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Thread: Alternating-ish sequence...

  1. #1 Alternating-ish sequence... 
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    Quick question: What kind of formula yields something like odd, odd, even, even, odd, odd, even, even, etc. ?

    If it starts with even or odd doesn't matter, as long as it goes in pairs. That's all. (if you're wondering, this has to do with finding a general formula for higher derivatives of a function) Oh, and no this is not homework

    Thanks in advanced


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    Forum Senior TheObserver's Avatar
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    You are opposed to piecewise functions?


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  4. #3  
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    Whatever works (why?)
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    Forum Senior TheObserver's Avatar
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    Well then just define it piecewise. For example define your function to be 1 for all integers congruent to 0 or 1 (mod 4), and be 2 for all integers congruent to 2 or 3 (mod 4).
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  6. #5  
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    Blargh! My ignorance is killing me... Never mind, it can't be piecewise-defined. But thanks a lot anyway.

    Shortly after I posted, I had an idea and figured out the problem. But I'm sure you had an answer in mind, so I didn't want to shut you off.

    And now, I realized it has to be a single formulation due to the context of the problem. Sorry
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  7. #6  
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    In case anyone's wondering, here's the explicit formula I found:

    This particular one goes 1, 1, 2, 2, 3, 3, 4, 4 ...
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    Forum Senior TheObserver's Avatar
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    Starting with n=3 that is! But yeah that works much better.
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  9. #8  
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    Yeah. When I referred to an "alternating-ish sequence", I was referring to the signs.

    The order of derivatives went - , - , + , + , - , - , + , + ... So I thought instead of finding a rule for alternating pairs of signs I could find a simpler rule for alternating pairs of evens/odds and raise -1 to that power. And much courtesy to Wolfram Alpha for its sequence tool.
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  10. #9  
    Ophiolater Nehushtan's Avatar
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    Quote Originally Posted by halorealm View Post
    Quick question: What kind of formula yields something like odd, odd, even, even, odd, odd, even, even, etc. ?


    Recognize the sequence?
    Holding on to anger is like drinking poison and expecting the other person to die.
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