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From: Peter T. Breuer on 24 Sep 2005 23:10 Unruh <unruh-spam(a)physics.ubc.ca> wrote: > "Peter T. Breuer" <ptb(a)oboe.it.uc3m.es> writes: >>Unruh <unruh-spam(a)physics.ubc.ca> wrote: >>> "Peter T. Breuer" <ptb(a)oboe.it.uc3m.es> writes: >>>>Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >>>>> In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>>>>> Jean-David Beyer <jdbeyer(a)exit109.com> wrote: >>>>>>> Peter T. Breuer wrote (in part): >>>>>>>> Here. Here's a chance for you. Next number in this series, please: >>>>>>>> >>>>>>>> 1 2 4 6 10 12 .. >>>>>>>> >>>>>>>> Answers by next friday. >>> There are an infinite number of answers. Any number from minus infinity to >>> infinity can be justified as the next number. >>Well, justify "42" to me then! > 1-211/20*x+4459/180*x^2-905/48*x^3+959/144*x^4-263/240*x^5+49/720*x^6 Very good! (I suppose - I am not going to evaluate that). Urrrr, I suppose that one can just write Sum f(n)/An (x-1) .. (x-n-1) (x-n+1) ... (x-7) where f(n) is the sequence I gave, and An is (n-1) .. (-1) (1) ... (n-7) I'm not going to check if that gives your polynomial. >>(the series is actually perfectly well defined). > Of course it is. You wrote it down up there. Nevertheless, there is a "much simpler" way of writing it down than writing out its elements one by one! Peter
From: Michael Heiming on 25 Sep 2005 01:52 In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: > Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >> In comp.os.linux.setup Unruh <unruh-spam(a)physics.ubc.ca>: >>> Michael Heiming <michael+USENET(a)www.heiming.de> writes: >>>>In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>>>> Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >>>>>> In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>>>>>> Jean-David Beyer <jdbeyer(a)exit109.com> wrote: >>>>>>>> Peter T. Breuer wrote (in part): >>>>>>>>> Here. Here's a chance for you. Next number in this series, please: >>>>>>>>> >>>>>>>>> 1 2 4 6 10 12 .. >>>>>>>>> >>>>>>>>> Answers by next friday. >>>>>> 22 >>>>> No, but that's not a bad attempt. It's a later member of the series all >>>>> right! >>>>So it's "18" (euler phi function or so), you used? >>> Or 14 (base 8) >> Exactly there are multiple possible answers. Peter was trying to >> "fool" us here. with this nice attempt. ;-) > No, I couldn't fool you lot! There was no trick! Sure there was, put "fool" into quotation marks because of this. The "trick" was just that there are multiple possible answers, so it was just a random possibility for us to guess the one you had in mind. Presuming you were honest not to switch the answer, while we were looking for it. ;-) BTW Nice excess, just be aware that it seems more or less impossible to drop you from the top stats position for this week.;) -- Michael Heiming (X-PGP-Sig > GPG-Key ID: EDD27B94) mail: echo zvpunry(a)urvzvat.qr | perl -pe 'y/a-z/n-za-m/' #bofh excuse 186: permission denied
From: Enrique Perez-Terron on 25 Sep 2005 04:53 On Sun, 25 Sep 2005 05:00:17 +0200, Peter T. Breuer <ptb(a)oboe.it.uc3m.es> wrote: > Enrique Perez-Terron <enrio(a)online.no> wrote: >> On Sat, 24 Sep 2005 22:55:39 +0200, Peter T. Breuer >> <ptb(a)oboe.it.uc3m.es> >> wrote: > >>> Peter T. Breuer <ptb(a)oboe.it.uc3m.es> wrote: >>>> Jean-David Beyer <jdbeyer(a)exit109.com> wrote: >>>>> Peter T. Breuer wrote: >>>>>> Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >>>>>>> In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>>>>>>> Jean-David Beyer <jdbeyer(a)exit109.com> wrote: >>>>>>>>> Peter T. Breuer wrote (in part): >>>>>>>>>> >>>>>>>>>> 1 2 4 6 10 12 .. > >> Add one and you get a prime. > >> f(n) = "the n'th prime, minus one" > > Very good. Correct. > > Exactly how did you think of it? That's very hard to produce by > analytic resolution. No analytic resolution. After having warmed up the gray matter with writing the previous post, I asked myself again: Don't I know any simple sequence that increases in this somewhat irregular fashion? and something inside there echoed a word from the previous post: "the sequence of primes". I looked at the first number, 1, and thought "The first prime is two, difference: one." Then I realized it instantly. I had it perhaps no more than 30 seconds after posting. Do you know the Physics researcher's proof that all odd numbers are prime? 1 satisfies most definitions of 'prime', 3 is one, and so is 5. 7 too. looks good. 9... must be a measurement error, lets get some more samples. 11: good, 13: good. QED. Actually I concluded from writing the first post that the solution should involve at most a single choice for a starting value, and hardly more than two more steps. But, as touched in the post, the initial set of "primitive" operations was too narrow. Actually the original idea when I started "analyzing" the problem in the post was that I felt I was blocking myself from seeing the obvious, and I have sometimes managed to force myself over that barrier by looking hard at the search space definition. I started writing with the conviction I was not going to post it, but since I did not find out much I thought perhpas it could spark off something in one of the others. It did, but in myself. -Enrique
From: Peter T. Breuer on 25 Sep 2005 05:25 Michael Heiming <michael+USENET(a)www.heiming.de> wrote: > In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >> Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >>> In comp.os.linux.setup Unruh <unruh-spam(a)physics.ubc.ca>: >>>> Michael Heiming <michael+USENET(a)www.heiming.de> writes: >>>>>In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>>>>> Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >>>>>>> In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>>>>>>> Jean-David Beyer <jdbeyer(a)exit109.com> wrote: >>>>>>>>> Peter T. Breuer wrote (in part): >>>>>>>>>> 1 2 4 6 10 12 .. >>>>>>>>>> >>>>>>>>>> Answers by next friday. >>>>>>> 22 >>>>>> No, but that's not a bad attempt. It's a later member of the series all >>>>>> right! >>>>>So it's "18" (euler phi function or so), you used? The euler phi function goes 1 1 2 2 4 2 6 4 6 4 10 4 12 6 8 8 so I don't see the resemblance! (phi(n) is the number of coprime numers to n in the range 1:n). Are you taking only the (new) peaks? That would give you 1 2 4 6 10 12 OK! Of course the peaks are p-1, where p is prime ;). I'm surprised you didn't notice. >>>> Or 14 (base 8) That attempt gets the first element wrong. >> No, I couldn't fool you lot! There was no trick! > Sure there was, put "fool" into quotation marks because of this. > The "trick" was just that there are multiple possible answers, so There are going too be "answers" of varying complexity that explain the observed facts (the elements of the series discovered so far). The problem is to discover a simple explanation with predictive power. I was willing to give more elements of the series on request. But that should not be necesary, since the "right" answer is self-evident once it is discovered. > it was just a random possibility for us to guess the one you had There is clearly only one good/best answer. > in mind. Presuming you were honest not to switch the answer, > while we were looking for it. ;-) > it seems more or less impossible > to drop you from the top stats position for this week.;) :( Peter
From: Michael Heiming on 25 Sep 2005 06:00
In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: > Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >> In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>> Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >>>> In comp.os.linux.setup Unruh <unruh-spam(a)physics.ubc.ca>: >>>>> Michael Heiming <michael+USENET(a)www.heiming.de> writes: >>>>>>In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>>>>>> Michael Heiming <michael+USENET(a)www.heiming.de> wrote: >>>>>>>> In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: >>>>>>>>> Jean-David Beyer <jdbeyer(a)exit109.com> wrote: >>>>>>>>>> Peter T. Breuer wrote (in part): >>>>>>>>>>> 1 2 4 6 10 12 .. [..] > 1 2 4 6 10 12 > OK! Of course the peaks are p-1, where p is prime ;). I'm surprised you > didn't notice. Yep, didn't looked that close it somehow reminded me of euler summatory function or so, but then it's decades ago I had to do with those.;) [..] > There are going too be "answers" of varying complexity that explain the > observed facts (the elements of the series discovered so far). The Exactly what I meant there are quite a few answers possible, complexity or not. [..] -- Michael Heiming (X-PGP-Sig > GPG-Key ID: EDD27B94) mail: echo zvpunry(a)urvzvat.qr | perl -pe 'y/a-z/n-za-m/' #bofh excuse 460: Here's a nickel, kid. Get yourself a better computer. |