A solution
In the last puzzle I asked if anybody could find the pattern governing the sequence {1, 11, 21, 1211, 111221, 312211, …}. Leafdude got the answer first, and mequemeyahorahueloapollo rightly added that this is called the “Look and Say” sequence. You read off the digits present in the nth term to get the next one. You can actually start this pattern with any “seed”; for instance, starting with 42, the next few terms are 1412, 11141112, and 31143112. If you start with the seed “1”, the only numbers that ever appear are 1’s, 2’s and 3’s. Also, the terms tend to get larger by 30% with each step. A lot of what we know about Look and Say sequences is due to John H. Conway, who is simply one of the coolest dudes breathing.
