184 core sequences in the oeisdata repo:

$ find seq -name "*.seq" | xargs grep -P '^%K A\d\d\d\d\d\d .*\bcore\b' | wc -l

184

$

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[Sean A. Irvine]

Yes, there are only 183 core sequences.

I don't think more id's is a good idea, after all primes, A000040, already has 2 other id's: M0652 and N0241, and you don't see those id's used much.

Sean.

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[David desJardins]

Yet another idea, which people may or may not like, is to give core sequences mnemonic names. E.g., A000040 could be CPRIMES.

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[Antti Karttunen]

On Fri, Jan 23, 2026 at 10:47 AM David desJardins <da...@desjardins.org> wrote:

Yet another idea, which people may or may not like, is to give core sequences mnemonic names. E.g., A000040 could be CPRIMES.

How is "CPRIMES" more mnemonic (= "intended to help in remembering") than "Primes" ?

-- Antti

 

[M F Hasler]

On Thu, Jan 22, 2026 at 10:47 PM David desJardins <da...@desjardins.org> wrote:

Another idea for giving sequences easy-to-reference names would be to give “core” sequences an additional “C-number” starting with C001, as well an “A-number”. That would be a lot more recognizable than a 6-digit A-number. Are there more than 1000 core sequences?

 

Y'all know that oeis.org/A27, oeis.org/A217 etc. are a valid reference, do you?

I mean, leading zeros are not mandatory (and mostly ignored) in the OEIS.

And since most core sequences have 2- and 3-digit numbers,

I don't think we need C-numbers, just use the 2- or 3-digit A-numbers (A40 = primes, etc.)

-M.

[Bob Lyons]

Good point that leading zeros in the A-number are optional in oeis.org URLs and in OEIS searches (e.g., id:A41).

Within an OEIS entry, all A-numbers should include any leading zeros, so that the A-numbers are rendered as hyperlinks.

For example, in the following Crossref, the first A-number will not be rendered as a hyperlink: Cf. A19, A000079

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Bob

[Bob Lyons]

Also, it's okay if the A-number in an oeis.org URL or in an OEIS search has too many leading zeros (e.g., id:A0123456).

But within an OEIS entry, if an A-number has too many leading zeros, then it won't be rendered as a hyperlink.

--

Bob

[Ali Sada]

I'm sorry I don't want to hijack this conversation, but I've been trying to ask these questions for some time now. What's the history behind the numbering of the OEIS sequences? Why is the sequence of natural numbers A27, for example? What are the M and the N numbers? I am sure there is a really interesting history here and I would really appreciate it if you could tell me where I can find this information. 

Best,

Ali 

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[David desJardins]

On Fri, Jan 23, 2026 at 11:22 AM M F Hasler <mha...@dsi972.fr> wrote:

Y'all know that oeis.org/A27, oeis.org/A217 etc. are a valid reference, do you?

No, I did not know that! Why does the site generally display the leading zeros if they are not needed?

[Ruud H.G. van Tol]

On 2026-01-23 20:22, M F Hasler wrote:
> On Thu, Jan 22, 2026 at 10:47 PM David desJardins
> <da...@desjardins.org> wrote:
>
> Another idea for giving sequences easy-to-reference names would be
> to give “core” sequences an additional “C-number” starting with
> C001, as well an “A-number”. That would be a lot more recognizable
> than a 6-digit A-number. Are there more than 1000 core sequences?
>

> Y'all know that oeis.org/A27 <http://oeis.org/A27>, oeis.org/A217
> <http://oeis.org/A217> etc. are a valid reference, do you?

> I mean, leading zeros are not mandatory (and mostly ignored) in the OEIS.
> And since most core sequences have 2- and 3-digit numbers,
> I don't think we need C-numbers, just use the 2- or 3-digit A-numbers
> (A40 = primes, etc.)

An issue with that is that search engines don't all derive that alias.
To facilitate it, the phrase like A1's "(Formerly M0098 N0035)" could be
extended,
for example to "(Formerly M0098 N0035, also A1)".

Try for yourself, a simple search like: oeis a27
will not likely find A27.

My browser supports shortcuts, like: !oeis A27
which constructs an oeis.org search URL.

-- Ruud