We found that the different values of equivalent resistance of all the possible combinations of n equal unitary resistors in series and/or in parallel form a list composed by a set of numbers and their inverses. This property is demonstrated and used to justify the symmetry and the peaks and valleys observed in the histogram representing the distribution of the values on the real axis. The number of different values obtained with n resistors is approximately 2.55n, defining a geometric series with a ratio smaller than the one that could be expected. The characteristics of the histograms, when some connections other than series or parallel as well as when nonplanar arrangements are allowed, is also suggested.