We study a simple nanocomposite, consisting of a single spherical nanoparticle in a dense melt of coarse-grained copolymer chains, using molecular dynamics simulations. The polymers contain equal amounts of two monomer types, which differ only in their monomer-nanoparticle interaction (adsorption) strengths, and are placed in a random sequence or in a sequence of alternating blocks with various block lengths. This model is motivated by a need to understand copolymer sequence effects relevant to designing tire tread compounds, given the synthetic ability to adjust copolymer architecture (e.g., amount of blockiness) in styrene-butadiene rubbers and the ability to choose fillers and covering agents that functionalize the filler particles to give them different affinities for the styrene and butadiene monomers (it is also possible to use coupling agents, which form covalent bonds between filler particles and polymer chains). Our simple, generalized model considers linear polymers of uniform length that are not cross-linked, and thus we do not attempt to capture the overall mechanical properties of tire tread materials. Instead, we focus our analysis on how copolymer sequence impacts polymer adsorption on the nanoparticle, known to be a significant factor in determining polymer nanocomposite properties. We find that copolymer sequence impacts both the range and magnitude of the interphase of slowed dynamics surrounding the nanoparticle, with longer block lengths yielding a greater reduction in mobility over a wider region.