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Expansion of (1 - x) / (1 - x - x^3) in powers of x

Please comment on [1]--Adi Dani 05:39, 25 May 2011 (UTC)

I added a link to the index. You made a comment and added a program. What else am I to say?

Charles R Greathouse IV 13:13, 25 May 2011 (UTC)

A084984

Hello,

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 a(n) > n^1.285, but that (using Vinogradov notation). This means that there exist constants k > 0 and N such that, for all n > N, a(n) > kn^1.285. 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

http://math.crg4.com/oeis-quadratics.html

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.

But

[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)

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

Concerning

'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)

{2,1677721,...}

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 [2] 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)

Backscatter

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.

W E R W A I T I N G F O R U

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)

A217681

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 http://go.helms-net.de/math/tetdocs/TetrationForSeqFans.zip

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)