Look and Say Sequence

We have about 8 minutes for class today. I thought we would spend some time discussing the Look and Say Sequences. They have many fascinating properties, which are certainly worth discussing at any level.

First, I love the idea of Conway's constant. This sequence seems to jump all over the place, but the rate of growth always converges to about 1.303 (except the degenerate sequence, 22, which is also a fascinating thing to discuss).

This is especially interesting, because earlier steps really jump all over the place!

Conway explains in this Numberphile video that each sequence is like a compound, but made from different elements. He has found that there are 92 distinct elements, matching the first 92 elements of the periodic table.