Antipaths in oriented graphs

We show that for any natural number $k\ge 1$, any oriented graph $D$ of minimum semidegree at least $(3k-2)\mathrm{/}4$ contains an antidirected path of length $k$. In fact, a slightly weaker condition on the semidegree sequence of $D$ suffices, and as a consequence, we confirm a weakened antidirected path version of a conjecture of Addario-Berry, Havet, Linhares Sales, Thomassé and Reed.