May 2005 - mathfun@mailman.xmission.com

[math-fun] ham
by David Wilson 10 May '05

10 May '05

You will notice that my posts sometimes often include "ham" among the recipients. This will result in a bounce if you "reply all" to my posts, and several people have commented on this. By way of explanation: I am currently using MicroSuck Outlook Express, the free but rather hobbled version of Outlook that came on my PC. About a year ago, my spam ratio finally exceeded my patience ratio. Since Outlook Express does not provide an effective spam filter, I decided to try Spambayes, of which I had heard good things (which were true). Most mail programs provide API hooks allowing Spambayes filtering to be integrated into the program. Not so Outlook Express. When using Spambayes with Outlook Express, Spambayes must be inserted upstream of Outlook Express, where it marks incoming mail so that Outlook Express can classify it using its (lame) native mail filters. From a small number of unsavory choices, Spambayes chose to include "ham", "spam" or "unsure" in the "To:" line, so that Outlook Express could identify and route spam by detecting "spam" in the "To:" line. I am guessing that this Spambayes feature was included solely to deal with Outlook Express. Unfortunately, because good incoming mail has "ham" in the "To:" line, "ham" is replicated to the "To:" line of reply-alls to that mail. If I fail to remove "ham" from the recipients, it makes its way into the mailing list and subsequent "reply-alls". Since "ham" is not a valid recipient, bounces occur. I don't know if Seqfan and Math-Fun could filter "ham" out of the "To:" line of incoming mail, this would solve the mailing list problem. A more general solution would be for Spambayes to allow me to put "spam" in the "To:" line of spam, but leave the "To:" line of ham alone; this is consistent with my own personal mail filtering. - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] Courtesy
by David Wilson 10 May '05

10 May '05

Just a reminder. As a courtesy to subscribers who labor under restrictions or charges for downloads or disk space, Seqfan and Math-Fun mailing lists encourage voluntarily limiting the size of messages. We should all try to avoid posting huge data tables, large amounts of irrelevant quoted text, and/or data file attachments where possible. Personally, if a have voluminous data that I think may be of interest to list, I will offer my data on request. ----- Original Message ----- From: "Robert G. Wilson v" <rgwv(a)rgwv.com> To: <ham>; <alexandre.wajnberg(a)skynet.be> Cc: "Eric Angelini" <keynews.tv(a)skynet.be>; <seqfan(a)ext.jussieu.fr> Sent: Monday, May 09, 2005 7:55 PM Subject: Re: Semiprime's dividers concatenated > Dear Alexandre, > > They do not quite cycle. Using the Mathematica coding: > t = Union[ Flatten[ Table[ FromDigits[ Join[ IntegerDigits[ Prime[i]], > IntegerDigits[ Prime[j]]]], {i, 250}, {j, 250}]]]; Mod[t, 10] produces a > sequence that never quite falls into a pattern. > > Sincerely yours, Bob. > > 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, > 3, 5, [Very large data table and remainder of message elided]

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[math-fun] polygon inscribing constant
by R. William Gosper 10 May '05

10 May '05

is Weisstein's name for the x = pi case of inf /===\ | | x | | cos(-), | | n n = 3 the inner/outer radius ratio of the annular nesting of all the regular polygons, alternated with circles. (With the right z(r), might make a nice drinking cup.) Perhaps equivalent to his Mathworld circumscribing formula, simply expand the log of the quadrisected product, inf inf inf /===\ /===\ /===\ | | x | | x | | x log(( | | cos(-------)) ( | | cos(-------)) ( | | cos(-------)) | | 4 n + 3 | | 4 n + 4 | | 4 n + 5 n = 0 n = 0 n = 0 inf /===\ | | x | | cos(-------)) | | 4 n + 6 n = 0 4 i 2 i 2 B pi inf 2 i 2 i i 2 i 2 i ==== (1 - 2 ) B (--------------- + (- 1) (2 + 1)) x \ 2 i 2 (2 i)! = > ---------------------------------------------------------- , / 2 i (2 i)! ==== i = 1 a series with convergence radius 3 pi/2, hence 2 lg 3 - 2 ~ 1.17 bits/term. Note the unusual Bern^2. Because B_n ~ n!/(2 pi)^n, the radius appears to be only pi/2 (useless), but the factor 4 i 2 i 2 B pi i 2 i 2 i i 2 i (- 1) 2 --------------- + (- 1) (2 + 1) ~ - ----------- 2 (2 i)! 2 i 3 saves the day, at the cost of 3.17 bits/term of subtractive cancellation. Adding more terms without raising the intermediate precision will actually ruin your accuracy. To 30 places, 1/8.70003662520819450322240985911. --rwg

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[math-fun] (Fwd) [NOBNET 4625] Mathematical Games
by Bernie Cosell 09 May '05

09 May '05

I know that in addition to your likely being interested in this, I know that several of you have contributed to Mathematical Games over the years and so might want to get in touch with Ed... /Bernie\ ------- Forwarded message follows ------- Date: Mon, 8 Nov 2004 06:30:37 -0800 (PST) From: ed pegg <ed(a)mathpuzzle.com> Subject: [NOBNET 4625] Mathematical Games To: nobnet(a)iijnet.or.jp Martin Gardner just recently celebrated his 90th birthday. Also, maa.org is *finally* releasing the entire collection of Mathematical Games on CD rom next month. There were frightening amounts of copyright issues to work out, but they have been resolved. Catalog Code: TDG/FW04 ISBN 0-88385-545-3 List Price: $54.95 This is all 15 Mathematical Games books on a CD-Rom. I'd like to do a "behind the scenes" look at Mathematical Games for an article. Martin did lots, but he avidly used a lot of help from hundreds of people. I'd like to write an article about the background help. If you ever assisted in one of Martin's columns, I'd like to hear from you -- a note about what you did. I'll use these notes in my article. Ed Pegg Jr http://www.maa.org columnist http://www.mathpuzzle.com ------- End of forwarded message ------- -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--

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[math-fun] While playing with A103314
by David Wilson 08 May '05

08 May '05

In attacking A103314, I decided to try to plot the sums of subsets of the roots of 1. For square roots, I got 1 2 1 where numbers count multiplicities of points. The 2 at the origin corresponds to A103314(2) = 2. For cube roots, I got 1 1 1 2 1 1 1 so A103314(3) = 2. For fourth roots, I got 1 2 1 2 4 2 1 2 1 so that A103314(4) = 4. Now, notice that the square root plot includes the vertices you would see sighting a square along its diagonal. The cube root plot includes the vertices you would see sighting a cube along its great diagonal. Is the fourth root plot what you would (might) see sighting a tesseract along its great diagonal? Does the analogy extend to higher roots? - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] Prime signature functions
by David Wilson 08 May '05

08 May '05

I notice that for some sequences, a(n) is a function of the prime signature of a n, that is, a function of the multiset of exponents in the prime factorization of n. For such a function, a(p) will be the same for all primes p, a(pq) will be the same for any two distinct primes p, a(p^2) will be the same for any prime p, etc. For the moment I will call there prime signature functions. Is there a standard name for such functions? There are prime signature functions which are not multiplicative and vice versa. Examples of prime signature functions that are not multiplicative are A001221 (number of prime divisors of n) and A001222 (number of prime divisors with multiplicity). Examples of multiplicative functions that are not prime signature functions are A000010 (totient) and A000203 (sum of divisors). A function that is both prime signature and multiplicative is A000005 (number of divisors of n). A function is both prime signature and mutliplicative if f(p^e) is strictly a function of e. What made me think of this is that I was recently working on A000028. Membership of n in A000028 depends entirely on the prime signature of n, so its membership function is a prime signature function. - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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Re: [math-fun] better posed problem? (small surprise)
by Phil Carmody 07 May '05

07 May '05

From: "Meeussen Wouter (bkarnd)" <wouter.meeussen(a)vandemoortele.com> > > it is a small surprise that, for w = Exp[ 2 Pi I /30 ] alias 1^(1/30) , > w+w^7+w^8+w^18+w^19+w^25 = 0 > no cancellation of symmetric pairs, triples or quintuples in sight, > but w+w^7+w^19+w^25 = -w^13 (* four out of five *) > and w^8+w^18 = -w^28 = +w^13 (* two out of three *) > > could be called "cancellation by missing parts" ;-)) As (a) {0,6,12,18,24} cancels, (b) {0,10,20} cancels, and (c) {0,15} cancels. {5,15,25} cancels, so {5,6,12,18,24,25} cancels. The largest gap (mod 30) between terms is that between 25 and 5, so {0,1,7,13,19,20} is the symmetry-less set with minimal largest member that cancels. You've exploited the gap of 6 between 18 and 24 instead. 2*p*q is easily so minimised - any takers for zeta_210? Phil When inserting a CD, hold down shift to stop the AutoRun feature In the Device Manager, disable the SbcpHid device. http://www.cs.princeton.edu/~jhalderm/cd3/ __________________________________ Do you Yahoo!? Yahoo! Small Business - Try our new resources site! http://smallbusiness.yahoo.com/resources/

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Re: [math-fun] Mark of the Beast reduced to 616
by Henry Baker 06 May '05

06 May '05

Ha, every computer scientist knows that the Mark of the Beast is the Goedel number of EVAL... Maybe Revelations was the first to Goedelize? At 11:37 AM 5/5/2005, Kerry Mitchell wrote: >http://www.canada.com/national/nationalpost/news/toronto/story.html?id=702d… > >Insert your own joke here. > >Kerry

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[math-fun] Mark of the Beast reduced to 616
by lkmitch＠att.net 05 May '05

05 May '05

http://www.canada.com/national/nationalpost/news/toronto/story.html?id=702d… Insert your own joke here. Kerry

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[math-fun] Found in the IHP cellar! 1/2
by Christian Boyer 05 May '05

05 May '05

---- DIOPHANTE magazine I have the chance to have discovered very recently, in the cellar of the Institut Henri Poincaré, Paris, the originals of all the issues of an old magazine on number theory named "Diophante" that everybody thought lost, written in 1948-1952 by André Gérardin at the end of his life. Gérardin (1879-1953), and its first magazine "Sphinx-Oedipe", is one of the most quoted authors referenced by Leonard E. Dickson in his "History of the Theory of Numbers", both Vol 1 and Vol 2. And also one of the most quoted authors referenced by Hugh C. Williams in his 1998 book "Edouard Lucas and Primality Testing". For example, in Diophante, there are several articles written by Aimé Ferrier, holder of the biggest known prime number in 1951: his prime is still today the largest prime found without electronic computer. http://mathworld.wolfram.com/FerriersPrime.html The IHP library will reprint this magazine for some other French libraries. If you know other libraries, out of France, which may be interested by this reprint, send me a message at cboyer(a)club-internet.fr. I will pass the info to the IHP library. To interested people, I can also send my preface published in this reprint (PDF file... written in French). Best regards. Christian.

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