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 its 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 structural order. It is
organized in well-defined "generations'', separated by smooth and
predictable regions.
The article is complemented by a study of two further recurrence
relations with definitions similar to those of the $Q$-numbers.
There is some evidence that the different sequences studied
share a universality class.