Plethora of q-oscillators possessing pairwise energy level degeneracy

Using the q, p-deformed oscillators as basic generating system, we obtain diverse classes (which form distinct sectors of functional continua) of novel versions of q-deformed oscillators, all of which share the property of accidental degeneracy within a fixed pair of energy levels E-m = Em+1, m >= 1, occurring at the real deformation parameter fixed by an appropriate value q(m) that depends on m and on particular model. Likewise, the degeneracy E-0 = E-k (where k >= 2) takes place, for properly fixed q = q(k), in most of those models. The formerly studied model of q-oscillator known as the Tamm-Dancoff cutoff deformed oscillator is contained in the continua as isolated special case.