  We identify the structure of the lexicographically least word avoiding
5/4-powers on the alphabet of nonnegative integers. Specifically, we show that
this word has the form $p \tau(\varphi(z) \varphi^2(z) \cdots)$ where $p, z$
are finite words, $\varphi$ is a 6-uniform morphism, and $\tau$ is a coding.
This description yields a recurrence for the $i$th letter, which we use to
prove that the sequence of letters is 6-regular with rank 188. More generally,
we prove $k$-regularity for a sequence satisfying a recurrence of the same
type.
