Not sure I'm interpreting your question correctly, but you seem to be asking about about the mathematical relationship between the frequency (Hz) of a pitch and the sequences of pitches that we organize into scales and octaves.
So at the risk of being too pedantic, we map frequencies to pitches using a logarithmic scale (in base 2).
Because our ears don't perceive pitch distance linearly with frequency, as the wikipedia article for "12-tone equal temperament" says:
the ratios of the frequencies of any adjacent pair of notes is the same, and, as pitch is perceived roughly as the logarithm of frequency, equal perceived "distance" from every note to its nearest neighbor.
So to answer your question, an octave is a unit of frequency used with logarithm base-2. (A semitone is one twelfth of an octave. A cent is one hundredth of a semitone.) The "series" of octaves itself would just be referred to as a base-2 logarithmic scale.