I assume the cycle is the portion of a snowflake that repeats? Because certainly the snowflake of 12 is (12, 6, 3, 8, 4, 2, 1, 2, 1, ...) which contains a multiple of 3, but it doesn't start repeating until the "2, 1, 2, 1, ..." portion.
Starting with any positive integer n we produce another number m as follows.
- If n is odd, then m = 3n-1
- If n is even, then m = n/2
By repeating this process, n generates a sequence called a snowstorm the numbers of which are called snowflakes of n
For example, the snowstorm of 4 is: 4, 2, 1, 2, 1, ... and so on. SOmetimes we arrange the snowflakes in a diagram to indicate cycles.
Here we have a cycle of length two
Questions:
1. show that starting with 12 also produces a length two and that starting with 13 produces a cycle of length five
2. Find a cycle with length greater than five
3. Explain why no cycle can coantin a number that is a multiple of three
4. Find all cycles of length five