One of the simplest examples of W-algebras is the Bershadsky-Polyakov vertex algebra W∧k(g,f), associated to g=sl(3) and the minimal nilpotent element f. We study the simple Bershadsky-Polyakov algebra W_k at positive integer levels and obtain a classification of their irreducible modules. In the case k=1, we show that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple affine vertex superalgebra $L_{_}k^{\prime}(osp(12))$ for k′=−5/4. This is joint work with D. Adamovic.