3
$\begingroup$

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

  • 0
    @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.

  • 0
    @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
11

I was told, that every mathematician would know this sequence

Mmm I highly doubt that.

6

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