  We present the results of our investigations of physical properties for the
novel Ce$_{1-x}$Pr$_x$CoGe$_3$ system performed with a number of experimental
methods: magnetic susceptibility, specific heat, electrical resistivity,
magnetoresistance, and thermoelectric power. Moreover, the electronic structure
was studied by means of photoelectron spectroscopy measurements and
first-principles calculations. All investigated compositions of the
Ce$_{1-x}$Pr$_x$CoGe$_3$ series crystallize in the tetragonal BaNiSn$_3$-type
structure. The lattice parameters and unit cell volumes decrease with
increasing Pr concentration. On the basis of the measurements taken, a
preliminary magnetic phase diagram was created. A continuous suppression of the
long-range magnetic ordering was observed with increase of Pr concentration.
The critical Pr concentration for magnetic moment ordering was determined from
linear extrapolation of the ordering temperature $versus$ $x$ to the lowest
temperatures ($T = 0$ K) and is equal to about 0.66. Based on the
first-principles calculations we show how the substitution of Pr for Ce affects
the electronic structure and magnetic properties of the considered alloys.
Within a single model we take into account the magnetic ordering,
fully-relativistic effects, and Hubbard U repulsion on Ce and Pr. The impact of
Hubbard U on the results of calculations is also discussed. We present the
valence-band analysis, Mulliken electronic population analysis, and calculated
electronic specific heat coefficients. For CeCoGe$_3$ it is found that the
$++--$ configuration of magnetic moments on Ce is slightly more stable than the
$+-+-$ one, and also that the calculated value of total magnetic moment on Ce
(including spin and orbital parts) is in good agreement with the measurements.
