I need a new hobby, what can I do that's productive and fun?

I have a lot of free time, any suggestions?

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Most Helpful Guys

  • You are a Mathlete.

    Try to solve this problem:

    Let X (k) be a sequence of positive integers defined here:
    X (k+1) = 3 * X (k) + 1 if X (k) is odd.
    X (k+1) = X (k) / 2 if X (k) is even.

    Show that, for any starting value of X (0) that is a positive integer, the sequence will eventually become {...,4,2,1,4,2,1,4,2,1,...}

    For example:
    X (0) = 7
    7 is odd, so
    X (1) = 3 * X (0) + 1 = 3 * 7 + 1 = 21 + 1 = 22
    22 is even, so
    X (2) = X (1) / 2 = 22 / 2 = 11
    11 is odd, so
    X (3) = 3 * X (2) + 1 = 3 * 11 + 1 = 33 + 1 = 34
    34 is even, so
    X (4) = X (3) / 2 = 34 / 2 = 17
    17 is odd, so
    X (5) = 3 * X (4) + 1 = 3 * 17 + 1 = 51 + 1 = 52
    52 is even, so
    X (6) = X (5) / 2 = 52 / 2 = 26
    26 is even, so
    X (7) = X (6) / 2 = 26 / 2 = 13
    13 is odd, so
    X (8) = 3 * X (7) + 1 = 3 * 13 + 1 = 39 + 1 = 40
    40 is even, so
    X (9) = X (8) / 2 = 40 / 2 = 20
    20 is even, so
    X (10) = X (9) / 2 = 20 / 2 = 10
    10 is even, so
    X (11) = X (10) / 2 = 10 / 2 = 5
    5 is odd, so
    X (12) = 3 * X (11) + 1 = 3 * 5 + 1 = 15 + 1 = 16
    16 is even, so...
    (In fact, it's a power of 2, so...)
    X (13) = X (12) / 2 = 16 /2 = 8
    X (14) = 4
    X (15) = 2
    X (16) = 1
    1 is odd, so
    X (17) = 3 * X (16) + 1 = 4

    So, just to summarize the sequence:

    7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 -> 4 -> 2 -> 1 -> 4 -> 2 -> 1 -> ...

    It so happens that, no matter what positive integer you start with, you end up with...
    ... -> 4 -> 2 -> 1 -> 4 -> 2 -> 1 -> 4 -> 2 -> 1 -> ...

    Why is that?

    Prove it.

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    • I appreciate the time you took to find this or write it, but this is not at all what I had in mind

  • The 'fun' part depends on what sort of person you are. Running, wall climbing, dancing, gardening or cooking/baking may be fun. You could also pick up something creative like painting/drawing.

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Most Helpful Girl

  • You can learn to paint 🎨
    You can go workout
    You can learn a Play piano, guitar etc
    You can learn to cook
    You can sing
    list goes on and on

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Recommended Questions

Have an opinion?

What Guys Said 8

  • Giving free blow jobs is a great hobby to get into. Here I'll be your practice partner.

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  • boxing. gets you in great shape and you'll learn to kick some ass

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  • Archery perhaps? I find it very relaxing.

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  • Reading

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  • Learn how to play an instrument

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  • Cooking 🍳 is best.

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  • A hand craft like knitting or wood carving

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  • start flying drones

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What Girls Said 3

  • Hiking. Good exercise, amazing views. And plenty of good pictures to be taken.

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  • yoga, zumba, read a self help book, learn to cook, learn to play piano, go hiking...

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  • Crochet

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