  In this paper we present a theoretical investigation of the effect of a
superlattice potential on some properties of non-interacting bosons in one
dimensional lattices with Aubry-And\'re disorder potential. In the first part,
we investigate the single particle localization properties. We find a
re-entrant localization-delocalization transition and the development of
multiple mobility edges for a range of superlattice potential strengths. In the
second part, we study the Bose-Einstein condensation with an additional
harmonic trapping potential. We find that an increase in the superlattice
potential leads to an increase in the depletion of the condensate in the low
temperature limit.
