What are the manifolds whose Curvature tensor has a globally vanishing $k$th order covariant derivative

Let $$(M,g)$$ be a boundaryless Riemannian manifold whose curvature tensor have the property that there exists $$k\geq 2$$ such that $$\nabla^k R\equiv0$$. What is known about such Riemannian manfiolds ? Is there a classification ?

I vaguely remember that I came (a long time ago) across a paper that claims that if $$(M,g)$$ is also known to be irreducible then we must have $$\nabla R\equiv 0$$. However, I cant find this paper anymore and I m starting to doubt myself so I decided to ask the question here.