  We carried out detailed high-precision study of Ag-like Nd$^{13+}$,
Sm$^{15+}$ and In-like Ce$^{9+}$, Pr$^{10+}$, Nd$^{11+}$, Sm$^{13+}$,
Eu$^{14+}$ highly-charged ions. These ions were identified to be of particular
interest to the development of ultra-accurate atomic clocks, search for
variation of the fine-structure constant $\alpha$, and quantum information
[Safronova et. al. Phys. Rev. Lett. 113, 030801 (2014)]. Relativistic
linearized coupled-cluster method was used for Ag-like ion calculations, and a
hybrid approach that combines configuration interaction and a variant of the
coupled-cluster method was used for the In-like ion calculations. Breit and QED
corrections were included. Energies, transition wavelengths, electric-dipole,
electric-quadrupole, electric-octupole, magnetic-dipole, magnetic-quadrupole,
magnetic-octupole reduced matrix elements, lifetimes, and sensitivity
coefficients to $\alpha$-variation were calculated. Detailed study of various
contributions was carried out to evaluate uncertainties of the final results.
Energies for several similar "reference" ions, where the experimental values
are available were calculated and compared with experiment for further tests of
the accuracy.
