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Re: [math-fun] Sum of reciprocals of 8877690 integers with distinct digits
by Schroeppel, Richard 08 Apr '06

08 Apr '06

[This is from Eric Weisstein, sent a week ago.] ------ On Thu, 30 Mar 2006, Robert Baillie wrote: > Problem E2533 in the American Mathematical Monthly (1975 or 1976) says there > are 8877690 integers that have distinct digits. The problem is to estimate > the sum of their reciprocals. > > I thought I read someplace that someone had computed the exact sum. Does > anyone know how big the numerator and denominator are? And, by the way, what > is the approximate sum? Assuming I have not made a silly computation error, the exact sum is 6745140117...4801548051 (14816583 digits) ----------------------- 7553392231...8000000000 (14816582 digits) given to 100 digits by 8.929948174755443424171179403981525048667286767255408480936913993018768120557239657437064181411273952 which will appear shortly on http://mathworld.wolfram.com/Digit.html http://www.research.att.com/~njas/sequences/?q=A117914 Cheers, -Eric

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[math-fun] Re : Early Goodbyes
by David Wilson 06 Apr '06

06 Apr '06

Re : Re : Early GoodbyesI've managed to calm things down for the moment. Life without money is a never-ending roller coaster ride.

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[math-fun] Intransitive dice re-tossed
by dasimov＠earthlink.net 05 Apr '06

05 Apr '06

Does anyone know if there is a recent summary of all that's known about intransitive dice? Searching on MathSciNet doesn't seem to get me very far. Suppose you have a cyclically ordered sequence of n dice, each of which has s sides, and each of which beats the (cyclically) next one with the same probability p > 1/2. I believe I saw some reference that claims p <= 3/4 under all circumstances; maybe another that sharpened this to p <= sqrt(5 - 1)/2 = .618.... --Dan

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[math-fun] Bases for closure of a finite field?
by Mike Stay 05 Apr '06

05 Apr '06

For finite fields, every element can be written as a finite power of a generator, and there are typically two different bases used: - the polynomial basis, where elements are written as sums of consecutive powers of a generator - the normal basis, where elements are written as sums of (prime-power) powers of an element For example, take polynomials over F_2 mod x^4-x-1. Then x is a generator and we can write every element y in the polynomial basis as y = \sum_{i=0}^3 y_i x^i where y_i is in F_2. Let z=x^3. Then we can also write y in the normal basis as y = \sum_{j=1}^4 y_j z^{2^j} Let a_n = lcm(1,...,n). Then F_{p^{a_n}} contains a copy of F_{p^{a_m}} for each m less than n. "The" limit (there are actually several, but they're all isomorphic as fields) is the algebraic closure of F_p. I haven't been able to find any information about how to write down specific elements of this field. It looks like there's an "infinitesimal" generator x, and every element of the field can be written as a rational root of unity times a finite power of x. Is that right? Are there bases corresponding to the polynomial or normal basis for the closure? If not, what kind of bases are there? -- Mike Stay metaweta(a)gmail.com http://math.ucr.edu/~mike

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[math-fun] Early Goodbyes
by David Wilson 05 Apr '06

05 Apr '06

I lost my last computer job on April 11, 2002. I have not been able to break back into the industry since, I have only been able to find temporary work. At the moment, I'm working at a supermarket deli. My forays into teaching and medical transcription have come up empty. Today, the strain broke my marriage. On my desk beside me sit my wife's engagement ring, hers and my wedding ring in a pile. After the divorce, I will have no car, no lodging, and will not be earning enough to keep myself alive. I certainly won't have Internet, so my chances of ever getting another decent job are now officially nil. It was nice knowing you all. -------------------------------- - David Wilson

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Re: [math-fun] Very important moment coming up momentarily
by dasimov＠earthlink.net 05 Apr '06

05 Apr '06

Henry writes: << Ha! Physicists don't care about these things -- they look for 'coordinate-free' representations... >> Now that you mention it, so do mathematicians... --Dan

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[math-fun] Very important moment coming up momentarily
by dasimov＠earthlink.net 05 Apr '06

05 Apr '06

In just a few minutes it will be 01:02:03 04/05/06 EDT. By morning it will have been 01:02:03 04/05/06 all over the U.S. --Dan

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Re: [math-fun] Very important moment coming up momentarily
by Richard Guy 05 Apr '06

05 Apr '06

You mean June 5: 07-06-05 04:03:02.01 R. On Wed, 5 Apr 2006, zak seidov wrote: > Neil, > is "monment" typo or what: >> Don't blink or you'll miss once-in-a-lifetime monment > Thanks, Zak > BTW > If digital watch shows hundreds of sec (and why not?!) > then we may have next year on May 6 > 01:02:03.04:05:06:07 > > > --- "N. J. A. Sloane" <njas(a)research.att.com> wrote: > >>> By morning it will have been 01:02:03 04/05/06 all >> over the U.S. >> >> Which is a sequence, so I got interviewed by a >> reporter: see >> http://www.post-gazette.com/pg/06094/679172-115.stm >> >> Neil >> > > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.com >

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RE: [math-fun] Very important moment coming up momentarily
by Eric Angelini 05 Apr '06

05 Apr '06

> split a day in 10 hours of 100 minutes of 100 seconds. > cancelled only 2 years later, in 1795. > Some watches were built in this period. > They have now a great value. http://www.fraclr.org/closky/# Best, É.

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[math-fun] April update of multimagie.com
by Christian Boyer 05 Apr '06

05 Apr '06

April update of www.multimagie.com/indexengl.htm, including details of some news previously announced through [math-fun]: - multiplicative cubes (thanks again to Edwin Clark for his checkings) - first known 6x6 bimagic square, by Jaroslaw Wroblewski - smallest possible pandiagonal Sudoku - and some other news But you will see that it remains a lot of open questions! As for example the very difficult factorization problem in 3 dimensions, asked for multiplicative cubes. Best regards. Christian.

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