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Math Help - Snowstorm numbers

  1. #1
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    Snowstorm numbers

    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
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  2. #2
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    Sacramento, CA
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    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.
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