The effects of sodium counterion presence and chain length on the structure and dynamics of single DNA strands of polythymidylate were studied by means of molecular dynamics simulations. The importance of the base-base stacking phenomenon increases with the chain length and partially reduces the flexibility of the strand. Sodium ions directly interact with the phosphate groups and keto oxygens of the thymine bases, complexes showing lifetimes below 400 ps. Simultaneous phosphate and keto complexes were observed for one of the sodium ions with lifetimes around 1 ns. The implications of such complexes in the folding process experienced by the strand are considered. Structurally, cation inner- and outer-sphere complexes were observed in the coordination of phosphate groups. For the inner-sphere complexes, the structural information retrieved from the simulations is in very good agreement with experimental data. The diffusion properties of the sodium ions also reflect both types of coordination modes.