  A series of high-quality under-doped La2-xSrxCuO4 superconductor crystals
with x = 0.063 - 0.125 were prepared by traveling-solvent floating-zone (TSFZ)
technique. We found by dc magnetic measurements that, in this series of
crystals, the superconducting transition was quite sharp in the vicinity of the
hole densities of x = 1/16 and x = 1/9 while it was much broader away from
these two "magic numbers", and the Meissner fraction showed a remarkable
minimum near x = 1/9. We concluded that these phenomena are reflections of
intrinsic properties of this cuprate system. Our observations are discussed in
light of recently proposed composite charge model together with charge
inhomogeneity and electronic phase separations.
