  We study the condition for a topological superconductor (TS) phase with end
Majorana fermions to appear when a quasiperiodic lattice modulation is applied
to a one-dimensional quantum wire with strong spin-orbit interaction situated
under a magnetic field and in proximity to a superconductor. By density-matrix
renormalization group analysis, we find that multiple topological phases with
Majorana end modes are realized in finite ranges of the filling factor, showing
a sequence of reentrant transitions as the chemical potential is tuned. The
locations of these phases reflect the structure of bands in the non-interacting
case, which exhibits a distinct self-similar structure. The stability of the TS
in the presence of an on-site interaction or a harmonic trap potential is also
discussed.
