Posted by: Prof. Kate | November 29, 2008

## A Mysterious Sequence

Hi all,

A good friend of mine showed me this sequence.  I thought you might enjoy figuring out what it is.

1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, …

Once you’ve figured out the trick to generating the sequence, look it up on Sloane’s On-line Encyclopedia of integer sequences to find out a little bit more about it.  Amazingly, it has not yet been proven that the limiting proportion of 1’s and 2’s is half-and-half, that is to say

$\lim_{\# terms \rightarrow \infty} \frac{\# 2's}{\# terms} = 1/2,$

although it seems to be true according to data generated by computer so far.

Happy Thanksgiving!

Prof. Kate.