A chaotic cousin of Conway's recursive sequence

I introduce the recurrence D(n) = D(D(n-1))+D(n-1 -D(n-2)), D(1) = D(2) = 1 , and study it by means of computer experiments. The definition of D(n) has some similarity to that of Conway's sequence defined by a(n) = a(a(n-1))a(n - a(n-1)), a(1) = a(2) = 1. However, unlike the completely regular and predictable behaviour of a(n), the D-numbers exhibit chaotic patterns. In i ts statistical properties, the D-sequence shows striking similarities with Hofstadter's Q(n)-sequence, given by Q(n) = Q(n - Q(n-1)) + Q(n - Q(n-2)), Q(1, = Q(2) = 1. Compared to the Hofstadter sequence, D shows higher struct ural order, it is organized in well-defined "generations", separated by smo oth and predictable regions. The article is complemented by a study of two further recurrence relations with definitions similar to those of the Q-num bers. There is some evidence that the different sequences studied share a u niversality class.