  We perform a systematic investigation of the chemical composition of the
inner crust of a neutron star, using the extended Thomas-Fermi approximation,
the Strutinsky integral correction for shell effects, and the BCS approximation
for pairing. Fifteen Skyrme functionals were selected, which cover the range of
values of important bulk properties of infinite nuclear matter, while also
having pure neutron matter (PNM) equation of states (EoS) with varying degrees
of stiffness. We find that a functional's low-density PNM EoS is correlated
with the number of protons found in the inner crust's nuclear clusters and, in
the lower-density region of the inner crust, with the pressure.
