Steve Adler wrote:
If I remember its called a "Morse-Thule sequence"
I've seen this called "Conway's Recursive Sequence" or similar, but not sure that he was the first to think of it. There are a number of variations on the idea.
You might be thinking of the Thue-Morse Sequence
. There may well be a connection, though: each term of the CRS contains only 1,2,3 (so you don't get more than 3 consecutive digits that are the same), whereas the Thue-Morse sequence contains only 0 and 1, with never more than 2 consecutive digits (or even strings
of digits) the same.