In this paper we introduce the well distributed occurrences (WDO) combinatorial property for infinite words, which guarantees good behavior (no lattice structure) in some related pseudorandom number generators. An infinite word $u$ on a $d$-ary alphabet has the WDO property if, for each factor $w$ of $u$, positive integer $m$, and vector $\mathbf v\in\mathbb Z_{m}^{d}$, there is an occurrence of $w$ such that the Parikh vector of the prefix of $u$ preceding such occurrence is congruent to $\mathbf v$ modulo $m$. We prove that Sturmian words, and more generally Arnoux-Rauzy words and some morphic images of them, have the WDO property.