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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

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It is not true that every mathematician would know this sequence. I can think of at least one counterexample. –  KCd May 5 '11 at 17:50
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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. –  Gadi A May 5 '11 at 17:50
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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. –  KCd May 5 '11 at 17:51
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Yes Asaf, I was thinking of you! –  KCd May 5 '11 at 18:02
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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... –  PseudoNeo May 5 '11 at 23:58

3 Answers 3

up vote 24 down vote accepted

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). –  Yuval Filmus May 5 '11 at 19:01
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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 :) –  levu May 5 '11 at 19:04
    
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... –  Gottfried Helms May 5 '11 at 19:47
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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. –  Phira May 5 '11 at 21:56
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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! –  The Chaz 2.0 May 5 '11 at 23:33

I was told, that every mathematician would know this sequence

Mmm I highly doubt that.

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