The recently published general method of studying adsorption on terraces and nanotubes is applied to adsorption on nanotubes in hollows or on-tops, which form a zigzag equilateral triangular adsorbate lattice. We consider adsorbate-adsorbate first- and second-neighbor interactions, with attractive first neighbors. In addition to empty and full coverage, there are three phases of occupational characteristics which are independent of the diameter of the nanotube. The low temperature energy phase diagram is the same for nanotubes of increasing diameters and, thus, is also valid in the infinite-diameter limit. As expected, this diagram is the same as that of the infinite-width limit of an equilateral triangular terrace, on which we have recently reported. The current study also includes temperature effects on the phases and the transition between phases.