I can see that because the FS starts with a 1, successive additions will guarantee odd numbers appear. If the FS started with a 2 (as 2 2 4 6 10 16 ...), then ONLY even numbers will appear.
What I don't understand at the moment is how the 1-based FS produces even AND odd numbers. Once I understand that, perhaps I can see why the OOE pattern exists.
Is it purely a case of O+O=E and E+O=O?
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4tran2007-08-02 23:46 ID:O5ExrWu0
>>4
You might notice that the FS sequence you gave is exactly twice the original, since you started off with base cases that were twice in size.
Yes -> we can analyze by considering the finite cases mod 2
1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181
Atleast its not pascals triangle?
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Anonymous2007-08-03 9:49 ID:WydgGZyi
Also, You notice that every 5 numbers it changes from Tens, To Hundreds, To thousands, to tens of thousands and so forth. Something I just happened to notice right now.
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Anonymous2007-08-03 11:55 ID:oDt9PIaW
That's because the pattern is fractal--when you add the tens places, they're the Fibbonacci sequence over again, or almost.
lists them vertically, just look at a place's digit in each number.
it is somewhat because of the fractal nature of it though, it stops happening because of the lower place values carrying over i guess. youre doing the same pattern for the sequence,
F_n+1 = F_n + F_n-1 at each digit, with lower digits carrying over one place when they exceed 9, if that makes sense. like the pattern holds vertically down the ones column, and down the tens column, etc, but only mod 10.
>>11
I think it seems safe to place an upper limit of 5 on the addition of a new digit.
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Anonymous2007-08-03 15:20 ID:zYFLmeIN
It's called exponential growth. Since the number of digits in an integer x is floor(log(x))+1, exponential growth for x results in linear growth for the number of digits.
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Anonymous2007-08-04 1:34 ID:aIUVQh0h
ah a good example of the kind of thing math majors waste their lives on.
Why is the Fibonacci Sequence a waste of life, #14? It's seen in the natural world. I recall that biologists had been noticing that patterns of leaf buddings on branches follow the FS. If we undertake to better understand the FS, we might better understand plant growth.
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Anonymous2007-08-06 10:01 ID:liqdM6AN
#14, I'm from England and here there are no majors and minors: we pick one subject and do it for three years (Bachelor's): so if you class merely majoring in maths as a waste thing about doing ONLY maths.
We start university (ie. college) at 18 and after about a year maths students know about as much as graduates from America who majored in math.
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Christopher Logan Hanssen2007-08-07 1:23 ID:kJAt1/Wx
>>15
This is the harrassment I am talking about. You have no right to call me names even on the internet and I will never tolorate it on my forum. If you dont believe me you can look at the thread where it says "banned members" and see a list of people I have already banned so you know I AM NOT JOKING
>>15
Other way around, actually. New research suggests that some plants previously thought to grow to fit the FS actually don't. What appears to be FS spirals actually aren't and are just our wishful thinking and giving the FS spirals too much wiggle room when we superimpose them.
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Christopher Logan Hanssen2007-08-08 3:39 ID:2pDpVBH1
>>18
I am geting sick and tiard of your constant rudeness and lack of moral in your postings, they are always about something dirty or else they contain rude and inapropriate langwidge. I am disgustid by it and am reporting this incidant and many others like it to the 4chan authoritys. Good day.