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A262721 and A264011

Please comment on A262721 and remove A264011



I added a formula for A084984 (draft version) and found that your estimation a(n) >> n^1.285 seems not to be true, since a(n)<10^log_6(n-1) for 6^k+1<n<=2*6^k, k>0.

Would you please check this.

Thanks and greetings,

Hieronymus Fischer

The claim is not that but that (using Vinogradov notation). This means that there exist constants k > 0 and N such that, for all n > N, In this case k = 0.1 and N = 0 are permissible; presumably these can be improved. Charles R Greathouse IV 13:24, 31 May 2012 (UTC)

Good articles

I second your nomination of The OEIS and its potential for expansion (bit of background: it started out as a very interesting digression by Dan on Timeline of the OEIS).
As for my page "Is this sequence interesting?", those are my opinions and I suspect even Neil might disagree with some of them.
There is an article I ought to nominate but I can't remember what it is at the moment. I'll get back to you later tonight. Alonso del Arte 23:30, 18 July 2012 (UTC)
I will look for good [and non shadowing] article pages (authored by other editors). — Daniel Forgues 20:19, 20 July 2012 (UTC)
Thanks, Daniel. As I mentioned on the other page I'd be happy to include your articles as well -- though perhaps your modesty forbids self-nomination? Charles R Greathouse IV 20:22, 20 July 2012 (UTC)
Does Classifications of figurate numbers qualify? — Daniel Forgues 20:59, 20 July 2012 (UTC)
Yes! I don't think I'd ever seen that before. Charles R Greathouse IV 22:00, 20 July 2012 (UTC)

"Trapezoidal" numbers

I was going to answer your question in the pink box comments, but here goes instead: a trapezoid can easily be turned into a parallelogram by chopping off a right triangle off one end, flipping it and reattaching it. For example, a trapezoid with top 1 unit, base 9 units, height 4 units, left and right side 5 units each, has an area of 20 square units. This can be turned into a parallelogram with a base of 5 units (and consequently a top of also 5 units). The height is still 4, and the area is still 20 square units. Alonso del Arte 23:11, 2 August 2012 (UTC)
It's not clear to me that this always works. What about a trapezoid of top 1, bottom 5, and sides 3 and 5? (3-4-5 right triangle plus a 3x1 rectangle) Charles R Greathouse IV 23:20, 2 August 2012 (UTC)
What's the height of that trapezoid? Alonso del Arte 00:37, 3 August 2012 (UTC)
3. Charles R Greathouse IV 01:24, 3 August 2012 (UTC)
I will try to draw such a trapezoid and get back to you. Alonso del Arte 11:41, 3 August 2012 (UTC)
I see, that's a right trapezoid (a trapezoid with two right angles). I think I'm going to to have to have to revise the definition of A214602 to exclude those, or add some more terms (if it doesn't turn out that every composite number above a low threshold is a term). Alonso del Arte 20:56, 3 August 2012 (UTC)
Are you sure right trapezoids are the only problem? Charles R Greathouse IV 21:34, 3 August 2012 (UTC)

No, I'm not sure. Having thought about that sequence for so long, it would just be my luck that I have overlooked something even more obvious than right trapezoids. Alonso del Arte 01:17, 4 August 2012 (UTC)

You've certainly thought about it more deeply than I have, but maybe it would be worth taking this to SeqFan? Charles R Greathouse IV 06:52, 4 August 2012 (UTC)
I have put the question to SeqFan. Alonso del Arte 01:51, 5 August 2012 (UTC)

Quadratic Equations in the OEIS

May I add a link to your page

on Category:Recurrence, linear, order 03, (3,-3,1)? — Daniel Forgues 00:39, 16 August 2012 (UTC)

Sure, if you like. Charles R Greathouse IV 00:47, 16 August 2012 (UTC)

Suggestion/Question about computational effort notes

I observed that you recently added some terms to one of my sequences while browsing. If there is not already a place to properly note computational efforts, this might be a good idea where either a very long search is entertained or where the recent character of a sequence leads to a high likelihood of simultaneous search. I have been sitting on two of the terms you submitted for days, and my program is still running (for example); so I could have saved a little computational effort knowing that more effective resources were being employed. If people either of known or not-so-well-known capacities had a good general place or specific one to note publicly that they are starting/stopping searches, it might improve things. Of course, the question is if this already exists to a meaningful degree, and if so where.James G. Merickel 20:55, 19 October 2012 (UTC)

Open problem (Invitation):

Given an integer N>0, and after been found all the first N! terms of A217626, you were asked find either a function or algorithm which counts the number of different "trivial" palindromic patterns that could be built from these terms.

For example:

[1,9,2,9,1] is a "trivial" palindromic pattern.


[2,18,4,18,2] is not trivial, until it is re-written it as: [2,2*9,4,9*2,2]

So the "triviality" of such kind of patterns depends on the prime factorization of their components. Such behavior can not be reproduced by the prime numbers.

I can not spot it yet "the how", but the study of this matter might have deep implications in the number theory. (These patterns teach us how to build odd numbers in a similar way as what described by the Goldbach's Conjecture for the even numbers).

If you decide to face this friendly challenge,

Good Luck!!!

Sincerely, with regards:

R. J. Cano 18:56, 15 December 2012 (UTC)

... ... ... ... ...(Continued)... ... ... ... ...

Dear Charles.

Well, after some time re-thinking these matters, Fortunately I was able to improve a little my published content at A215940, A211869, and A217626, from a Linear Algebra approach.

These were nice times beyond the remaining parts in the day-to-day living of a mortal.

I wish you health, success and good luck. Like Mr. Spoke would say "Live long and prosper".


R. J. Cano, On Jun 26th 2014 19:59 VET.

Unreasonable Editors

Please do something! This sucks!James G. Merickel 05:05, 18 December 2012 (UTC)

I'm on a vacation from the OEIS at the moment, but I'd be happy to discuss the matter with you after the holidays. Charles R Greathouse IV 18:18, 18 December 2012 (UTC)

Well, I usually find my own objections to what I've submitted when somebody objects unreasonably anyway. Not always, though. It is bothersome in the extreme, though, that I can't have my limitation shrunk to only include new sequences, or to at least permit the smallest of changes (addition of single terms or cross-references to my own older sequences, for example) from being counted.James G. Merickel 18:31, 15 February 2013 (UTC)

On another note, I would like to change the titles to my large collection concerning numbers of the form (p^r)*(q^s). If you or some editor could find any 45-minute span M-W 9:30AM to 8PM or Th-Sat 9:30AM to 5PM (Eastern) for editing in all these changes in one go, that would allay part of my issue about the restriction to 3 sequences. Jens Kruse Andersen pointed out to me that the titling is ambiguous.James G. Merickel 19:17, 18 February 2013 (UTC)

Edit at Extensions

Oh yeah, I agree; in many cases I delete where people have taken credit for such things (especially cross-references).
Happy Boxing Day, and happy 13th baktun! Alonso del Arte 23:13, 26 December 2012 (UTC)
It's been a good Boxing Day -- though I didn't know you Americans celebrated it. (I'm a Brit by upbringing if not present location.) Met with family after work for get-together, food, and cheer. Quite a lot of snow, though; has it hit you yet?
Charles R Greathouse IV 03:06, 27 December 2012 (UTC)
Just a few inches, but it is a lot compared to last year. Alonso del Arte 23:47, 27 December 2012 (UTC)

Chase sequences


'Chase sequences': Axxxxxx refers to Ayyyyyy, which refers to Azzzzzz...

Does that allow 'circular chase sequences': Axxxxxx refers to Ayyyyyy, which refers to Azzzzzz... which refers to Axxxxxx? :-) — Daniel Forgues 05:18, 28 December 2012 (UTC)


I wouldn't personally submit this sequence, but since the almost certainly complete sequence {82000} exists here and this one is actually most likely infinite (I mention in the entry currently submitted, as well, because of the coincidental value in the 5th term (1627177)), I think somebody should enter it. I have most of a search through 14000 done. Rule: Primes by truncation on right at last non-zero. James G. Merickel 23:17, 4 March 2013 (UTC)14000 because I am waiting on two PARI/GP runs intending to shut down larger one after its first thousand.James G. Merickel 23:20, 4 March 2013 (UTC)

If you don't want to submit it you might consider something like Chris Caldwell's prime curios. I don't quite understand the definition but I'm sure you could elaborate before sending it his way. Charles R Greathouse IV 00:45, 5 March 2013 (UTC)
I have a backlog there. I submit in multiple places where possible. Sometimes this can be a detriment, as when I end up being too hasty and need to retract (With my current available computer time, this is inevitable). This sequence and the one just removed by a few editors (new policies on short sequences and my non-editor status, it seems) would make actually a rather nice short trio of sorts (if short sequences may be here). I have done a quick run on {82000} (a rediscovery I happened on some while ago at wikipedia prior to re-entering direct association with the mathematical world) and a good comment on its super-astronomical certainty of being single-term is possible beyond what the original editor did. This sequence would be 2-term until at least and probably beyond 6-digit numbers. And the 5th of 6 possible-to-compute terms of what editors erased (Hasler, Arndt and Noe, though Mr. Hasler is really only responsible for the last comment prior to 'can we' by the other 2, where I said I happened to know it belonged (I was only able to edit a very small amount per week for a while and was continually fixing my own work without prompting)) is as mentioned. Better is probably the Prime Puzzles pages. Anyway, could they/you? I suppose, but where are they going and how fast? This is not sane. I'll do something a bit more serious. Happy Rasta Toaster, as I say, the day after Black Saturday.James G. Merickel 00:17, 1 April 2013 (UTC)
The rule on short sequences has been, for a long time, that 3 terms are required and 3 lines of terms are recommended. Sequences with fewer than 4 terms should have keyword:bref.
So if your sequences have 3 terms you can submit them (but add the keyword) and if they have 4 or more you can submit them without bref. If you have only one or two then either submit them to Prime Curios or the like, or else post them to SeqFan to see if someone else can extend them. (On rare occasion these sequences are approved but this doesn't happen at all most months.)
I'm not sure what incident you're talking about but you can still see content that has been removed by editors. For example, A218505 was recently deleted because it duplicated an existing sequence, but if you look at [1] you can see the sequence as submitted ("Decimal expansion of 6/Pi^2") and all its information. Generally, go to the affected sequence, hit "history", then choose "older changes" until you're at the right part. So whatever terms you had submitted earlier should be retrievable.
I do not know to what "Anyway, could they/you? I suppose, but where are they going and how fast? This is not sane." refers.
Charles R Greathouse IV 02:16, 1 April 2013 (UTC)
Don't worry about it (as far as last is concerned). I said it was not sane anyway. Feel free to count the particular sentence and those immediately preceding. I will eventually, probably, figure out what was deleted. If not, I have more anyway.James G. Merickel 15:22, 6 April 2013 (UTC)

Seq. o' th' Day for April 19

Charles, could you look over Template:Sequence of the Day for April 19 and possibly approve it? The first draft was entered by Peter Luschny and I've reviewed it. Alonso del Arte 18:19, 5 April 2013 (UTC)

You're the one who proved Peter's conjecture? In that case maybe someone other than you should be the one to approve. In the meantime, I will add a line to the effect of "Charles Greathouse proved it." Alonso del Arte 01:33, 7 April 2013 (UTC)
You can see my reluctance to either edit or approve (though I will approve, if needed, as long as someone else reviews it).
If I was writing the entry I'd just say it can be computed by ... rather than giving attribution. It's not a hard theorem. But do as you wish.
Charles R Greathouse IV 02:13, 7 April 2013 (UTC)
I will ask Tony. But first I will ask Peter Luschny if he'd rather write up the theorem to replace the line I just added. Alonso del Arte 02:17, 7 April 2013 (UTC)
Sounds good! Charles R Greathouse IV 02:35, 7 April 2013 (UTC)


At about 16:00 (I don't know the name of the hot Asian girl so I'll just call her "Shan" here):

Charlie: Maybe it's a modular polynomial, which can be restated as a string of numbers.

23 5 18 23 1 20 9 14 7 6 15 18 21

Charlie: I don't want to overthink this, but why this string of numbers?

Shan: 23 5 18 is W E R in Sloane's Encyclopedia of Integer Sequences. Maybe it's [a] simple alphabetic cypher.


It turns out that in showing off his FBI work in an ongoing case, Charlie has walked his brother right into an ambush. Shan might be referring to A002252. Alonso del Arte 19:53, 28 April 2013 (UTC) P.S. I don't feel like watching the rest of the episode, but I suppose there are other things I can use the Amazon Prime free trial for. This particular episode of NUMB3RS is also available on YouTube but I think it should get pulled from there.

Hmm, not much to say then. I think "Shan" is Prof. Ramanujan; I've seen some episodes (though not this one). Thanks for looking into it! Charles R Greathouse IV 19:57, 28 April 2013 (UTC)
She looks kind of Chinese, whereas I'm assuming Ramanujan is more Indian. But yeah, it doesn't seem like much, like the writers couldn't figure out a better way to work the OEIS into the script. Alonso del Arte 23:02, 28 April 2013 (UTC)


I noted your remark at the above before its a(9)=9221 was published. Of course, the verifications you are speaking of concern primes stemming from values in [540,9220] (There is an ABSENCE for 9221 through base 20), but I am sure I could do a lot more and better with any number of better pieces of software, however good PARI is.James G. Merickel 14:03, 3 May 2013 (UTC)

I'm a big fan of PARI/GP, and indeed I contribute code to that project. It's terrifically fast for many things, often the fastest program out there. But it happens that for factorizations above 60 digits and primality testing above, say, a thousand digits is lacking. In a pinch it can be used but other software does it better.
Now PFGW isn't a fair comparison here, since it uses a weak Miller-Rabin test compared to PARI's much stronger BPSW test. But for testing values this is much better and at the sizes you're using, at least two orders of magnitude faster. At the least it's worthwhile to test values with PFGW before testing them in another program like PARI to see if they're really prime. This is what PFGW is designed for, after all!
For the dual problem of factorization I would say the same thing, but recommend yafu instead.
You can do whatever you like, of course, but I hate to see you spend months on what could be done in a day or two.
Charles R Greathouse IV 14:27, 3 May 2013 (UTC)

Hmmm. yafu is a new one to me. Anyway, thx for advice. I will be downloading a good deal of stuff as soon as I can do so without losing a lot of stuff to the inevitable Microsoft updating process.James G. Merickel 19:08, 4 May 2013 (UTC)

Your comment on the tetration-talk-page

Dear Charles -

I've written a remark/an answer at the tetration-talk page addressing your complaint about tetra-roots. (This note is just to inform you here)

Gottfried --Gottfried Helms 15:21, 16 May 2013 (UTC)

Dear Charles: I've uploaded a first version/first part of a new version of an article. I'll use that version later on my own site, but have it a bit focused for the OEIS/Seqfan user. I've uploaded in an editable format (winword) and if you find this worth in style and approach then you might even add improvements directly in the text and send me your ideas (or just extract text for the OEIS/Tetration-article). See

Gottfried --Gottfried Helms 12:00, 17 May 2013 (UTC)

That looks good. Just to keep licensing straight, could I have you put that in the article? (I'd be happy to tweak the formatting as needed.) Charles R Greathouse IV 14:24, 17 May 2013 (UTC)
You're welcome. It's an offer to the OEIS-community: just do with it what you want. I'm also going to improve the text because I want to have it for my own homepage, too (Likely I'll only reduce the strong OEIS-focus in the version for my homepage). Because the whole thing will get some length and weight you possibly want to ask for some specific sub-question which I might answer/comment on in advance (sometimes such requests even help to organize the draft-material "on-demand", so don't mind asking) P.s. I've also done some minor updates in the draft. Newest version is of about 19:00 in my time-zone.
Gottfried --Gottfried Helms 18:54, 17 May 2013 (UTC)
Ahh, p.s., I didn't got aware that you asked me to insert the text into the article. Well, I don't like it to try this myself. Since I've got now familiar with MathJax the wiki-math has become difficult for me to re-learn/to re-establish. But even more difficult is it for me how to insert that text in the current version of the wiki-article: this has also much text and much and fixed structure and I don't want to spoil Daniel's enhtusiasm and invested sweat with this. So I beg your and Daniel's pardon, and that someone else instead of mine would do that.
Second p.s.: References, naming of important researchers and examples are currently in a very narrative and cursory state, maybe I missed important things here or expressed causality in the wrong direction. It seems also that I erred with the Mandelbrot-iteration, as it lightens up to me now, that it it iterated raising-to-powers and not iterated exponentiation and I've to insert a correct example instead. So if you find some errors, don't mind to inform me, also I'll take the next days to improve the text in that regard.
Gottfried --Gottfried Helms 19:36, 17 May 2013 (UTC)
OK, I'll add the text once you have it ready, maybe Monday. Charles R Greathouse IV 20:41, 17 May 2013 (UTC)

Reference to new sequences I will not be free to submit

I'm taking a breather from things and, as you know, I have limited online space. If you would not mind, the data for the two missing sequences attached to the one I have in edit could use submission at this point, and any edits of the third you and/or your chosen proxy might wish to include would be appreciated (with myself on as editor), if that is comprehensible and possible. What's wanted should be clear from the final section of my talk and the sequence in edit. Thanks.

In addition, as an unrelated note, I have now that the amazing sequence with first k concatenated being product of k distinct primes has been resolved as having no solution for k=13, and through about k=17 is probably doable if anybody wants to waste so much computer power. Base ten hits a sweet spot with this, too, in that .. through (not quite yet) base 500000 there is some solution for k<7. For base 10, it's probably not hard at all to improve the quasi-technical remark I've made about finiteness to be much nicer. Edit regarding this is up to you or a reader here, and I expect to touch it up eventually if it's not done.

A separate unrelated note is that I would appreciate if my sequences from a large grouping that caused me some problem in edit were to have the ambiguity in title removed for me. Wording replaced by algebraic is an easy solution, but I have not been permitted really to do so when I wished to pay attention (I could theoretically have fit this in myself despite my technical limits, but it hasn't been a constantly-thought-of matter). Okay, some more thanks. And adieu.James G. Merickel 04:05, 20 August 2013 (UTC)

I took a quick look at the three sequences in your queue and made some changes as appropriate. I don't tend to find base sequences interesting, though, especially those relating to decimal concatenation, so I'm not the best resource.
I don't understand your final paragraph.
Charles R Greathouse IV 20:56, 20 August 2013 (UTC)
I had a large number of sequences approved concerning numbers of the form (p^a)*(q^b), and because I titled them using verbiage instead of using such a formula there is ambiguity in the meaning that only looking further into the sequences can resolve. This was pointed out to me by Jens Kruse Andersen, and I'm really not around much to fix such a thing if people other than the author myself and Mr. Andersen agree the change is needed.James G. Merickel 18:31, 22 August 2013 (UTC)
Thank you for helping to get through A227775.James G. Merickel 19:52, 22 August 2013 (UTC)

October 30, 1775

I'm reading a book on the history of math in America in the 18th Century. I'll give you a full biblio later. Alonso del Arte 00:56, 23 August 2013 (UTC)
Curiously, I see that [2] gives the date of "On the usefulness of mathematics" as October 30, 1735; I wonder which is correct? In any case I can't figure out how to find the text of such an early paper, maybe I should ask my uni librarians.
Charles R Greathouse IV 02:24, 23 August 2013 (UTC)
I think I screwed up on the year.

"Of the great public leaders who did much for the encouragement of mathematics in the New World ... two stand out as especially prominent. The first of these is Benjamin Franklin ... His essay "On the usefulness of mathematics" for example, although too elementary to demand our attention today, meant a great deal at the time it was written."

Footnote 6 reads "Pennsylvania Gazette, Oct. 30, 1735." The paragraph starts on page 57 and ends on page 58 of David Eugene Smith & Jekuthiel Ginsburg, A History of Mathematics in America Before 1900. New York: Arno Press (1980). Alonso del Arte 16:34, 23 August 2013 (UTC)


You added a program to this sequence and I asked if it did something that seemed important, and I have not heard back since. This was 3 weeks ago, and I have continually submitted the sequence, edited it a little, and re-submitted in the interim, because, primarily, of the fact it's still not approved (while also some edits were too quickly done). If your program is satisfactory (I don't know exactly what it does and have not been inclined to find out yet), I don't imagine doing anything else to change the program. If there is something wrong with your program that you want to change or if you'd rather I dig out my program and substitute it--efficient but written in a much different style, please let me know. Otherwise, I don't know of any reason it would still be sitting there other than my impatience to edit a basically complete COMMENTS section repeatedly.James G. Merickel 16:35, 24 September 2013 (UTC)

I've been busy -- attending to personal matters (death in the family). Hopefully the other editors can help. Otherwise I'll look at it as I work through my backlog. Charles R Greathouse IV 17:15, 24 September 2013 (UTC)

Okay, thank you for the explanation, and I offer condolences.James G. Merickel 11:51, 25 September 2013 (UTC)

Dr. Greathouse, the program you have in this sequence does nothing quickly. If there's a simple (or not-so-simple) fix you can make, it looks better than what I would need to submit in its stead. I'd like to re-submit this sequence by Thursday if possible. Thank you if you can find the time. I will take license and at least erase your program then if I don't get a reply.James G. Merickel 00:33, 8 October 2013 (UTC)

You should not erase a program just because it is slow. I added the program because it gives an unambiguous definition of the sequence, not to allow rapid computations. At some point I think I wrote—or began to write?—a fast program, but it does not resemble that script. If I add it it will be as a link since a fast version would likely have a large code footprint.
Charles R Greathouse IV 01:37, 8 October 2013 (UTC)

Not slow. It returns the standard prompt immediately. James G. Merickel 13:56, 8 October 2013 (UTC)

The script defines a function a(n) which, given n, returns the n-th term of the sequence. Charles R Greathouse IV 14:01, 8 October 2013 (UTC)

Okay, I will just chalk this up to my ignorance of programming. What you're saying is that there should be an n-value included in the program for each n separately, and that the program does work (or something like that). I will submit again as is, then. Still, not getting any input on why not being approved, explaining why I tried to run your program at all.James G. Merickel 17:16, 8 October 2013 (UTC)

I don't know what you mean when you write "there should be an n-value included in the program for each n separately". My program merely defines a function named a; once defined you can use it however you desire. For example, you could type a(7) to get the 7-th value of the sequence, or vector(100,n,a(n)) to get the first hundred values, or n->my(m);while(a(m++)<n,); a(m)==n to define a function which tests (inefficiently!) whether a given number is a member of the sequence. These three would apply to any sequence function a (with certain caveats, e.g. the last one assumes the sequence is monotonic).
Charles R Greathouse IV 18:16, 8 October 2013 (UTC)

I will try to see what you mean at home. My practice has not been to include any predefined functions in what I could do at the standard prompt. Each program (so far) I have done has been stand-alone without any thought of being able to expect that at the normal PARI prompt I could compute anything that was not essentially on the line, using the curly brackets for anything long. I've been aware this wasn't necessarily the way things had to be, but have seen no (urgent) reason to make any advance beyond this state of affairs. At any rate, if not your program then I am unaware of why the sequence isn't going through. James G. Merickel 12:49, 9 October 2013 (UTC)

I prefer programs which define programs to programs which merely print output to the screen, since you can use the former to do the latter but not vice-versa. My general thoughts on programs can be seen here: User:Charles R Greathouse IV/Programs, and you're welcome to give feedback if you feel the need, either here or on User Talk:Charles R Greathouse IV/Programs. Charles R Greathouse IV 13:34, 9 October 2013 (UTC)

Okay. Thank you. I will take a look at that sometime this week. I really should be better at this, since my father worked his whole working life (starting at Colombia Records and ending at Ford Motor Company) as a Computer Systems Analyst (and I myself was actually the first psychiatric in-patient nationwide allowed to have a computer, though hardly much of a bragging point). I've really only had one pretty elementary course at Temple in C/C++ programming, plus a Numerical Analysis course employing Matlab, though, aside from my own independent efforts. And have always much preferred math that a computer is still mostly useless with (despite current appearances, doing the stuff I am here).James G. Merickel 13:50, 9 October 2013 (UTC)

I apologize for not looking at that until now. I see it's recently added this year and will consider.James G. Merickel 00:42, 23 October 2013 (UTC)

No worries -- we have no deadlines here. :)
It's both a collection of current OEIS practices and suggestions for further improvements: best practices, standardizing notation, etc. I hope you found/find it useful.
Charles R Greathouse IV 02:59, 23 October 2013 (UTC)


Likely very simple but I cannot follow how your Pari code there relates to the seq entries.--Bill McEachen 01:23, 11 November 2013 (UTC)

It defines a function is() which is the indicator function for the sequence.
So is(11) returns 1 (true) since 11 is in the sequence, but is(13) is 0 (false) since 13 is not in the sequence.
All my programs with the name is are predicates/indicator functions, see User:Charles R Greathouse IV/Programs#Naming conventions.
Charles R Greathouse IV 01:35, 11 November 2013 (UTC)


From the definition of this sequence no term should divide any other, yet there are many instances of this in the terms provided (e.g., 168*3=504). So it seems something needs to be changed. - Eric M. Schmidt 17:03, 19 November 2013 (UTC)

This seems to be a serious issue. I'm looking into it. Charles R Greathouse IV 17:57, 19 November 2013 (UTC)

Riordan arrays and index

Hi Charles, in your Consistency page you mention the search for Riordan arrays, presumably to add missing index links. I think it better to first complete this List of Riordan arrays and use it for placing even more specific links to subgroups. Also I notice that changes in the index were not visible (approved) for a long time now - maybe A-numbers there are not so important, but I think the other changes are. Can you help/approve there, please? --Ralf Stephan 09:19, 30 December 2013 (UTC)

Your list is very nice!
I'll take care of the Index, thanks for the heads-up.
Charles R Greathouse IV 13:42, 30 December 2013 (UTC)
OK, I've approved each of the pages on the index (along with your page). Charles R Greathouse IV 15:25, 30 December 2013 (UTC)
Many thanks! --Ralf Stephan 16:06, 30 December 2013 (UTC)

OK Charles, that list is now finished, and I have removed the A-numbers from the index page. Please eventually approve both too, but there's no hurry. --Ralf Stephan 16:48, 3 January 2014 (UTC)

Ralf, it looks great. I approved both and sent a note to Dr. Sloane apprising him of the page (since he's usually the one taking care of the Index).
You may also consider -- but only if you want, and in any case there's no hurry as you say -- writing an article Riordan arrays, especially since Wikipedia's is lacking and MathWorld doesn't seem to have one at all.
Charles R Greathouse IV 18:34, 3 January 2014 (UTC)

You asked (?)

You asked me if my new titles on some badly titled sequences should be clear that exponent 0 is excluded, and I've settled on just the word 'factoring' and it's been quite a while I've had 5 sequences in edit. So, I have new data, new sequences, and the completion of that re-titling project on hold right now because of my limit. Any chance these could be moved along? I expected the simple change to result in quick approval, but have gotten silence since your question and wonder why. I understand you must be busy, but you're the one who engaged me on what may or may not have been a triviality (I suppose that canonical-form factorization, which should be entirely clear with the single word, should have been explicit; and it was something of a slip to omit words ('of the form') I had been using to that point in the re-titling).James G. Merickel 20:38, 14 January 2014 (UTC)

Bad timing, sorry! I've been away at the 2014 JMM for the last week, and I'm just now catching up on things. Charles R Greathouse IV 15:31, 20 January 2014 (UTC)

It's okay, and somebody helped not long after this complaint (so thank you if you requested that).James G. Merickel 20:57, 10 February 2014 (UTC)

If you happen to have time...

Dr. Greathouse, I have some sequences in edit that might raise eyebrows because of some premature cross-referencing, but this is partly because the server has spoken on one that refers to another that had been in edit for a while. If you yourself happen to have any time to take a look at them it would probably be helpful. If too busy, no problem. I'll just respond to what other editors throw at me. Thank you.James G. Merickel 05:25, 18 February 2014 (UTC)

Thanks for your help there. I've aborted that heuristic computation, removed from submission (for now) A232657, and edited A152397 to be self-contained; because the heuristic computation was going to show an over 20% chance of missing terms for A232657. I have considerable resources now working to improve things and will be re-editing when results are in.James G. Merickel 18:10, 19 February 2014 (UTC)

I'm covering the entire set of stem values giving one prime of 4000 or fewer digits, and running a heuristic computation on the remainder (still just uding PARI, so it will take a little while before I can re-submit A232657).James G. Merickel 17:12, 25 February 2014 (UTC)

I don't know what you mean by your pink-box comment "though I need to go back and insert trial-division code to speed things up a bit (IS THERE A TABLE ON THIS FOR PARI's ispseudoprime?)". Charles R Greathouse IV 18:17, 25 February 2014 (UTC)

For very large numbers I've found some speed-up by doing checks on small primes before putting numbers through ispseudoprime (at least on the version currently installed). The question (/recommendation?) was on what size numbers should be checked through which primes to get the optimal expected speed-up. BTW, I see Sloane published A232657 when I thought it premature. I don't think it was placed in submission accidentally. Does this mean more work had been done by others or that it's better to have it accepted as is than waiting in limbo, with the understanding a better edit will eventually be coming along (if you know)?James G. Merickel 18:20, 28 February 2014 (UTC)

Well, ispseudoprime does trial division up to 101, as you can see here [3]. Next it does a 2-strong probable prime test, then finally a Lucas test. To a first approximation all composites are caught by the first two tests, so additional trial division only saves the cost of a prp test. You could test this directly by using ispseudoprime(..., 1) which should take an amount of time similar to the time for the 2-strong prp test. So find an odd number of the size you're interested in and see how long a prp test takes:
for(i=1,1000,ispseudoprime(N,1)) \\ divide results by 1000
(use ## to see the time taken if you're not already in # mode). Say the time is 10 milliseconds. Now see how long it takes to divide by your prime, say p = 101:
for(i=1,100000,N%101) \\ divide results by 100000
say 0.02 milliseconds. Then the test is probably worthwhile if p times the time for a division is less than the time needed for a 2-strong prp test. Keep increasing the size of the primes until you get equality. This is a slight overshoot, since now your prime tests are in the 'wrong' order (2..101 in pspseudoprime), but probably not too bad.
You can improve on it by taking the product of these primes and saving it as G, then computing gcd(N, G)>1. The advantage of incremental factoring is gone but the overall time required is greatly reduced (factor of 10 in my quick test).
As for A232657, I won't speculate on the reasons for approval but you can continue to work on it.
Charles R Greathouse IV 18:55, 28 February 2014 (UTC)

Okay. Thanks. I guess the knowledge of the small trial division means I should consider doing something strange like rmoving those small primes from the prime table too, though it's probably a pretty small relative amount of time.James G. Merickel 19:00, 28 February 2014 (UTC)

Don't add primes below 2^24 to the prime table. - Charles R Greathouse IV 21:20, 28 February 2014 (UTC)

I can't think of why I would. I just meant that with the pre-testing there is duplication through 101 (but they should should be checked before the larger primes); so unless I substituted my own probable-prime test--requiring constant justification, removing those through 101 after the pre-test and before ispseudoprime might work to cut time a little more (based on what I know). The only thing I've done so far with the prime table is to change the default to larger (up to 2^32).James G. Merickel 00:46, 4 March 2014 (UTC)

I think we're talking about different prime tables. You're talking about default(primelimit), I think, and I'm talking about addprimes().
For prime testing, try something like this:
  if(n<1369, return(n>1));
  if(gcd(n,B0)>1, return(n<1229));
  if(gcd(n,B1)>1, return(n<7927));
  if(gcd(n,B2)>1, return(n<48619));
which does a series of quick tests (the first 5000 primes) before passing the number off to ispseudoprime. Of course whether this is faster or slower depends on how many Bs you use, what value they hold, and what numbers you test. I get a 4x speedup around 10^40, though, so that's not bad.
Charles R Greathouse IV 01:26, 4 March 2014 (UTC)

Well, I was talking about both, but actually about removeprimes more than addprimes (saying that ispseudoprime is currently duplicating my pre-search). The idea of substituting gcd of products of primes adds a layer of complexity to the potential ideal program, one I had vaguely considered; but (over the long run) the best thing would be if a later version of PARI includes whatever size-optimized code can be worked out. I suppose when I have time I will test how much multiplying out primes and testing them en masse helps; but the main thing is to avoid running ispseudoprime when a small(ish) prime is a factor, and right now I'm just testing through 10^7 through 10^9 depending on the number of digits (I think using gcd for products is probably a significant second way to speed things up I should be using, so thanks). Btw, I've just recently installed the newest available version to one of my computers, and I've noted that the primepi function will go beyond the default (an improvement) but appears to be spending enough time to be finding all of the primes, which is far from optimal. As I'm not a developer, I can hardly complain about these weaknesses, but they still do exist.James G. Merickel 20:56, 9 March 2014 (UTC)

I don't know what you're trying to do with removeprimes().
I don't think adding the extra tests to ispseudoprime() would be a good idea, at least not directly. It might make the function faster on composite inputs but it would slow it down on prime inputs, and it's not clear what the tradeoff should be. Maybe they could add a flag, though, for the two behaviors.
PARI doesn't have a reasonable version of primepi() implemented; the current one just steps through primes (though it does at least skip ahead a bit for small inputs). But coding advanced algorithms here is tricky.
Charles R Greathouse IV 02:36, 10 March 2014 (UTC)

Not actually using either addprimes or removeprimes, like most of PARI. But I was saying that testing through 101 must be done in my own test.

I started with product through 10^8 for my purposes (alternative to your suggestion), and it finally started spewing in one window today. Thanks again for that. As for ispseudoprime, I did need to use maximal allocatemem to get the preceding, so your probably right that it must be tailored by the user (essentially).

The reason I am using through 10^8 is that is close to the max primorial allowed, and I figure just one really bad use of the division algorithm (in gcd) and am testing a large number of gigantics. The program has a preceding test through the first prime to multiply heuristic probability by 20 (70000s, something), so few that can avoid going to ispseudoprime need to use the big test.James G. Merickel 13:58, 12 March 2014 (UTC)

Probably that's too large. You catch only 1/7 more primes going up to 1e8 than 1e7, but spend at least 3 times longer, assuming you have GMP ([4]). But actually it should be worse, since the number is too large to fit in L1. So the extra time is probably not worthwhile unless the numbers are quite large -- better to get to ispseudoprime sooner. (Certainly I recommend testing the two against each other.) Charles R Greathouse IV 15:25, 12 March 2014 (UTC)

Did you respond to me overly quickly or with much thought? I just wonder, because it's not clear that you know what exactly it is I'm doing and wouldn't want to spend time making a bad adjustment. You may have full comprehension of what it is I've said. At any rate, now that I have the newer version of PARI there is not much excuse to not try to settle this pretty scientifically. Seems like good (near perfect for PARI) programming should be possible. A saved collection of different-sized primorials would be one way to improve things to nearly ideal; but then a lot of system dependency would come into play, right? (Just not that much of a geek to know for sure on this last technical point/question)James G. Merickel 12:32, 19 March 2014 (UTC)

Well, I had to look up all of my figures, so not overquick.
Probably there's no need to cache primorials; generating them is pretty fast with binary splitting. In my implementation I do store the wordsize primorials (up to 28 or 52 on 32- or 64-bit, respectively) but beyond that I just compute them in a straightforward way.
Charles R Greathouse IV 14:35, 19 March 2014 (UTC)

Well, I may need to ask you to define terms at some point, but this is not a major concern of mine right now (and if it's not arcane I can find it).James G. Merickel 17:22, 19 March 2014 (UTC) Translation: Don't put yourself out with details & I have yet to read much of the first thing you linked to.

You know, oddly enough the primorial never came up in my studies until I re-started with mathematical curiosities. That's a summer at University of Chicago number theory in hs, and through to 2nd-year graduate level number theory courses. I still have not read how primorials are theoretically best calculated, but it's now clear to me that multiplication is NOT the way to do it. Obviously, using the Stirling approximation to the factorial and inclusion-exclusion is faster, but I hadn't given it any thought until recently.James G. Merickel 15:37, 19 April 2014 (UTC)

A simple and efficient method would be binary splitting: generate the primes up to n, cut the list in half, and find the product of each half recursively. Once the size is less than, say, 8, you can multiply normally. Charles R Greathouse IV 00:35, 20 April 2014 (UTC)

Sounds like a use of parallel processing. I don't see the difference in terms of number of multiplications. Each prime must be generated, too, though that can be straight from pre-computation for vast numbers of purposes. Isn't what you suggest making one multiplication per prime? I don't know the cost per multiplication based upon sizes of numbers, though, and this is probably where your claim of efficiency is directed.James G. Merickel 20:36, 20 April 2014 (UTC)

Same number of multiplications, but vastly faster. If you start from the beginning and multiply upward you get a very large number times a small number many times over, and this is slow. If you multiply as I indicated (only on a single core machine, no parallelism) you're multiplying numbers of about the same size and this is much faster. You don't need to use big numbers at all until the last few steps.
For comparison, I just computed (10^7)# with both methods. Bottom-up multiplication took 4 minutes, 56.5 seconds. Binary splitting took 0.454 seconds, or 650 times faster. (10^8)# might be tens of thousand of times faster with binary splitting but I haven't the patience to try -- it would take months for the bottom-up calculation.
Charles R Greathouse IV 23:31, 20 April 2014 (UTC)

Okay, that does confirm the reason to prefer binary splitting. I have it taking days, however, bottom up for (10^8)#, and I wouldn't know why other than system-dependency issues causing problems more on your end than mine, which would be a surprise.

As for my own idea (using the Stirling approximation), I should work out the details before pronouncing upon its speed. It's a lot of terms for, say, a billion factorial to the digit.

Thanks for your aid, and I will TRY to figure out what all else you've referred me to, and hope to do that sooner rather than later again.James G. Merickel 19:38, 21 April 2014 (UTC)

OEIS database

Can you point me to where I can see discussion about the actual OEIS database? By this I mean what is it coded in, does it use SQL, Access, or  ??? This would be a good subject to have a blurp on in this wiki I would offer....--Bill McEachen 14:43, 28 March 2014 (UTC)

We're running sqlite as our database, with a lot of custom scripting on top of that. I don't know of any discussion of this on the wiki or elsewhere. Charles R Greathouse IV 15:38, 28 March 2014 (UTC)

Regarding sequence you edited in 2010 (A080695)

I will be referring--in my changed A239412, which originally had to do with island-size ranks(!)--to the natural analogue of home primes (I suggest the term 'away numbers', for no phenomenal reason I can recall other than merging capital 'H' and the '^' symbol suggests capital 'A', etc.), where this sequence is iteration 1 in the process. If you or anybody else wishes to edit this sequence ({1,2,3,4,5,23,7,8,9,25,11,43,13,27,1129,16,17,29,19,36389,37,211,23,83,25,3251,27,47,29,547,31,32,311,31397,...}) in, I have no desire to claim priority and it would speed my own editing not to have to do it myself.James G. Merickel 20:01, 24 April 2014 (UTC)

I erased one sequence and have started editing this suggested one in myself.James G. Merickel 20:17, 27 April 2014 (UTC)

Submitted as A239448.James G. Merickel 20:58, 28 April 2014 (UTC)

Extension request


I have exhausted my 7 "active edits" and read in an answer of yours in the OEIS_Help_Page that, in special cases, requests are considered to increase editing limits. I don't know how these requests can be made, but let me try through your talk page.

I plan to submit 4 interrelated sequences: 2 are already recorded, and 2 extra slots are needed. This is, I can only submit those if I am granted temporarily 9 instead of 7 "active edits". It is not my intention, however, to abuse of the editors' work, so I'll wait if necessary.

Álvar Ibeas 16:15, 7 November 2014 (UTC)

Drop In Edits

I have had some submissions deleted without personal notice. Is there a way to track this? Specifically, while trying to generate the wherewithal to complete some of my sequences here (in addition to other things), I'm not sure why my count of in-editing plus a stable count of changing perhaps but approved sequences has declined. It may be that I was simply taken off authorship, as I have not looked into this; but I did receive no notice by email (A specified collection of sequences was worked out, but perhaps it was decided to shift all credit to one who either 1) showed priority outside the purview of the OEIS or 2) gave me mention for the initiation; and, then again, it may be that 3) the work was simply deleted entirely with no notice or 4) something even worse happened with a removal of other sequences and a high-jacking but approval of what I've done recently OR one with my password said go ahead and erase). Things should be easy to clarify at the top of 'the OEIS editing party', but I'm not sure whether or not you want to handle this question yourself. Please let me know.James G. Merickel 22:34, 24 November 2014 (UTC)

To update, I do find that Sloane published, and may possibly be wrong about the number that were approved but don't believe so (i.e., either my memory is poor on the number already approved or the number approved equals the number deleted without notice. At any rate, you may strike the 'no email' matter (This was mistaken, and there may even be no issue whatsoever other than a slightly poor memory (and likewise slightly pessimistic expectations)).James G. Merickel 22:44, 24 November 2014 (UTC)

You should get an email whenever the status of one of the sequences you're currently editing is modified. You can always go back through your history (click your name in the top-right corner of the screen when logged in) in case you missed something.
If you think that one of your submissions was rejected but you deleted the corresponding email, you can always check at
where it appears that none of your sequences have been rejected since May 2013.
Charles R Greathouse IV 00:18, 25 November 2014 (UTC)


ensure that when I online next there is no demand placed on what I edit. I only came out primarily to do some necessary things regarding my banking situation. It's a long walk, and it's cold, and I am quite disorganized now. But I do only have one pending and I was not able to say anything about that and wanted to update an older submission of mine. Thank you editors.James G. Merickel 03:58, 11 December 2014 (UTC)

Draft (A257077)

Hi, Professor Charles!

I've seen that you edited this Draft and left status as "Editing". Do you have more changes to do?

Thanks for your code.


Hi Carlos! I actually intended to finish up with the sequence yesterday but I was otherwise occupied. I finished my edits just now and approved the sequence. Charles R Greathouse IV 18:49, 23 April 2015 (UTC)

Draft (A258328)

Hi, Professor Charles!

I had started to draft this sequence, but I noticed there were errors and I've stopped editing it. I would like to release the number for other people. Could you help me please?

Thank you.


Doesn't one need some place to create and send a b-file from if one wants to add it? I can't make out how to do this from the library. I also don't understand your fellow editors' objections to my sequence currently in edit. Two references are to terms that would be invisible if reduced to three lines, and what is 'uniformity' and how important?! Once I explain that I think all the terms are called for, to enough of a degree in my opinion, it seems the editors should take on why the sequence should be reduced with more reason.James G. Merickel 20:43, 4 June 2015 (UTC) And, by the way, I noted that I did not add a program because one was not used. The tool at the Prime Pages is faster. No objection, of course, to your having added one, but I didn't think it important for me to do so.James G. Merickel 20:45, 4 June 2015 (UTC)

On A258433, I agree with Joerg and the others that the extra terms belong in a b-file rather than in the sequence entry. (There are times that we include lots of terms in a sequence entry, but I don't think this is one of them.) Generally speaking, it makes an entry harder to read -- and in any case tools that need lots of terms should all be geared for reading b-files anyway. It's fine to refer to terms which are only in the b-file in the comments -- in fact, it's not rare to refer to terms beyond even the b-file.
For computing large terms, I think the state of the art is primecount. Perhaps if I have time I'll find a few terms with it.
Charles R Greathouse IV 17:09, 5 June 2015 (UTC)
PARI/GP has capacity for calls to c++ routines that will allow me to use the material at your link, in a larger PARI program (once that is downloaded), right? By the way, the sequence of mine you recently commented (always put program if there is one) is done.James G. Merickel 00:48, 1 July 2015 (UTC)

I was getting ready to concede on this. It's obviously not all that important. Thanks for the b-file. I guess to do that myself I need to have webspace, like a blog, somewhere?James G. Merickel 22:45, 5 June 2015 (UTC)

I addressed your most recent question immediately. Cross-referenced wrong sequence. Fixed.James G. Merickel 23:16, 11 July 2015 (UTC) The basic problem is I am a pedestrian with only cellphone internet service of my own. Was a kind of misquote of other sequences in the group because both were mentioned in the 1st sentence of the earlier one. That one was the one offset by 1 from the particular sequence of mine, and the correct one is supersequence of the bunch.James G. Merickel 23:25, 11 July 2015 (UTC) Thank you for the b-file addition to A259350 and approval of the sequence. Having it accepted as it was, without doing anything else with the program, was my preference. I can see the point of the other editors' opinion on it, so I hope it wasn't confusion over the nature of change preferred and assistance needed by me that got it through.James G. Merickel 15:16, 13 July 2015 (UTC)

Usually it's best to upload long programs and reference them in the program section:
(PARI) See Merickel link.
This allows better formatting, long comments, and no disruption of the entry's flow. But there's a gray area where both are OK.
Charles R Greathouse IV 17:13, 13 July 2015 (UTC)

Yes, my plan for 8 primes is to have a go-to link that will suffice in terms of full commenting for both the just-approved and the 9-primes case (with no program planned shown for that, but an adequate brief description of how to get the right program from the linked one). I don't know what exactly the hold-up now is for A259349, I should say. It could be punitive (about cluttering the wiki with a dispute over moot capitalization and period with an editor who too long went without mentioning a source), an unwritten need for me to change something (and I now may have too few terms shown, but not too many), or merely an oversight by you because you are unaware others are taking their time. I can see also the possibility written in comments there that you yourself are engaged in debugging a fast program to put a b-file and new comment there yourself. I had no plans to put more than could be in the sequences proper, and for days to a week it wouldn't now even be possible (and commenting the addition would look stranger from me than another contributor as well, with comparison becoming internal rather than across the two sequences (a hassle of sorts in rewording things that a second contributor wouldn't need to contemplate)).James G. Merickel 21:46, 13 July 2015 (UTC) If having terms up and then removing them without putting a b-file is at issue, I can't get around to do much about it. This isn't a state-of-the-art phone either. I can see more easily editing in a new program and b-file in a month than a b-file for a handful of terms in the next few days.James G. Merickel 21:54, 13 July 2015 (UTC) Perhaps it is odd to submit with a simple program that works in under a week when it is known an improvement is essentially available to print terms as quickly as the print command can. It tends to make the two sequences a possibly unwanted lesson on efficient programming. But it's the order in which results came out for me, looking for minor tweaks to the weak program and finding larger improvements instead.James G. Merickel 22:23, 13 July 2015 (UTC)

A087155 (Title bad: 1 digit=pal.)

Currently editing correction of this sequence (title wrong), and think my current edit is pretty much best. If you could please render a verdict so I can clear one of the three at least, I'd appreciate it because the two editors who have appeared there didn't respond as though they comprehended. You'll see in the pinkboxes that I had a simpler change than the current one or will pretty much accept a 'Who cares if it is a little imprecise?!'. Just seems the best (most reasonable of the three) to move along on (either with another change and rapid acceptance, or no change and the same).James G. Merickel 01:44, 26 July 2015 (UTC)

Primarily mentioning this one because it's the one that I might need to change further, so if you don't feel put upon by it I don't think further immediate changes to the other two are needed (though for one my comments dealing with later unseen terms is really hard reading and I plan to link an article to clear it up as soon as I complete it).James G. Merickel 02:00, 26 July 2015 (UTC)

Since these other two were brought up, I'll just say that A152396's changes are no more than a better title (a 2nd and final time) with one matching change to comments; and A171775's are first-and-foremost a fix of comments from when I didn't understand that a(1) only exists if the offset is under 2, and then a change to offset 1 with a trivial a(1) given -- to match a recent change I see Neil Sloane and another editor decided upon quite recently (A171740), plus addition of a whole bunch of palindrome cross-references (many mine and many not, with no particular critically important linkages). This just to ease your attempt to discern the changes if you want to skip pinkbox reading. As for the section title here, what I have there now is a use of 'non-trivial' in the title with specified definition in a comment (this being about representation as a palindrome, a single-digit or 11 is so regarded). My first attempt to fix was the simpler addition of 'multidigit' (and I thought a bigger change better afterward).James G. Merickel 04:03, 26 July 2015 (UTC)

A187749 b-file goof

Sorry to bother you, but I'm concerned I cannot do what I think I should with this without a delay. You'll be aware that I only recently began adding b-files (or changing them) and was under the wrong impression non-automatic ones for sequences not filling 3 lines were even desired. While trying to get the above sequence just right, I apparently only removed the extension mentioning my b-file and not the b-file itself. If this is expected to matter, would you please do this? I'm really worried it will block my other edits if I do it myself (with my 3 limit). Thanks. If you think it's trivia that won't create a later issue, I guess you don't need to do anything (nor I).James G. Merickel 23:20, 7 August 2015 (UTC)

Link expired to Beal conjecture

Hello! At your "Useful links", didn't work anymore. Feel free to remove this after you fix that. Cheers, --Juhani Heino 15:56, 21 August 2015 (UTC)

Indeed, thanks for the heads-up. - Charles R Greathouse IV 16:28, 21 August 2015 (UTC)


I very much appreciate the Pari code you added on A129912.--Bill McEachen 03:52, 3 November 2015 (UTC)

Glad to help! Let me know if you need anything else. - Charles R Greathouse IV 18:03, 3 November 2015 (UTC)


Thank you for your table of 10,000 terms in A268594, n=p^k-k = q^i-i, primes p<q. Do any of the values of q appear to higher than the first power (i.e. is i ever greater than 1)? illegible 16:04, 8 February 2016 (UTC)

Glad to be of service. I don't see any instances of q^i with i > 1 up to 10^40. Under some form of Pillai's conjecture there should be only finitely many. - Charles R Greathouse IV 17:03, 8 February 2016 (UTC)
Thank you. I'm working on this with another guy and he wants to conjecture that there aren't any, but I'm not so sure. illegible 00:53, 9 February 2016 (UTC)

Request: add to your /Projects page

Hello, and thank you for the variety of resources you've provided for our edification. I am involved with a small community on reddit at r/factorize_request [5]. It is less than a year old, but one of its major milestones (at least in terms of other reddit communities) is its indexing of factors through its participation in Berkeley's BOINC project, as well as some clever bots written for the subreddit.

If this is something which belongs on your /Projects page, would you add it? If not, what can a small community like ours do to provide a more accessible or reliable academic resource?User:J. Conrad 20:44, 5 September 2016 (PST)

I'm not entirely sure that fits into what I'm collecting, but why not -- I've included it. - Charles R Greathouse IV 06:28, 6 September 2016 (UTC)


There are many interesting proposals on improving the OEIS, some of which are really good (I mean Features Wishlist, Suggestions for new keywords and so on). Are there any chances that some of them will be implemented? It is by no means a claim, I'm just asking in case you know something about it. And in addition to this general question, there is a specific request: if you have time, please take a look at the t-file proposal. It is an attempt to solve a problem of machine-readable representation of arrays. Feel free to edit it if you find it worthy of attention. --Andrey Zabolotskiy 21:17, 12 December 2016 (UTC)

The situation is somewhat complex. Most of the software running the OEIS was written by Russ Cox, who is largely (albeit not entirely!) too busy to work on it further. I started to learn Go in order to share duties with Russ, but I'm (understandably, I think) not comfortable enough to make changes to the live code running the OEIS. Ideally we would have (1) a virtual server clone where I and eventually others could make and test changes without causing downtime and (2) a way to roll back changes in case things go horribly wrong when updating code. Without at least one of these I'm not likely to make changes.
But I like many of the feature requests (indeed, I've proposed some of them). I think I saw an early version of the t-file proposal, I'll look at it now. I think support for dimension greater than 1 (triangles, irregular tables, tetrahedra, etc.) is weak in general, and perhaps t-files are one of the things we can implement to better our support.
Charles R Greathouse IV 22:09, 12 December 2016 (UTC)
Thanks for the explanations!
Could you please estimate the probability that this changes in the nearest several years, so you (or someone else) finally become able to develop the OEIS?
And one more question, if you don't mind: is there any non-public working communication mechanism for the Editor's Board? I mean, if an Associate Editor or an Editor-in-Chief has doubts if he or she should approve some kind of sequences, or whether one or another kind of formatting should be used, and so he/she wants to know the opinion of other Editors, what does that editor do apart from leaving a pink box comment?
--Andrey Zabolotskiy 16:29, 29 April 2017 (UTC)
Very high. I'm a software developer and I'll be working toward that, and we may have others do the same. It won't be quick because there are a lot of other OEIS projects for me to work on, but it will happen. I'm already comfortable enough that when Neil has a feature request I can generally point to the right piece of code and what changes need to be made (even if I'm not yet comfortable making them).
Yes, the editors have a private mailing list for discussion. It's not common that they will use it to discuss a particular sequence, though; they're more likely to discuss in the pink boxes. The list is more for discussing general editing principles. I'm sure the list is sometimes used because there's a tricky sequence no one knows how to handle. But more often that would be handled with an email between the involved editors and Neil. For an idea of scale, I'd say that out of 100 sequences with issues, 93 are handled just in the pink boxes with the balance handled by email (of which maybe 1 would go to the whole list).
Charles R Greathouse IV 13:32, 12 June 2017 (UTC)
Thank you. It sounds quite reassuring. --Andrey Zabolotskiy 19:59, 12 June 2017 (UTC)

What do you think about granting the "Associate Editors" wiki-group the "validate" right? As far as I understand, currently Associate Editors can "review" and "approve" pages -- moreover, their (our) edits are "automatically sighted", which hints that it as intended that Associate Editors should be able to turn drafts into approved versions for protected wiki-pages, but in fact all this "review" and "approve" stuff doesn't do anything. The only right that affects the protected pages seems to be "validate". --Andrey Zabolotskiy 21:44, 28 October 2017 (UTC)

Sounds like a good idea, let me look into it and talk to Neil. - Charles R Greathouse IV 20:53, 29 October 2017 (UTC)

Hello again. If I understand correctly, all development of the OEIS software is now still done by Russ. Why? Is it just because of lack of time, or something else? Again, I don't claim anything of blame anyone, I'm just trying to form a view of the processes behind the OEIS software development and, generally, the OEIS Foundation guidance. --Andrey Zabolotskiy (talk) 11:51, 9 June 2020 (EDT)

We have a small group of people who are willing and able to make changes to the server software. I'm taking care of a newborn so that greatly reduces my ability to help out here. Others likely have their own reasons. But generally this is how it goes with an all-volunteer outfit. If we had a large enough endowment to support several salaries we could have a half-time developer and that would be great, but that's not likely to happen any time soon. Since COVID-19 funding has rather dried up; we're just trying to keep afloat, nevermind expand. - Charles R Greathouse IV (talk) 15:37, 9 June 2020 (EDT)
(1) Have you considered getting Georg Fischer involved? He already does some work on automated consistency control of the OIES content, and he is willing to get his consistency checks integrated into the server software. (2) When I asked NJAS whether he thinks that there are any technical improvements or user interface changes that the OEIS needs, he answered simply "No". Russ Cox said that he too thinks that the focus should be "mainly on the sequences themselves" (one could hardly argue with that), not the software, and his priority is the search engine (which indeed works better and better over time). At first glance, fixing long-standing bugs and adding new features seem to contradict these views, especially Neil's. How is the developers team going to make changes to the server software if the President of the OEIS Foundation doesn't think it's needed (according to himself)? [Once again I emphasize that I understand that we all work as volunteers and I am grateful to Neil, Russ, you, and other people who work on the OEIS.] --Andrey Zabolotskiy (talk) 07:13, 10 June 2020 (EDT)
Any kind of response will be appreciated --Andrey Zabolotskiy (talk) 04:05, 17 June 2020 (EDT)
I'm not getting enough sleep, at present, to devote any thought to OEIS server development. When I can get some bandwidth I'll get caught up with my life and see if there's a way ahead. But there's a reason I had to step down as VP: just not enough hours in my days. Charles R Greathouse IV (talk) 15:43, 17 June 2020 (EDT)
OK, thanks and sorry for being obtrusive. --Andrey Zabolotskiy (talk) 16:21, 17 June 2020 (EDT)
I wish I could be more help! One day. - Charles R Greathouse IV (talk) 14:28, 18 June 2020 (EDT)


A117825 vector graphics

Hi, commons:File:A117825.svg is based on data in your b-list. IANAL, but Commons clearly does not permit CC-BY-NC. OTOH it's only data, and maybe the uploader is entitled to create an SVG of your data published as CC-BY-SA. He's certainly entitled to compute the values and do whatever he likes with the result, but that's not what happened. How should it be handled, just let it stay as is? Copy it as CC-BY-SA and add it here as illustration created by ... (for the BY business)? Propose it for deletion on Commons (for the NC business) after copying it? –Frank Ellermann 03:52, 8 October 2017 (UTC)

I'm not a lawyer, but it's my opinion that b-files are compilations consisting of nothing but raw data, and hence by Feist v. Rural are not eligible for copyright. In that case the image could be created with any license or even put in the public domain. - Charles R Greathouse IV 13:51, 10 October 2017 (UTC)
Great, OEIS might use the SVG, and commons can keep it, thanks. –Frank Ellermann 03:51, 11 October 2017 (UTC)
That's my take on the situation. There can be copyright on a compilation (and I would argue that collections like stripped.gz are covered, there's substantial originality in the selection of sequences from the uncountably many integer sequences), see the United States Copyright Office's Circular 14, but the raw data itself should be fair game. - Charles R Greathouse IV 13:48, 11 October 2017 (UTC)
The CC 4.0 licenses cover databases under EU law, maybe the OEIS could be "upgraded". But not everybody likes this, 3.0 allowed more abuses by copyright owners. CC-BY-SA 4.0 even claims to be GPLv3 compatible. –Frank Ellermann 02:16, 13 October 2017 (UTC)
That would be a serious issue to decide with our legal counsel. Since the intellectual property of the OEIS is essentially all we are we'll need to make sure we're doing everything properly there. - Charles R Greathouse IV 15:06, 13 October 2017 (UTC)

Fermat-Catalan conjecture

I've been fiddling with this a bit this morning, and applied an equation I found here: | 1. I used Pari/GP, and evaluating the cases from [2], I get an annoying round-off for the first 2 of the 10 cases. I'd like to explain this. Specifically, I compute q as : 3.075, 4.009, 9, 7, 5, 3, 7, 7, 3, 3 for the cases presented in the paper in order (note there is a typo in that paper for the eq'n). The form I used was: (log(x^q-y^2+sqrt((y^q-x^2)^2+4*y^q*x^2)-log(2)))/log(y)

Any suggestions ?--Bill McEachen 15:30, 10 December 2017 (UTC)

I'm not quite following, what arguments are you taking and what are you solving for? (And to be clear, is the underlying equation y^p = x^q + z^c?) I see x, q, and y in your formula but surely if you can use q it's trivial to derive q itself? - Charles R Greathouse IV 05:33, 16 December 2017 (UTC)

Comment in A020492

A020492 has this comment:

"The quotient A020492(n)/A002088(n) = SummatorySigma/SummatoryTotient as n increases seems to approach Pi^4/36 or zeta(2)^2 [~2.705808084277845]. - Labos Elemer, Sep 20 2004, corrected by Charles R Greathouse IV, Jun 20 2012"

The SummatorySigma is A024916 instead of A020492, isn't it? illegible 06:47, 28 December 2017 (UTC)

Actually I don't know which sequence is SummatorySigma, but I don't think it is A020492 (balanced numbers (sigma(x) mod phi(x) = 0). illegible 06:52, 28 December 2017 (UTC)

Missing sequence

This is unusual, since normally one simply edits in a sequence believed worth adding, but a) I probably still am not free to do this despite what was to be a 1-year block, and b) I won't be online at all for a while and haven't time to look into editing in a new sequence. 1,3,13,57,541,... gives the number of ordering possibilities on n-tuples from a linear ordered set, and seems so basic it should be in. Anybody?James G. Merickel (talk) 13:53, 12 August 2018 (EDT)


(Remember what you put on my talk page a year ago about 4366's sequence similar to A152466. I used your prime suggestion to take the sequence past the C85 it got stuck on and I continued until I either reached a prime number or got stuck again. I reached a P154. J. Lowell (talk) 19:04, 29 January 2019 (EST)

I'm glad it was useful. Charles R Greathouse IV (talk) 16:46, 1 February 2019 (EST)

Hi Charles, I saw that you edited Terret Trotter's (fake) user page. The issue is that the cached (and cleaned) copy of his collection (with the background for about 30 OEIS sequences) is still stored on my server, and that I would be pleased if you resp. the OEIS admins could move it onto the OEIS server like other cached documents, since the fate of my server might be similiar to that of Terret's server in some - hopefully distant - future. Best regards - Georg Fischer (talk) 02:42, 15 January 2020 (EST)

I can look into the situation. Are these just plain HTML files, or what? - Charles R Greathouse IV (talk) 02:44, 15 January 2020 (EST)

Help desk

Hi, after almost ten years I still haven't figured out where to report issues on the Wiki side of the OEIS, something like Wikipedia Project:Help desk, Project:Teahouse, Village Pump (technical), or their various admin noticeboards.

There is a OeisWiki:Community portal in the sidebar, I used this project page for a bug report—all SVGs broken—and an inquiry about pending reviews since 2013. –Frank Ellermann (talk) 19:11, 26 February 2020 (EST)

It's simply the wrong page in the sidebar. I copied everything to OeisWiki talk:Community Portal and redirected the p portal to the P Portal talk. The vintage 2012 P Portal can rotest in peace. –Frank Ellermann (talk) 01:36, 27 February 2020 (EST)
Frank, I'll look at the rough number pages. But generally I think that the plan is to move away from a WikiMedia backend, because it doesn't mesh well with our other half and it's hard to maintain. So I wouldn't recommend putting in a huge amount of effort here because we'll likely end up porting everything to some other system. (We don't have any concrete plans as of this moment, but it's something that's been tossed around.)
Charles R Greathouse IV (talk) 02:50, 27 February 2020 (EST)
Good to know, because I just stumbled over about 4 redirects to the about 12 local help pages arranged in about 20 help categories, now all unused (redirect bypassed / category empty) and tagged as discarded items.;-) –Frank Ellermann (talk) 03:10, 27 February 2020 (EST)

Bug reports

Hi, various bug reports and other issues ended up in limbo on OeisWiki talk:Community Portal, broken SVGs on the Wiki side, two OEIS proper nits, and various issues requiring elevated rights in three maintenance categories: Items pending approval, Protected items with edit request, and Discarded items. I need a clue where + how to report bugs, posting on user talk pages for 4 of 6 admins is spamjust wrong. –Frank Ellermann (talk) 08:01, 14 March 2020 (EDT)

My advice is to take the long view and assume that the wiki will be replaced with something else. Which questions survive a move like that and which are wiki-specific? I would take the former to SeqFan, and triage the latter: which ones are critical and also easy to fix? These should probably go to Russ, who can deal with them. Are any critical but not easy to fix? Then maybe we need to move forward the transition away from the wiki. Otherwise, they go in the Features Wishlist (you'll see a number of my requests there). - Charles R Greathouse IV (talk) 00:49, 16 March 2020 (EDT)
  1. The something else plan could be announced on the Main page, where the few folks putting lots of work on the OEIS wiki side have a chance to see it.
    My efforts were mostly limited to red links on technical pages, e.g., Help:Group rights in 2020, listed as "missing pages" on ToDo since 2011. Meanwhile the "missing pages" section is gone (empty => blanked). Nobody can know this, because ToDo wasn't reviewed for over six years. One of only nine pages in Category:Items pending approval, you (collectively) are not flooded by review requests, you are also free to reject requests, but over six years cannot work.
    IOW, I won't hold my breath for something else and don't expect to be still around when it happens. If something else is phpBBS the maintenance issues won't go away, phpBBS also requires at least biannual updates, with backwards incompatible new versions at this lazy update frequency. Not recommended for security updates, I have no idea how bad the MediaWiki 1.30 still used here was wrt security, but it is certainly past its very last "best before" date.
  2. I don't get what the OeisWiki talk:Community Portal has to do with the SeqFan list. Sometimes, say, more than once since 2014 and when I'm active here, I look into the list archive, read/only, I don't know if I still have write access. Mail is one of the things where I use an "annual" update frequency. But if I find a bug report (actually only a nit) on Talk:The OEIS End-User License Agreement and can't help that user with a better place to report this it makes me nervous: Main reason why I spammed four of six admins on their user talk pages, Russ got exactly the same message from me on his user talk page. Inspired by a SeqFan post in 2019 from ~njas introducing a new admin, who also got the same message from me, and is now interested to fix the SVG issue. David was #4. I'm used to almost dead wikis with lots of long gone admins, the Freeciv wiki is certified worse than the OEIS wiki in this regard.
  3. I don't know how urgent nine of ten issues in category:Protected items with edit request actually are. When I stumble over something that is clearly obsolete or makes no sense for me I remove or disable template:edit request, that takes the page out of the maintenance category, case closed as far as I'm concerned. For the 10th issue, that's new and simple and urgent enough, iff we agree that OeisWiki talk:Community Portal is the correct place to report technical issues on both OEIS proper and the wiki, after ruling out admin user talk page shopping as not much better than Special:RandomPage.
  4. Category:discarded items is not urgent, but should be handled about annually, "deletions" require admin rights. A normal wiki "deletion" only hides the page from public view, admins can still see it, and restore it in case of errors. Real deletions for legal reasons are of course also possible, but rarely needed, I doubt that this ever happened here.
Frank Ellermann (talk) 07:56, 16 March 2020 (EDT)
This is my advice to you based on my own knowledge. We haven't announced anything yet and there are, as of yet, no firm plans. Take it cum grano salis. My advice about SeqFan is useful because that is the active OEIS community, where you will get people reading and (perhaps) commenting on your questions, where the wiki is not very active even on its most active parts.
As for security upgrades, you might bend Hugo's ear; he may be willing to upgrade us, if it wouldn't be too disruptive.
I should note that I recently stepped down as OEIS Vice President due to a lack of time to participate; Russ had been in a similar situation a few years earlier. Our main difficulty is lack of time in our officers and editors, so new requests on their time are never easy when they add to long lists of demands on their time (to be expected in a small, all-volunteer effort such as ours).
Charles R Greathouse IV (talk) 12:27, 16 March 2020 (EDT)

Deletion of my account

Hi Charles, very sorry if this is a trivial task, but I would like to delete my account but have been unable to figure out how to do so as there's no option for it in the preferences menu... Would you know happen to know how I could do so/be able to do so for me? Many thanks in advance for your help with this matter. sig (talk) 15:18, 19 March 2020 (EDT)


Maybe add a link to the Numberphile tribute to his profile. Not my time to be "bold" and "just fix it" :-( –Frank Ellermann (talk) 01:00, 16 April 2020 (EDT)

Thank you for the suggestion. - Charles R Greathouse IV (talk) 11:38, 17 April 2020 (EDT)

A lost EiC

Greetings Charles, please fix the following discrepancy: User:Michael Somos is, as far as I know, an Editor-in-Chief (is this correct?), but he is not on the list. (Are there others?) Andrey Zabolotskiy (talk) 11:58, 28 January 2021 (EST)

News about you

Hi Charles, long time I don't hear you.

My work con the Complicate Modulus Algebra arrive at a very good point: Fermat the Last seems now blind proved with an inequality becomes an equality at the limit just...

for more, pls e-mail me, or post onto my page here...


Ciao Stefano