You may be missing some terminology:
Oscillation: an alternating phenomenon, usually periodic.
Cycle: a full... cycle, of an oscillation.
Also, what would the 1st and 23rd cycles be referenced to? If the oscillation is steady state, it doesn't really have a beginning or an end. (An ideal sine wave, for all times t < 0, is identical to all times t > 0, give or take a simple symmetry.) Would the count repeat immediately, so the 24th cycle from one count is the first cycle of the next count, and so on? Or should there be some dwell in there also, in which case how much?
But in any case, yes, that's a thing: a cycle-skipping controller, is typically used for AC loads, that have high power factor, and large time constants, so that the skipped cycles average to a smooth output. In short: heaters, thermostats, that sort of thing, are a prime application.
The pattern of cycle-skipping may resemble PWM, or a sigma-delta converter, or anything else that works.
PWM would run, for a duty cycle 0 <= D <= 1: on for N*D cycles, off for N*(1-D) cycles, for a total (repeating) period of N cycles, or a frequency of F_mains / N.
Sigma-delta is something of an approximation method, which can give lower ripple than PWM. A running average is calculated by the controller, and the output is turned on or off depending on whether that average is above or below the setpoint.
The simplest, commonest circuit you could make, that accomplishes this, would be a simple hysteretic controller (i.e., a sensor's output is compared to the desired setting, and this turns the output on or off directly), paired with a zero-crossing switch. Downside, this gives much slower cycles, and quite a lot more ripple (fluctuation in sensed value), than a PWM or SD control would. (Most home thermostats do operate this way, in part because the furnace or A/C should not be switched on and off too quickly.)
Tim