8 ms·
Would it be at all useful to be able to state the rule for calculating the coefficients (in base-3) from one odd number to the next in the Collatz conjecture's
by bakgatviooldoos 6y ago
Would it be at all useful to be able to state the rule for calculating the coefficients (in base-3) from one odd number to the next in the Collatz conjecture's evolution? That is, given an odd number's base-3 expansion, you could calculate the next odd number in the sequence from its coefficients.
I've done some work on this and have an idea of this rule but haven't been able to find anyone that is knowledgeable enough to comment on it.
- bakgatviooldoos 6y agoTo 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.