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# User talk:Daniel Forgues

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## Contents

### Kronecker delta

Ah, by squaring ij, you sidestep the possibility of raising 0 to a negative power if i < j. Though I wonder if it wouldn't be just as effective to take the absolute value of ij. — Alonso del Arte 23:31, 28 June 2010 (UTC)

That is a clever way to rescue the Kronecker delta on that one. The multiplicative identity! I should've thought of that. — Alonso del Arte 21:31, 5 November 2010 (UTC)

### Sequence of the Day

Could you change Template:Sequence of the Day if Robert doesn't do it? I think he might be out of town. — Alonso del Arte 03:16, 11 October 2010 (UTC)

Or if you could change it later today for Oct. 12. — Alonso del Arte 13:47, 11 October 2010 (UTC)

Thank you very much for keeping it going. And very nice choice for today's. — Alonso del Arte 00:58, 12 October 2010 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── Thank you for inviting me to choose the Sequence of the Day for tomorrow! — Jaume Oliver Lafont 09:08, 12 October 2010 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── Daniel, could you choose the Sequence of the Day for the 18th? Charles has signed up for the 20th. — Alonso del Arte 00:42, 18 October 2010 (UTC)

OK — Daniel Forgues 01:04, 18 October 2010 (UTC)
David W. Wilson is proposing a sequence for 18 Oct 2010, so I won't... (although I had something ready...) — Daniel Forgues 01:41, 18 October 2010 (UTC)
I thought he had to go to sleep before 0:00. (I don't know what time zone he's in). He said he'd have to write it up in advance and have someone else post it, so I thought there was no time for him to do it for the 18th. But if he can do it for the 18th, maybe you can do it for the 19th, and hopefully several people can sign up to fill up the 21st up to the 29th. I should be going to sleep pretty soon myself; had to get up early today for the Detroit Marathon. — Alonso del Arte 02:01, 18 October 2010 (UTC)
Never mind, I just saw today's. — Alonso del Arte 02:07, 18 October 2010 (UTC)
OK, I'll do the Sequence of the Day for 19 Oct 2010. Thanks — Daniel Forgues 22:30, 18 October 2010 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Could you sign up for a spot in November for Sequence of the Day? Right now I'm the only one signed up for that month. — Alonso del Arte 22:51, 26 October 2010 (UTC)

I signed up for 12 Nov 2010 Sequence of the Day. Thanks — Daniel Forgues 05:14, 27 October 2010 (UTC)

### OEIS Wiki formatting

Glad you could figure it out. I had no idea why it wasn't formatting the programs the same. — Alonso del Arte 00:27, 4 November 2010 (UTC)

### Logical quantifiers: Greek or Latin?

Daniel, are you sure the logical quantifiers $\forall$ and $\exists$ are really attributable to letters of the Greek alphabet rather than A and E of the Latin alphabet? — Alonso del Arte 21:09, 14 December 2010 (UTC)

You're right, they are inverted A and E from the Latin alphabet, I'll remove them. — Daniel Forgues 03:04, 15 December 2010 (UTC)
And I added them to the Latin alphabet page. — Daniel Forgues 02:53, 18 December 2010 (UTC)

### Subfactorial numbers

I am sorry. I took many of the text from the german wikipedia, where i worked on the article. I try my best, to remove the german from the article. — Karsten Meyer 10:39, 17 December 2010 (UTC)

### Aligning numbers in tables

Daniel, is there a way to right-align numbers in the table of Stieltjes constants so that both the positive and the negative constants have their decimal points aligned? — Alonso del Arte 03:09, 2 February 2011 (UTC)

Using + and − (the real minus sign) gets the dots aligned (with left alignment) — Daniel Forgues 04:57, 2 February 2011 (UTC)

Actually, Daniel, I think only Editors in Chief can delete pages in the OEIS Wiki. — Alonso del Arte 16:43, 14 February 2011 (UTC)

I created, a long time ago, the template Template:Discarded to display a request for deletion when you view a discarded item (page, category, ...) and to automatically categorize an item in Category:Discarded items for convenience. This is to facilitate the maintenance of the wiki by OEIS Editors, by making it easy to locate pages that were created by mistake (typo, wrong naming convention, ...) or pages considered inappropriate by Editors-in-Chief (N. J. A. Sloane sent me an email asking me to delete all pages and categories named after living persons, as he considers it inappropriate to have such pages since in that case only User:Username pages created for registered users are appropriate. Since I am only a regular user, I can't delete pages, but I could use the template {{Discarded|Not appropriate: only User:Username pages created for registered users are appropriate for living persons.}} to try to fulfill N. J. A. Sloane's request that I delete all pages and categories named after living mathematicians. — Daniel Forgues 02:22, 15 February 2011 (UTC)
Tagging is the most you can do in this case, but it's still a big task and much appreciated. — Alonso del Arte 17:28, 15 February 2011 (UTC)

### Review upcoming Sequence of the Day

Daniel, could you review the Sequence of the Day for July 1 before this month is over? If it makes sense to you, just mark it reviewed, but if anything is unclear, then give some indication of what needs to be changed. — Alonso del Arte 23:33, 20 April 2011 (UTC)

And if it's not too much trouble, could you also review those for June 28, June 29 and June 30? — Alonso del Arte 23:35, 20 April 2011 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── All reviewed. — Daniel Forgues 23:03, 21 April 2011 (UTC)

### New sequence

Hello Daniel. In my work on partition and composition are treated eight sequences one of them is missing from OEIS. please go to my talk page — Adi Dani 23:55, 24 April 2011 (UTC)

### CMRB - 1/2

I noticed you have included a section on CMRB - 1/2. Have you noticed that the Cesàro sum of the divergent series $\scriptstyle \sum _{n=1}^{\infty } (-1)^n ~ n^{1/n} \,$ is CMRB - 1/2? I found that out while discovering MRB2 at http://www.mapleprimes.com/posts/35778-MRB-Constant-F [1]. Thanks; it's great to see a lot of my work displayed so professionally! — Marvin Ray Burns 02:12, 3 May 2011 (UTC)

Did you intend the notation MRB2 or CMRB2? — Daniel Forgues 18:27, 3 May 2011 (UTC)
I have been using MRB as a symbol for the MRB constant. I know Wolfram Alpha uses CMRB; likewise it uses the capital script C for most miscellaneous constants followed by an abbreviation or known symbol for the miscellaneous constant. However, here on OEIS if C is used for other constants then we should use it for MRB also.
Likewise capital script CMRB2 would be fine for here to.

### Convergents constant

Daniel, I started a new page for the constants that comes from repeated Convergents@FromContinuedFraction. Convergents constant

### Question on convergents constant

I don't know if you've seen it or not, but I reached out to a bigger audience in talking about the cc's. See http://math.stackexchange.com/questions/39981/list-of-convergents-constants.

I got one very interesting answer: they thought the issue of most numbers giving a cc reminded him “of Khinchin's constant http://en.wikipedia.org/wiki/Khinchin's_constant because it is also the limit value of a function on almost all continued fraction parameters.” He added, “According to the wiki article in my previous comment, solutions of quadratic equations do not produce Khinchin's constant. – Dan Brumleve”

────────────────────────────────────────────────────────────────────────────────────────────────────

You mentioned the possibility of (the apparently irrational) cc's being produced by quadratic numbers; this could lead us that way. I know quadratic numbers are solutions of quadratic equations, but how do I make a list of them and be sure I don’t have any non-quadratic numbers in it?

Marvin Ray Burns 18:25, 22 May 2011 (UTC)

I've seen the MathWorld article on Khinchin's constant when I searched for continued fractions constants there, I thought I had put a link to it in the "External links" section of the convergents constants page, now its done. I actually suspect that quadratic numbers $\scriptstyle x \,$ might not give the convergents constant of "most" numbers in $\scriptstyle n \,<\, x \,<\, n+1 \,$ since the simple continued fraction of quadratic numbers is eventually periodic.
Weisstein, Eric W., Khinchin's Constant, from MathWorld—A Wolfram Web Resource. [http://mathworld.wolfram.com/KhinchinsConstant.html]
Weisstein, Eric W., Continued Fraction Constants, from MathWorld—A Wolfram Web Resource. [http://mathworld.wolfram.com/ContinuedFractionConstants.html]
Daniel Forgues 21:24, 22 May 2011 (UTC)

### Sequence of the Day for a day in September

Daniel, would you like to choose the Sequence of the Day for September 3? (Template:Sequence of the Day for September 3) — Alonso del Arte 02:14, 27 May 2011 (UTC)

Yes, I'll look for some interesting sequence to choose over the next few days. Thanks. — Daniel Forgues 02:53, 27 May 2011 (UTC)
I entered the draft for SoD of Sept 3, 2011. — Daniel Forgues 00:22, 31 May 2011 (UTC)
Excellent, thanks. Alonso del Arte 00:28, 31 May 2011 (UTC)

### Some analytic support for our work

I don't mean to impose; however, I will be working a lot this week (for once) and won't have much "me time." However, at

Yuval Filmus gave what seems to be a real supportive answer to my question about convergents constants. You might understand it quicker than I anyway; so if you can incorporate any of it, into the article(s) that would be great! Marvin Ray Burns 00:41, 1 June 2011 (UTC)

### Sequences of the Day for August

So, does this mean all the Sequences of the Day for August (which have first drafts entered by me) are now reviewed by you? Alonso del Arte 01:51, 2 June 2011 (UTC)

I did not yet go to the end of August, I can finish it tomorrow. These are mainly presentation reviews, addition of wiki links and comments, they are only superficial reviews... — Daniel Forgues 01:56, 2 June 2011 (UTC)

### Differing Notation?

Per a conversation I had at http://math.stackexchange.com/questions/39981/extract-a-pattern-of-iterated-continued-fractions-from-convergents, I added “3 steps to computing convergents constants” on the cc page. I hope it is understandable, because I am worried about what might be conflicting notation; where you have p/q, he has r. Is there anything you can do to smooth out the differing notation? Thank you! — Marvin Ray Burns 19:51, 4 June 2011 (UTC)

### Answer to our Open Question

I believe I found the answer to our open question! https://oeis.org/wiki/Talk:Table_of_convergents_constants#Open_Problem

### Just now Found a Pattern

I just now found a pattern for :$a_6(n) \,$ Would you turn it into latex? —Marvin Ray Burns 00:30, 9 June 2011 (UTC)

Done. — Daniel Forgues 01:42, 9 June 2011 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── The $a_6(n) \,$ pattern for mods 1-5 continue for as far as I can tell; I think ' will change the upper limit for them to a ? mark. Thanks for the latex; I'll try to catch on. —Marvin Ray Burns 02:35, 9 June 2011 (UTC)
On second thought the part of the function for mods 1-5 should be added to the >24 interval. I'll try to do that. — Marvin Ray Burns 02:43, 9 June 2011 (UTC)

Dan,for n<=24 and mod(n,6)=0:

$a_6)6) =9 \,$
$a_6(12)=9 \,$
$a_6(18)=2 \,$
$a_6(24)=16 \,$

Marvin Ray Burns 15:00, 9 June 2011 (UTC)

I think I added the data for n<=24 and mod(n,6)=0 correctly.

Marvin Ray Burns 20:19, 9 June 2011 (UTC)

### Dear Daniel

Dear Daniel I have a text or a void page you created, can I transmit it to you via this page? Thanks. — Haydar Rahmanov 12:05, 12 June 2011 (UTC)

I don't understand what you mean. Since you are a registered user, you can edit pages. — Daniel Forgues 17:28, 12 June 2011 (UTC)
Sir, first, thank you for answer!
Second , the page is created by you
Finally ; since not too used to the style, I asked you if you can kindly do it.

──────────────────────────────────────────────────────────────────────────────────────────────────── That is all, if you are busy then please excuse me. Regards — Haydar Rahmanov 20:24, 12 June 2011 (UTC)

If you transmit the text to me and I copy and paste it, your contribution won't appear in the page history. Just put the text you created in the page in question (which page is it?,) so in the page history it will show that you are the author of the text. If you give me the name of the page, I'll gladly look into it to see how I could improve the formatting, presentation style, etc. I do these presentation reviews regularly. Thanks. — Daniel Forgues 21:20, 12 June 2011 (UTC)
Dear Daniel, please see there [2] and correct if necessary. Thanks --Haydar Rahmanov 11:13, 16 June 2011 (UTC)

### Reference

Dan, I made a reference on Table of convergents constants‎ to a proof for cc([1,2]); the reference could use a little sprucing up. —Marvin Ray Burns 00:41, 22 June 2011 (UTC)

I have to debug the {{Cite web}} template, i.e. get rid of that spurious link that appears at the end (the link should only be wrapped under the title.) All the citation templates with web links (e.g. {{Cite web}}, {{Cite arXiv}}, ...) do that. Apart from that bug, all the citation templates work fine. — Daniel Forgues 01:43, 22 June 2011 (UTC)
────────────────────────────────────────────────────────────────────────────────────────────────────
Dan I made a small discovery on the cc(n) where 0<x<1: If an iterate (the result of FromContinuedFraction) is >1 then the cc will be the same as other cc's with the ame integral value of that iterate. Example, when computing cc(3/100)the iterates are
0.02997275204359673, 0.05968841510642278, 1.996553370372146,
1.4141268406012069, 1.4946426911647988, 1.4997306225168652,
1.4999865180117422, 1.4999993258613324, 1.4999999662930517,
1.4999999983146521, 1.4999999999157325, 1.4999999999957867,
1.4999999999997893, 1.4999999999999896, 1.4999999999999996,...

Once the iterate became 1.996553370372146, the cc was destined to become 3/2, as proven by Filmus, Yuval.
Fianlly if an iteration ever becomes an integer the cc will be that integer.

So for 0<x<1

if an iteration>1 and is not an integer, no other iteration will be an integer and the cc will be the same as other cc's with the same integral value of that iterate.

if an iteration ever becomes an integer the cc will be that integer. else the cc is 0.555753104279495.

### A037077

I deleted some of my comments that I wasn't proud of, and added a new oeiswiki link to http://oeis.org/history?seq=A052110. I just now noticed, however, that you have a reference to a oeiswiki link. There was only one when you wrote it, but now there are two. I just thought to give you a heads up so that you can adjust your comment accordingly if you want.— Marvin Ray Burns 23:16, 27 June 2011 (UTC)

### Continued Fraction for CMRB

See Continued Fraction for CMRB in the talk:MRB constant.
I think there is a pattern for the convergents.— Marvin Ray Burns 02:24, 29 June 2011 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── I think what appears as a pattern is only the partial quotients {3, 10, 1, 1, 4, ...} of the continued fraction itself! — Daniel Forgues 19:52, 29 June 2011 (UTC)

### Ease of zeta zeroes computability

Daniel, I find it admirable that you give credit to Andrew Odlyzko for the Riemann zeta zeroes data, but anyone with the right program and enough running time can get many digits of these numbers. For example, in Mathematica:

RealDigits[ZetaZero[47], 10, 100][[1]]

should give a hundred digits in a split second, and if you up to a thousand and give it a few minutes, you can get those, too. Alonso del Arte 17:41, 2 July 2011 (UTC)

Since I didn't find the nontrivial zeros of the Riemann zeta function myself (I extracted the values from Andrew Odlyzko's file[1]) I considered it appropriate to ask for his approval. — Daniel Forgues 19:21, 3 July 2011 (UTC)

### Sequence of the day for Sept 02, 2011

Dan, if you get a chance, would you mind looking at thee Sept 02 page and see if I described the range of the inverse functions correctly? Thanks. It is in the paragraph begining with, "There seems to be a parallel between..." — Marvin Ray Burns 20:05, 4 July 2011 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── Marvin, Dan, to get an idea of how it will look come September 2, take a look at User:Alonso del Arte/Test Area. Alonso del Arte 00:12, 10 July 2011 (UTC)

Usually SoD has much shorter comments. I think most of it should go on Tetration and Talk:Tetration, where it will be always easier to find. — Daniel Forgues 19:30, 10 July 2011 (UTC)
As for some that are coming up sooner: could you look review or approve (depending on which is the next step) the rest of the Sequences of the Day for this week? I asked Peter to approve the one about phi-torials but now I don't know if he's logging in to the OEIS of late. Alonso del Arte 05:01, 12 July 2011 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── With all the attention on this one, no one has looked at Template:Sequence of the Day for September 1. Could you look it over and see if it meets with your approval? Alonso del Arte 01:10, 1 August 2011 (UTC)

### Not sure about that one example of a counterexample

I'm not sure the non-primality of 1 is such a great example of a counterexample. There are people who to this day cling to the notion that 1 is a prime number because it has no divisors apart from 1 and itself. Whether or not you and I agree with that logic doesn't matter, it clouds the example with an issue that is still being debated. — Alonso del Arte 04:17, 19 July 2011 (UTC)

Although 1 has been considered prime until the beginning of the 20th century (former definition: no divisors apart from 1 and itself, itself not necessarily distinct from 1) the unit (i.e. multiplicatively invertible element) 1 is now widely known as the empty product (defined as the multiplicative identity, i.e. 1) of primes, where an integer $\scriptstyle n \,$ is now considered prime iff it has exactly two divisors, a unit and a nonunit, where associates of $\scriptstyle k \,$ (i.e. product of some unit $\scriptstyle u \,$ with $\scriptstyle k \,$) are not considered distinct divisors. This is the definition (resulting from the development of abstract algebra at the turn of the 20th century) now accepted by most mathematicians.

──────────────────────────────────────────────────────────────────────────────────────────────────── Cf. A000040 The prime numbers.

Cf. A008578 Prime numbers at the beginning of the 20th century (today 1 is no longer regarded as a prime).

Examples:

5 = +1 * 5 (positive prime, since 5 has exactly 2 divisors, the unit +1 and 5) (-5 is an associate of 5, not considered a distinct divisor)
-5 = -1 * 5 (negative prime, since -5 has exactly 2 divisors, the unit -1 and 5) (-5 is an associate of 5, not considered a distinct divisor)
-2i = -i * 2 (imaginary prime (thus a Gaussian prime,) since -2i has exactly 2 divisors, the unit -i and 2) (-2, 2i, -2i are associates of 2, not considered distinct divisors)
1+i = +1 * (1+i) (Gaussian prime, since i+1 has exactly 2 divisors, the unit +1 and 1+i) (-1-i, 1-i, -1+i are associates of i+1, not considered distinct divisors)
-1-i = -1 * (1+i) (Gaussian prime, since -i-1 has exactly 2 divisors, the unit -1 and 1+i) (-1-i, 1-i, -1+i are associates of i+1, not considered distinct divisors)

Daniel Forgues 21:31, 19 July 2011 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────
Mathematicians are one group of people. Scientists and philosophers are another group of people. Conservative commentator George Will, for example, clings to the old definition. That's the kind of people I'm thinking about: smart about their respective fields but perhaps with some outdated knowledge of math. For such people, I worry that this particular example of a counterexample is much too distracting to be enlightening or clarifying. — Alonso del Arte 23:54, 19 July 2011 (UTC)
Although this is a trivial example of a counterexample, I see this as an opportunity to highlight the new definition of prime number! It also emphasizes the fact that all it takes is one counterexample, even if there can't be any other! — Daniel Forgues 01:45, 20 July 2011 (UTC)
I don't know, I still think it's a weak example if anyone can quibble with it by splitting hairs over defintions. Alonso del Arte 03:47, 20 July 2011 (UTC)
I removed it. On page prime numbers, I do emphasize on modern versus old definition of prime number. — Daniel Forgues 19:57, 20 July 2011 (UTC)
Yeah, that's the right place for it, the place where it is on point and wholly relevant to the topic. As for the counterexamples article, I am glad you put in the stuff about Beal's conjecture. Alonso del Arte 04:37, 21 July 2011 (UTC)

### Seq. o' th' Day for Sep 04 2011

Daniel, could you approve today's Sequence of the Day? If you have time, I would also like you to look over some other drafts for this month which have been reviewed but not approved. Alonso del Arte 17:54, 4 September 2011 (UTC)

I did approve today's SoD, and will also do some more. — Daniel Forgues 23:28, 4 September 2011 (UTC)

### Edit request

I modified {{Edit request}} to reflect the fact that Associate Editors and even Editors-in-Chief are currently powerless to change protected pages.

Charles R Greathouse IV 06:53, 6 September 2011 (UTC)

### Logarithms

Just a quick pointer, see Template_talk:Log_2. –Frank Ellermann 13:42, 19 September 2011 (UTC)

Related, IMHO nobody needs min for 81 arguments in the template namespace. All it does is to create a maintenance nightmare if you are unavailable to fix whatever could be broken. Admittedly I'm a KISS fan, and admittedly I once also loved to create "esoteric" or "intricate" templates, e.g., the MJD stuff on Meta, and that's already a contradiction, the MJD stuff is not KISS. Of course if you like obscure math. templates have fun, but please keep in mind that this is supposed to work for others here even if you later decide (or are forced) to give up on OEIS. –Frank Ellermann 21:29, 19 September 2011 (UTC)

It is the first time ever that someone alludes that I might ever be forced to give up on OEIS. Yikes! I'm now wondering whether the mathematical function templates are a worthwhile contribution to the OEIS wiki. I was making them so we could use them on sequence related pages (e.g. the {{MIN}} and {{MAX}} templates to be used to automatically scale the histograms created with the {{histogram}} template, for example.) Maybe they detract from the main goal of the OEIS wiki, which is about integer sequences, and the focus should thus be on making sequence related pages. I'll make sure that the mathematical function templates that I already started up are in a clean and working condition. I'll ask advice from N. J. A. Sloane about what kind of wiki pages are worthy contributions to the wiki. — Daniel Forgues 00:37, 20 September 2011 (UTC)
ACK, I wrote that shortly after seeing a talk page with a comment by Klaus Brockhaus. I certainly hope to be online when Posix timestamps meet the end of 31 bits. –Frank Ellermann 13:52, 20 September 2011 (UTC)

### Reviewing first Sequences of the Day for the New Year

Daniel, could you review the first few Sequences of the Day for January 2012, starting with Template:Sequence of the Day for January 1? Because I moved the one for Nov. 6, 2013 to Jan. 8, 2012, you've already done one of them. Alonso del Arte 01:18, 7 November 2011 (UTC)

OK, I'll do it. — Daniel Forgues 03:42, 7 November 2011 (UTC)

In your opinion, of A199000 through A199999 (inclusive) which one should be in Template:Selected Recent Additions? Alonso del Arte 22:20, 24 November 2011 (UTC)

### Orderings

Hi. Please take a look at Talk:Orderings. Greetings, Tilman Piesk 11:58, 2 February 2012 (UTC)

### Number articles

My understanding is that Wikipedia does 1 (number), 2 (number), 3 (number), etc., because they also have articles about the years 1 (A.D. or A.C.E.), 2, 3, etc. But here, do we plan to have year articles, and if not, wouldn't it make more sense to name them without " (number)"? Alonso del Arte 01:40, 26 April 2012 (UTC)

Of course, I just previously procrastinated in removing those " (number)" and forgot about it! I'll just go trough those 1050 number links and make them as 1 instead of 1 (number), right now! — Daniel Forgues 21:57, 26 April 2012 (UTC)
I thought of doing a mass replace but didn't want to assume too much. After I posted that yesterday I noticed your article 1729. Alonso del Arte 22:26, 26 April 2012 (UTC)
Tables of prime factorization is ready for review (those " (number)" are ALL removed)! — Daniel Forgues 23:16, 26 April 2012 (UTC)

### Thanks

Thanks for reviewing those late May Sequences of the Day. Alonso del Arte 18:56, 14 May 2012 (UTC)

### Quaters & Quarters

Daniel, it is likely that I have perpetuated a common misspelling with quarter-imaginary. But, as I don't have Donald Knuth's book in front of me at the moment, the most reliable reference for "quater" that I can find is Wikipedia, which should be treated with the severest skepticism. Do you know where that word "quater" comes from? Alonso del Arte 18:20, 16 May 2012 (UTC)

I previously added this link to Donald Knuth's paper (April 1960) on the page Quarter-imaginary base (look on page 245, he calls it quater-imaginary base)
Donald Knuth (April 1960). "An imaginary number system". Communications of the ACM 3 (4), pp. 245-247.
On Wikipedia, two explanations are offered for why he called it quater-imaginary base
• It's a Latin adverb meaning "four times" (i.e. once beyond thrice). I would guess that it refers to the fact that the system can cover all four quadrants of the complex number system with a single numerical representation. AnonMoos 15:42, 23 February 2006 (UTC)
• Actually, it's because the system uses four different digits. -- Milo
(the second explanation seems more plausible to me, I'll read Donald Knuth's paper to confirm this)
Talk:Quater-imaginary baseWikipedia.org.
Daniel Forgues 22:28, 16 May 2012 (UTC)
I'm going to look in his landmark Art of Computer Programming when I go to the Library today. If I recall correctly, I looked up "quarter-imaginary" in the index, so I would have failed to notice the 'missing' R. Alonso del Arte 18:32, 17 May 2012 (UTC)
If you look at the scanned copy of his 1960 paper (.pdf link above) on the first page of "An imaginary number system" you see
The "quater-imaginary" number system uses the imaginary number 2i (...)
and the term quater-imaginary appears many times after. Like the quaternary number system (base 4, with digits from the set {0, 1, 2, 3}) his quater-imaginary number system also uses digits from the set {0, 1, 2, 3}, hence quater-(...)
Quarter-imaginary base - OeisWiki
A177505 - OEIS
and nothing else! Where did the term negaquartal (for base -4) come from? It seems to me that negaquartal should mean base -1/4, not base 4. negaquaternary seems a better name for base -4, although a Google search of the term gives nothing! Google searches of negabinary, negaternary, negadecimal (negadenary) are successful though.
Quaternary numeral systemWikipedia.org.
QuartalWikipedia.org. (Quaternary numeral system, a system for representing numbers based on powers of four) The only place where I see that quartal may refer to quaternary numeral system...
Quartal and quintal harmonyWikipedia.org. (it seems that quartal and quintal refer to 1/4 and 1/5...)
QuinaryWikipedia.org. (is base 5) (also pental)
SenaryWikipedia.org. (is base 6)
SeptenaryWikipedia.org. (is base 7)
OctalWikipedia.org. (is base 8) (octal should refer to 1/8...)
NonaryWikipedia.org. (is base 9)
DenaryWikipedia.org. (is base 10) (also decimal, which should refer to 1/10)
It would have been more consistent if all integral bases ended in -ary, while all fractional bases ended in -al...
Daniel Forgues 03:07, 18 May 2012 (UTC)
I would like to think I did not unintentionally invent "negaquartal" for base –4, but it's possible. At the moment I don't remember where I got the term from. Alonso del Arte 16:54, 18 May 2012 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Come to think of it, base n and base 1/n are essentially equivalent bases, the digits of base 1/n are just the digits of base n in the reverse order, e.g. 4/3 in base 10 is 1.333333... (big endian representation) while in base 1/10 is ...333333.1 (little endian representation)! — Daniel Forgues 20:06, 18 May 2012 (UTC)

### Multidisciplinary

Thanks for all your work on The multi-faceted reach of the OEIS, it looks terrific. This is really starting to go somewhere!

Charles R Greathouse IV 21:05, 13 June 2012 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── I also wish to express my thanks for your work on that page. Alonso del Arte 00:22, 14 June 2012 (UTC)

### Turing

I didn't realize today was the centennial of Turing's birth. At least I put in A028444 for the Sequence of the Day for next year. Alonso del Arte 00:32, 24 June 2012 (UTC)

### Calendars too wide?

That's what I was getting at editing individual entries like the one about Buffon's constant that had a long equation I broke up into two or three lines. The calendar pages are still wider than I'd like, but at a certain point we need to say "good enough." Though you might know some clever bit of template programming that would solve this problem. Alonso del Arte 21:38, 28 June 2012 (UTC)

For convenience, the links to the monthly calendars for Sequence of the Day are

Daniel Forgues 01:55, 29 June 2012 (UTC)

What about having week 1 in column 1, ..., week 4 in column 4, [week 5 in column 5]? Five columns might, or not, solve the width problem. (That would make for some non-standard calendar style though...) Or some other arrangement? — Daniel Forgues 02:05, 29 June 2012 (UTC)

### On an unrelated note

I'd like to spotlight some of our best articles here on the OEIS wiki at some point*. I'm looking for articles which are either about the OEIS (User:Alonso del Arte/Is this sequence interesting, The OEIS and its potential for expansion) or about topics central to the OEIS. In particular I'd like articles which are essentially the best resource for that piece of information, rather than one shadowing a more comprehensive article from Wikipedia/DLMF/MathWorld/MacTutor/etc. (since these are meant to promote the OEIS). Ideally they would be of general interest rather than hyper-specialized, but I could live without this in a pinch.

Any suggestions? I think you know our articles better than anyone.

* Actually soon, as in starting now, but I can find a few good ones on my own. I just used Template:Selected Recent Additions which, although living on the wiki, is sort of more on the sequence side. That was your work, I believe, with Alonso?

Charles R Greathouse IV 22:16, 12 July 2012 (UTC)

### Growth of sequences

The addition of asymptotic notation to the individual (sub)sections of Growth of sequences is good, but as currently written they do not appropriately bound the sequences. For example, "superlinear but subquadratic" has

$\scriptstyle a(n) \,\in\, O \left( n^k \right),\, 1 \,<\, k \,<\, 2. \,$

which ensures that the sequence is subquadratic (actually in too strong of a sense, as it disallows x^2/log x) but not that it is superlinear, in that it allows a(2n) = n, a(2n+1) = n^2. I would write

$a(n)\in\omega(n)\cap o(n^2)$

which does both. (I certainly wouldn't use \scriptstyle on a formula on its own line, either...)

Charles R Greathouse IV 16:01, 7 August 2012 (UTC)

Yes, it does disallow $\scriptstyle O\left( \frac{x^2}{\log x} \right) \,=\, O\left( x^2 / \log x \right) \,\in\, O\left( x^{2-\epsilon} \right) \,$ (or O(x 2 / log x) ∈ O(x 2−ε) in HTML, but then we will have a mixture of equations written in LaTeX and written in HTML throughout the wiki...) (a LaTeX formula on its own line is displayed with \displaystyle which is default style)
As for the second case, a(2n) = n, a(2n+1) = n^2 (or a(2n) = n, a(2n+1) = n 2 in more fancy HTML, although MathJax would do a much better job, e.g. use CSS to select a better font), I think it also disallows it, since
$a(n) \in \omega(n) \cup o(n^2) \,$
where we have the set union rather than the set intersection, if I got it right... — Daniel Forgues 06:11, 9 August 2012 (UTC)

### Three new templates needed

Daniel, as you have more experience about creating templates, could you create following three ones: Clarify, like Wikipedia's http://en.wikipedia.org/wiki/Template:Clarify, then something like Elaborate, and also Illustrate? I would like these to be very handy, when I write OEIS Wiki pages, as reminders to myself (and of course others can use them also!), that I should either clarify some obscure sentence, elaborate some point (the difference to clarify is that here there is no obscure sentence, but more details would be welcome in any case), or illustrate, that is, an image is needed. Like in the recent Extended Stern-Brocot tree, I'm now using just a crude programmer convention of adding three X's, like (XXX - We need here an illustration like above.) — Antti Karttunen 18:49, 26 August 2012 (UTC)

I finally made the {{to do}} multipurpose template for this purpose. (I'm sorry for having waited so long to implement it, but here it is.) — Daniel Forgues 06:09, 25 October 2012 (UTC)

### Seq. o' th' Day for Jan. 23

Daniel, could you look over and possibly approve Template:Sequence of the Day for January 23? Alonso del Arte 00:24, 17 December 2012 (UTC)

Done! — Daniel Forgues 05:58, 17 December 2012 (UTC)

### Chase

I've finished the draft of User:Charles R Greathouse IV/Chase sequences. If you have a chance to look it over and give feedback it would be appreciated. I'd like to have something that I can point to when I see this happening that won't come off badly. For me the basic idea is that the author can understand the tangled web of references by virtue of working through it all, but readers may not be able to.

Charles R Greathouse IV 06:53, 4 January 2013 (UTC)

I would call A179833 a "high-dependency" sequence, which is not only very hard to follow through (very few people would go through the whole graph!), but also presents a high risk of error propagation... (one erroneous sequence could affect lots of sequences!) — Daniel Forgues 03:57, 6 January 2013 (UTC)

### Edit request

The text of Template:Edit request says that it's designed to being these pages to the attention of an Associate Editor or Editor-in-Chief, but it actually takes either an Administrator or a Bureaucrat. (I can't distinguish between the two since all Administrators and Bureaucrats here.) I can verify that neither Associate Editors nor Editors-in-Chief can make the edits.

Otherwise, of course, I'd make the edits for you...

Charles R Greathouse IV 05:52, 27 January 2013 (UTC)

I'm surprised! I just changed [[OeisWiki:Administrators|Administrator]] (Administrator) into [[Editorial Board|Associate Editor or Editor-in-Chief]] (Associate Editor or Editor-in-Chief), thinking that an Associate Editor or Editor-in-Chief could edit protected pages. I changed it to "an [[OeisWiki:Administrators|Administrator]] (maybe an [[Editorial Board|Associate Editor or Editor-in-Chief]]?)". — Daniel Forgues 01:40, 29 January 2013 (UTC)
On Talk:Hot Sequences, Alonso del Arte says that it requires an Editor-in-Chief. Should I edit the {{Edit request}} template accordingly? — Daniel Forgues 01:40, 29 January 2013 (UTC)
An Associate Editor can't do it. I'm an Associate Editor, so naturally I assumed an Editor-in-Chief could do it. My understanding is now that it requires a Bureaucrat. Alonso del Arte 01:51, 29 January 2013 (UTC)
────────────────────────────────────────────────────────────────────────────────────────────────────
On User group rights, it says that both Administrators and Associate Editors (which would imply Editors-in-Chief) can: Edit semi-protected pages (autoconfirmed). That's what confused me... — Daniel Forgues 02:45, 29 January 2013 (UTC)

### Table of inertial primes

Daniel, I completely forgot about the tables of inertial primes, thank you for reminding me.I need to get back to work on that. Once I finish them in HTML format, is it easy or difficult to change them to wiki format? Alonso del Arte 06:07, 6 February 2013 (UTC)

It is easy (although this is grunt work...) to change HTML tables to wikitext tables, but simpler and more convenient to create wikitext tables from the get go! For instructions, see
Help:TablesMediaWiki.org.
Daniel Forgues 03:15, 7 February 2013 (UTC)
I agree but only for tables with a few columns. Here, because there are almost 20 columns, it gets a little harder to stay on track and not mistakenly put what belongs on one column on a neighboring column. Once I get that table all filled in, I'll see if I can take care of the conversion. Tonight I hope to get Z[sqrt(14)] filled in. Alonso del Arte 03:22, 7 February 2013 (UTC)
As I filled in the row for d = 14, I remembered I had given myself a better way to not go in the wrong columns, and I realized, thanks to you, that this works just fine in the wiki syntax. Alonso del Arte 05:49, 7 February 2013 (UTC)

### be careful when changing case in links/anchors

In the history of Index to OEIS: Section Di I saw

(cur) (prev) 02:41, 17 December 2012 Daniel Forgues (Talk | contribs) (24,577 bytes) (< span id="Diophantine"> capitalized (< span id="Pellian"> being so...)) (undo) [approved by N. J. A. Sloane]

but note that

(a) the "id"s are not necessarily in correct case (nor correct spelling, nor English words...), they are merely links; you should rather check what is used in the links from OEIS to here.
(b) It is "Eulerian", but "abelian": there is a distinction which has a meaning. (Roughly: It is a special dignity if you get "lower cased".) M. F. Hasler 07:02, 14 February 2013 (UTC)
Since I had created <span id="diophantine"> just before, I could safely change it to <span id="Diophantine"> a few minutes later. The only page using it was/is Diophantine equations. I won't modify preexisting id's though, unless asked to do so (in which case I would have to fix all pages that links to that anchor, obviously). — Daniel Forgues 02:53, 16 February 2013 (UTC)

### De Polignac–Legendre formula‎

I saw your new article and wanted to comment on notation. $\operatorname{ord}_p n$ is the p-adic valuation of n, while you write it for the p-adic valuation of n!. I'm concerned that this could cause confusion.

Charles R Greathouse IV 15:09, 9 April 2013 (UTC)

Thanks! It should be $\operatorname{ord}_p \, n!$ and I made the correction. — Daniel Forgues 01:38, 11 April 2013 (UTC)

### Porting page from Wikipedia

Daniel, I was wondering if I could lean on your expertise.

I've been thinking about porting my page http://en.wikipedia.org/wiki/User:CRGreathouse/Tables_of_special_primes to the OEIS wiki and I wondered if it was doable. At the moment it uses these Wikipedia templates:

{{cite book}}, {{cite journal}}, {{log-star}}, {{fact}}, {{arXiv}}

(not including two 'templates' in my own userspace). The last three don't present a problem as far as I know but the {{cite ...}} templates are, as I recall, enormous monstrosities which include from other templates which include from other templates and so on.

Is it reasonable to port these templates to the OEIS wiki (or recreate them)? Has any work been done toward that end? (Of course there's no hurry. The page has been on Wikipedia userspace for years and can stay there a bit longer.)

Charles R Greathouse IV 14:59, 9 May 2013 (UTC)

Quite some time ago, I've imported those (the citation templates were awfully entangled, you said it, it seemed like tackling the Hydra: every time I was cutting one head, more heads grew up...) templates from Wikipedia (look into Category:Citation templates, there's more!)
{{cite book}}, {{cite journal}}, {{log-star}}, {{fact}}, {{arXiv}}
I only have to pull the {{log-star}} function template from Wikipedia, I'll do it today. (In Category:Mathematical function templates you will find lots of other function templates...)
From your imported template, we will have to remove all calls to Template:OEIS2C, e.g. replace {{OEIS2C|A002145}} by A002145.
Daniel Forgues 00:59, 10 May 2013 (UTC)
That's awesome, thanks! Yes, the OEIS2C template will have to go, and I'll have to roll the user templates back into the page. Charles R Greathouse IV 13:10, 10 May 2013 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Dear Daniel:

(this is cc from my note to 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 12:04, 17 May 2013 (UTC)

### Logged off every five minutes

Why do I have to log back on every few minutes? — Daniel Forgues 19:51, 27 June 2013 (UTC)

### Copying integer sequences in the wiki is useful for wiki searches

The advantage of copying integer sequences in wiki pages is that Extension:MWSearch/Extension:Lucene-search can find wiki pages from sequence terms! Now that the sequence

{1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, 4, 8, 2, 0, 4, 5, 8, 6, 8, 3, 4, 3, 6, 5, 6, 3, 8, 1, 1, 7, 7, 2, 0, 3, 0, 9, 1, 7, 9, 8, 0, 5, 7, 6, 2, 8, 6, 2, 1, 3, 5, 4, 4, 8, 6, 2, 2, ...}

has been removed from the page golden ratio, doing the wiki search with 1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9

https://oeis.org/w/index.php?title=Special%3ASearch&search=1%2C+6%2C+1%2C+8%2C+0%2C+3%2C+3%2C+9%2C+8%2C+8%2C+7%2C+4%2C+9%2C+8%2C+9&fulltext=Search

doesn't find the golden ratio page.

For example, try the wiki search with 0, 1, 2, 3, 4, 5, 7, 10, 12, 19, 22, 27, 31, 41, 53, 72, 99, 118, 130, 152

https://oeis.org/w/index.php?title=Special%3ASearch&search=0%2C+1%2C+2%2C+3%2C+4%2C+5%2C+7%2C+10%2C+12%2C+19%2C+22%2C+27%2C+31%2C+41%2C+53%2C+72%2C+99%2C+118%2C+130%2C+152&fulltext=Search

the first search result that you get is Riemann zeta function, because the sequence is on the page (admittedly you have to do some scrolling to find where) in the section

Riemann zeta function#Peaks of the absolute value of the Riemann zeta function along the critical line

where it is the first sequence listed, A117536.

That's why I've been copying integer sequences in the wiki! Should I stop doing so? — Daniel Forgues 03:31, 26 July 2013 (UTC)

### Category named after the page

I don't do this anymore, since the time that I was told not to do so, although I've been doing it for quite a long time since the beginning of the wiki. The original purpose of making a category named after the page was to categorize sequences when they where in the wiki, which was the case in the beginning until they were pulled out, so that the [former] OEIS Wiki page A001622 (previously deleted) was categorized in Category:Golden ratio, where the Golden ratio page was the main page of the category, indexed under *, e.g. [[Category:Golden ratio|*]].

Daniel Forgues 03:57, 26 July 2013 (UTC)

### History of A182514

The simple answer is: In dealing with the right side of (prime(n+1)/prime(n))^n < prime(n) that has not broke use something smaller. The reason for > n comes from n*log(n) < p_n and n*log(n) ~ p_n, and only currently just 6 numbers < 10^18 have gone > n as to make them 'dangerously close' to breaking the conjecture. So, the name is correct.

Other conjectures are related to Firoozbakht conjecture. https://en.wikipedia.org/wiki/Firoozbakht%E2%80%99s_conjecture

John W. Nicholson 00:54, 28 April 2014 (UTC)

I was hinting what you said in the first paragraph, but I wasn't sure that was the case. Thanks for conforming this. — Daniel Forgues 21:53, 28 April 2014 (UTC)
Also, if Firoozbakht conjecture ever fails,
(log(prime(n+1))/log(prime(n)))^n < (1+1/n)^n
maybe the slightly weaker
log(prime(n+1))/log(prime(n)))^n < e

won't? — Daniel Forgues 21:53, 28 April 2014 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── To answer this last question see the comments with http://math.stackexchange.com/questions/1212427/lim-n-to-infty-left-frac-logp-n1-logp-n-rightn-c . John W. Nicholson 03:11, 5 April 2015 (UTC)

### How to add a lemma?

Daniel, how do you add a lemma? I clumsily tried to do add a lemma to Theorem R1 in quadratic integer rings. Alonso del Arte 02:15, 19 May 2014 (UTC)

See the source code at quadratic integer rings#Lemma R1a. — Daniel Forgues 06:32, 28 May 2014 (UTC)

### Revisiting "C"MRB

Some time ago I started a new section in the MRB constant titled "Inquiry on Feb 28, 2013." Can you add to it any or discuss anything from it in other places of the article? Marvin Ray Burns 21:59, 3 October 2014 (UTC)

### Template help

Daniel, I was trying to set up {{citation needed}} and {{fix}} following the basic model of Wikipedia's templates, but I think I've done something wrong with {{fix}}. As the resident template whiz, do you have any ideas?

Charles R Greathouse IV 16:35, 21 November 2014 (UTC)

I will look into it as soon as I have a chance. Currently, I'm looking for a new home for December, so I might not be able to do so promptly (when I get any time, I will gladly delve into it!). — Daniel Forgues 22:47, 21 November 2014 (UTC)
I'm doing my best to try to figure out the requirements of the template... If you gave examples on the doc pages, that would help. — Daniel Forgues 00:46, 28 November 2014 (UTC)

### 3x+1 problem

(from that talk page). I'm not known for my clarity. My comment presumes Collatz is not proven, otherwise disregard. I am fully aware of the way that any sequence ends hitting 2^Q etc. Maybe what I state or conjecture is too obvious but to me it offers a specific line of attack. I will reword in case that helps. My subconjecture is that every sequence will encounter a sequence value lower than itself. As the only implied condition is that we successfully evaluated (confirmed they reached 1) starts ascending from the lowest, this by logic leads to every (higher start) sequence as satisfying Collatz by default. So if I start at 7 or 27 or 8191, (by my subconjecture ) they respectively will encounter a sequence value <7,<27 and <8191. If this property can be proven, it eventually "rolls back" to the initial case of starting at 2, completing the Collatz proof. Fabricating hypothetical sequences, if we start 8191,24574,...7199, we can revert back to (start) 7199,21598,...6101...revert to (start) 6101,18304,...3299 etc etc until we reach (start) 2 for example. Is that more clear? To merely say something like every sequence will reach a power of 2 would just be restating Collatz, but if that statement is easier to prove, ...--Bill McEachen 00:25, 2 April 2016 (UTC)

So, we have at least one of the following three alternatives to prove the Collatz conjecture:
• Every sequence will encounter a sequence value lower than itself;
• Every sequence will encounter a power of 4;
• Every sequence will encounter either a sequence value lower than itself or a power of 4;
•  ?
Other alternatives? — Daniel Forgues 00:58, 2 April 2016 (UTC)
Obviously, if it reaches a power of 4 it necessarily encounters a sequence value lower than itself, but option 3 might be easier to prove... — Daniel Forgues
I see no reason to further specify that it reaches any power of 2 (though it will due to the "rollback" mechanism - it always rolls back to the lowest start sequence (2,1)). A start(VLN) where VLN is some "very large number" is indicted as soon as it hits any power of 2, so I see no need to specify a particular one. I did not specifically check for cases where a power of 2 is encountered before the "lower value", but most likely it does in some cases, but only as the "lower number" itself perhaps? I made the conjecture on a very small data set, I'll have to try to do up some code and assess this part further. Thanks for the continued dialog--Bill McEachen 21:19, 2 April 2016 (UTC)
ok, I have it coded in Pari, I can supply that. From the output, the lower value is never a power of 2, but I did have to add the code to check if a subsequence has been seen (the value before any encountered power of 2). It comes into play immediately for example at start(5), which has been seen from start(3) (3,10,5,...). I will email you the code using the wiki email link. The version I send will have screen output that hopefully is clear.--Bill McEachen 23:54, 2 April 2016 (UTC)
────────────────────────────────────────────────────────────────────────────────────────────────────
I will revert to the last link in the history of 3x+1 problem that seems to work (the server does not send any message, e.g. "time limit exceeded" or whatever, so we we are left wondering whether the database entry of the next version was corrupted somehow, although this is not supposed to happen with modern DBMS)
https://oeis.org/w/index.php?title=3x%2B1_problem&oldid=1562097 [2012-02-24T07:44:01] — Daniel Forgues 17:25, 3 April 2016 (UTC)
I sent an email to Neil Sloane about the last 8 edits of 3x+1 problem failing to render, to make sure there are no other options than to lose the last 8 edits. — Daniel Forgues 17:52, 3 April 2016 (UTC)

## Notes

1. Andrew M. Odlyzko, The first 100 zeros of the Riemann zeta function, accurate to over 1000 decimal places, were computed by Andrew M. Odlyzko of the University of Minnesota at his previous position at AT&T Labs - Research.

## Rigid packings of pennies

To see if any packing of 3 or more pennies is rigid:

1. Make sure all edges connecting penny centers are at angles that are multiples of 60 degrees. This is a must for being rigid.

2. Link together all pennies that touch. That is, DO NOT leave any edges between 2 touching pennies linkless.

3. Make sure that no rotating of some pennies can be done other than a rotation of the whole figure.

You can see that a straight line of 3 pennies is not rigid because either of the side pennies can be rotated to form a triangle. Have you tried to calculate any values past a(7)?? J. Lowell 14:31, 11 October 2016 (UTC)

On https://en.wikipedia.org/wiki/Circle_packing there are circle packings (rigid or not) which are loose packings (with large holes/cavities) so it appears that loose rigid packings should be admissible. Do you consider that the examples that I give on User talk:J. Lowell# Re: A171604 fit your intended definition of packing. All the examples of spider webs are rigid because all the chains are taut (you can't move any penny sideways because that would lengthen the chain and the struts are rigid: they cannot be stretched). — Daniel Forgues 02:21, 12 October 2016 (UTC)
Before trying to calculate any values past a(7), I must be able to find ALL rigid packings of pennies for a given number of pennies: I must be sure I don't miss any! Now, does your definition of rigid packings admits loose rigid packings? — Daniel Forgues 02:31, 12 October 2016 (UTC)
I noticed what you put on my talk page. The third and fifth of your 5 packings of 7 pennies are the same only rotated/reflected differently. Do you see this?? J. Lowell 12:19, 12 October 2016 (UTC)
Correction: the second and third. So, a(7) = 4, not 5. Also, look at the faulty info in your images of 8. Please triple-check to make sure your list is perfect. J. Lowell 13:34, 12 October 2016 (UTC)
I see for a(7): reflection about the 30° upwards diagonal. — Daniel Forgues 01:33, 15 October 2016 (UTC)

## Finding a(8) of A171604

You've proven it to be at least 4. I think you should try to find rules for both a lower bound and an upper bound for each value of a(n) whatever ways you can. J. Lowell 13:43, 14 October 2016 (UTC)

It's not obvious at all how the sequence will grow with n. It also depends on whether or not the spider web loose rigid packings (see User talk:J. Lowell#Re: A171604) are considered as packings or not.
http://mathworld.wolfram.com/Packing.html (either of the whole plane or inside a given boundary: doesn't suit this sequence)
http://mathworld.wolfram.com/CirclePacking.html (inside a given boundary: doesn't suit this sequence)
http://mathworld.wolfram.com/RigidCirclePacking.html (of the whole plane: doesn't suit this sequence)

For this sequence, the packing is neither of the whole plane (since we have a finite number of circles), nor inside a given boundary. — Daniel Forgues 01:33, 15 October 2016 (UTC)

There are examples of loose circle packings (rigid, since they cover the whole plane) on
https://en.wikipedia.org/wiki/Circle_packing
Thus loose circle packings are considered circle packings. — Daniel Forgues 01:40, 15 October 2016 (UTC)

A rigid spider web of pennies (all the chains are taut since the struts are rigid, so this a rigid packing of pennies):

..................o.o.o.o.o.o.o.o.o.o
.................o.o.o.o.o.o.o.o.o.o.o
................o.o.o.............o.o.o
...............o.o...o...........o...o.o
..............o.o...o.o.........o.....o.o
.............o.o...o...o.o.o.o.o.......o.o
............o.o...o.....o.....o.o.......o.o
...........o.o...o.....o.o...o...o.......o.o
..........o.o...o.....o...o.o.....o.......o.o
.........o.o.o.o.o.o.o.o.o.o.o.o.o.o.o.o.o.o.o
..........o.o.....o.......o.o.......o.....o.o
...........o.o.....o.....o...o.....o.....o.o
............o.o.....o...o.o.o.o...o.....o.o
.............o.o.....o.o.......o.o.....o.o
..............o.o.....o.........o.....o.o
...............o.o...o.o.o.o.o.o.o...o.o
................o.o.o.............o.o.o
.................o.o.o.o.o.o.o.o.o.o.o
..................o.o.o.o.o.o.o.o.o.o

Is this rigid packing of circles (with rigid struts between their centers) admissible? — Daniel Forgues 01:45, 15 October 2016 (UTC)
If you can think of multiple ways to extend the sequence depending on what arrangements are rigid, especially if the point they diverge at is at a value of n less than 20, feel free to add the other sequences to the database as separate sequences. J. Lowell 11:43, 15 October 2016 (UTC)

## Do you live in China??

I find it so natural to guess this because you make contributions while I'm in bed and I live in the United States. J. Lowell 14:19, 15 October 2016 (UTC)

I live in Vancouver, B.C., Canada. (Same time zone as West Coast U.S.A.) http://www.timeanddate.com/time/map/Daniel Forgues 02:44, 16 October 2016 (UTC)

## New problem now

Can you do some work on A152466, as well as other sequences that are similar (see my own user [not user talk] page for what I mean.) Do you have GNFS on your computer?? J. Lowell 12:29, 23 October 2016 (UTC)

## Re: A036462 Conjecturally, a power of 2 written in base 3 cannot have this many 0's.

Copy of email from David W. Wilson:

OeisWiki e-mail

Oct 21 (7 days ago)

to me
> Re: A036462 Conjecturally, a power of 2 written in base 3 cannot have this many 0's.

> Are you the author of the conjecture?

Let f(k) = number of 0's in 2^k (base 3).
My conjecture is that f(k) never assumes the values in the sequence.

This rests on a deeper conjecture which implies that for large k, the digits in 2^k (base 3) are uniformly distributed.
(which is an instance of a broader conjecture that the digits in large a^k (base b) are uniformly distributed if a >= 2 and b >= 2 are coprime).
This conjecture implies that about 1/3 of the digits in large 2^k (base 3) are 0's (since the possible digits are 0, 1 and 2).
There are about (log 3/log 2) k =~ 1.585 k digits in 2^k (base 3), if about 1/3 of these are 0, we have f(k) =~ ((log 3/log 2)/3) k =~ 0.528 k.

Under the uniform distribution assumption, for large k, f(k) should never stray too far from 0.528 k, and that is what we see empirically.
So if we want to find f(k) = 2013, we should look for k with f(k) =~ 0.528 k = 2013, which is to say, k around 3810.
For k much larger than 3810, say k = 6000, we would expect the number of 0's to be around f(k) ~= 0.528 * 6000 = 3170.
It would be unlikely verging on miraculous if any 2^k (base 3) were to have only 2013 digits for any k > 6000.
So if we check all k <= 6000, and find no 2^k (base 3) with 2013 0's, we can be utterly confident that no such k exists, that is, no f(k) = 2013.

I generated the sequence by computing 2^k (base 3) over a large range of k, and publishing the numbers that did not occur as f(k) on that range.
That's all the magic there is.

> A reference or link to some book/paper/web site should be provided to document/explain the conjecture.

Even the simplest questions in this arena are unanswered.
For example, 2^86 = 77371252455336267181195264 has no 0 in base 10.
No one has found a larger 2^k without a 0, no one has proved there isn't one.

> There is no recurrence/formula/GF or algorithm provided to obtain the terms of the sequence! Thus, there is no way to verify or extend the sequence...

I know of no way PROVE the terms correct, that's why the title says "Conjecturally".
You can verify and extend the terms by doing what I did: compute 2^k (base 3) for a large number of k, count the 0's, and see which counts don't show up.

Is the sequence finite?

Goo question. My feeling is no.

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Daniel Forgues 01:54, 29 October 2016 (UTC)