Ulam words and the Ulam sequence

The Ulam sequence is a sequence of positive integers x_n, where x₁=1, x₂=2, and where each x_n for n > 2 is defined to be the smallest integer that can be expressed as the sum of two distinct earlier terms in a unique way. The first few terms of the sequence are 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47. The third term is 3, because 3=1+2. The …