To clarify my question above, there seems to be a general rule for calculating the next step in any Collatz-like iterated sequence from one odd number to the ne

To clarify my question above, there seems to be a general rule for calculating the next step in any Collatz-like iterated sequence from one odd number to the next, given the parameters (c, D) where both c and D are positive odd numbers and c > D, using the coefficients of each step's odd number, expanded in base-c. That is to say, 3N + 1 becomes cN + D. The expansion's number of coefficients increases by 1 at each step until the leading coefficient becomes 0, and then continues. Although, it must be noted that the leading coefficient acts as a "pilot value" of sorts seeing that it is greater than c for most of the steps, given that each of the rest of the coefficients, call them s, are typical in that 0 ≤ s < c.