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What is this sequence? I was told, that every mathematician would know this sequence, because it's subject of research. Does anyone recognize it?

Thanks in advance, Florian

  • 24
    It is not true that every mathematician would know this sequence. I can think of at least one counterexample.2011-05-05
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    I'm not familiar with it, and the OEIS neither. I suggest you ask the person that told you that what he meant.2011-05-05
  • 0
    I'd like to ask this person, but it's a riddle and i try to solve it for nearly 4 hours without any result :)2011-05-05
  • 2
    And why don't you tell us where you heard about it from, who told you "every" mathematician knows the sequence, and why you are only giving us the first 7 terms.2011-05-05
  • 0
    @KCd: because i only have the first 7 terms, i get one every weekday...2011-05-05
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    A riddle? Then this is not really a serious sequence, or if it is then it is in disguised form.2011-05-05
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    levu: then wait one month and then come back.2011-05-05
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    @KCd: Am I the counterexample? If not, then there are at least two counterexamples... :-D2011-05-05
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    Yes Asaf, I was thinking of you!2011-05-05
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    @Asaf, KCd: Beware, this kind of reasoning about you knowing that everyone knows that someone is actually a counterexample and this sort of things usually ends with a massive ritual suicide...2011-05-05
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    @PseudoNeo: I did not reason that. I only asked whether or not he was talking about me when stating a counterexample, since I am one. KCd only said that he did in fact think about me. No one else said anything else about anyone else.2011-05-06
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    @Asaf: I know. I just made a stupid joke.2011-05-06
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    So what was the next term?2011-08-06
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    the next term of this secret series is surely 342011-08-10
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    @Gottfried: the next term of the sequence is 42. Always... http://en.wikipedia.org/wiki/Phrases_from_The_Hitchhiker%27s_Guide_to_the_Galaxy#Answer_to_the_Ultimate_Question_of_Life.2C_the_Universe.2C_and_Everything_.2842.292011-08-10
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    @Didier: uhmm, I forgot... Unfortunately in wikipedia a link to the great mathematician G.H.Hardy, the true inventor of that 42-matter was deleted: http://go.helms-net.de/math/divers/GHHArdyAndTheNumber42.htm2011-08-10
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    @Gottfried: Indeed... Thanks for the link.2011-08-10

3 Answers 3

26

This type of puzzle is underspecified; any integer could come next, and there would be nothing in the problem statement to show that that integer is not the correct solution.

Perhaps the following is what was in mind: consider the Collatz sequence starting with 7. It goes 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. If you interleave this with the sequence 1, 2, 3, ... you get the sequence in the question.

Or perhaps it's the sequence of values of the polynomial $$ (-1/60)(39x^6-934x^5+8800x^4-41300x^3+100451x^2-118116x+51000) $$ when you plug in 1, 2, 3, 4, 5, 6, and 7.

Which answer you think is "best" is just a matter of taste.

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    Your first answer might have lower Kolmogorov complexity in some model (certainly as more terms are added).2011-05-05
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    wow, thanks :) I have to look, if the answer tomorrow is 34, if yes, i think this is collatz, and i think, every one knows collatz, so the statement "every mathematician knows it" is true from a specific point of view :)2011-05-05
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    Because it is *obviously* underspecified the original question has something "meta" in mind, so the hints around the problem itself usually give the key. I second the "Collatz" idea - but because it is somehow obvious/too easy and the hint not much original there is not really fun at me...2011-05-05
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    @Carl: Thanks for the answer. Mathematicians get totally bent-out-of-shape with such open-ended (multivalued?) sequences. I once asked a professor what the solution to "3, 4, 3, 5, 3, 6, 8, 7, ... " was, and his reply was pretty rigid. (+1) I actually had never heard of the Collatz sequence. (Hint - my sequence is specific to the English language)2011-05-05
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    @levu: I have never ever before heard of the Collatz sequence. In fact I am fairly certain that only a proper subset of mathematician have heard of it. It is exactly the set of all mathematicians which have heard of it.2011-05-05
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    @The Chaz : While I disagree that it is always "just a matter of taste" how to continue a sequence of six integers, I can tell you very clearly that the annoying part for mathematicians is not the pattern-recognition part, but the moment where you ask for **the** solution and announce to judge whether they will get it **right**.2011-05-05
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    @use : I hear you on that. Maybe a comparison with Watson (the Jeopardy game show-winning computer) would work... This machine was programmed to compute a confidence value for each answer, then submit *one* answer, only if a certain threshold is passed. It's subjective... But when you "get" *the* (sic) solution to, say, my example, you will know it! And it won't be because you systematically formulated a polynomial or piecewise function. You'll guess the rule, try it, and be pleasantly surprised when it works! The fun in this process can be lost on the pedant.2011-05-05
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    @The Chaz: And what if a certain sequence fits *several* rules? For example, $2,4,\ldots$ - is it the even numbers? Powers of $2$ or maybe numbers which are not invertible in $\bmod 10$, which implies the next one is $5$?2011-05-05
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    @Asaf: I get your point, and have for many years. Each of {6,8,5} has a pretty simple justification, so to see this on a scantron test would be ridiculous! If you put "31" as next in the sequence 2,4,8,16... With reasoning related to intersecting chords of a circle, *that* would be interesting and equally valid as "32". But to me, some 763rd degree polynomial that might possibly never see integer values again is not interesting. Very subjective, I know!2011-05-05
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    @user9325: I would claim that to be a proper puzzle, "almost everybody" would agree that the "right" answer is right, once it is explained. And this one (assuming Collatz) fails that test. One thing that helps is giving enough terms that it "can't be anything else." I like these (at least good ones), but admit that they are not mathematics.2011-05-06
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    @Asaf: and there's the [Moser problem](http://mathworld.wolfram.com/CircleDivisionbyChords.html) as well.2011-05-06
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    @The Chaz: If you ask one of my engineering students they will tell you that mathematics is only a mere tool and has no interest on its own, I have heard many grown and well worked engineers say that as well. If you ask many mathematicians they will tell you that the play in set theory is not too interesting, and that I have heard from actual mathematicians (not to mention math students). I fail to see how the fact you find $8$ as the most exciting continuation of $2,4,\ldots$ relevant to the issue that mathematicians don't know or care about **the** rule for the next element in the sequence.2011-05-06
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    @The Chaz "The fun in this process can be lost on the pedant." Or on the person whose native language is not English which includes "almost everybody".2011-05-06
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I was told, that every mathematician would know this sequence

Mmm I highly doubt that.

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The terms of odd rank are the dimensions of the irreducible representations of the Lie algebra sl(2).