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} = E_{m+1}, m\ge 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\ge 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.