  We discuss the base 3/2 representation of the natural numbers. We prove that
the sum of digits function of the representation is a fixed point of a 2-block
substitution on an infinite alphabet, and that this implies that sum of digits
function modulo 2 of the representation is a fixed point $x_{3/2}$ of a 2-block
substitution on $\{0,1\}$. We prove that $x_{3/2}$ is mirror invariant, and
present a list of conjectured properties of $x_{3/2}$, which we think will be
hard to prove. Finally, we make a comparison with a variant of the base 3/2
representation, and give a general result on $p$-$q$-block substitutions.

Combinatorics