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#1 2014-01-29 14:48:21

Mcbattle
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Registered: 2014-01-29
Posts: 5

Something I found about the Fibonacci sequence

So after I failed math last semester I got kicked into general math. But I already knew the concepts (I got a 94 after paying attention for less than 15 minutes over the course of 4 weeks) so I did what any other board 14 year does... screw around. I knew that if you take the remainder after dividing the Fibonacci numbers you see a pattern. However I noticed a pattern in the length of the patterns, but only when it was divided by certain numbers. The numbers in question would be 2^n for example:
2^1=2 The sequence is 3 numbers: 0,1,1
2^2=4 The sequence is 6 numbers: 0,1,1,2,3,1
2^3=8 The sequence is 12 numbers: 0,1,1,2,3,5,0,5,5,2,7,1
The pattern I noticed is that the length of the sequence is equal to


I have confirmed the same thing with 16 and 32 while in math by writing a program on my calculator. I was unable to go higher due to technical reasons though. I plan on looking into this later and seeing if it does continue.

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#2 2014-01-29 20:03:20

bob bundy
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Registered: 2010-06-20
Posts: 7,706

Re: Something I found about the Fibonacci sequence

hi Mcbattle

Welcome to the forum.

Sorry, I'm not following you.  Would you fill in more details for an old brain.  smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2014-01-29 20:47:09

Nehushtan
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Registered: 2013-03-09
Posts: 880
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Re: Something I found about the Fibonacci sequence

Let

Then

Is that it?


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#4 2014-01-30 08:54:51

Mcbattle
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Registered: 2014-01-29
Posts: 5

Re: Something I found about the Fibonacci sequence

Yes that is it. Or to make it easier it is the sum of the last two numbers in the sequence.

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#5 2014-02-04 03:09:19

Nehushtan
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Registered: 2013-03-09
Posts: 880
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Re: Something I found about the Fibonacci sequence

I posted your query on another forum: http://www.artofproblemsolving.com/Foru … 8&t=573625.

As of now the thread has had 46 views but no reply. dunno


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#6 2014-02-21 05:18:57

Nehushtan
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Registered: 2013-03-09
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Re: Something I found about the Fibonacci sequence


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#7 2016-11-27 20:29:43

iamaditya
Member
Registered: 2016-11-15
Posts: 33

Re: Something I found about the Fibonacci sequence

In Fibbonacci sequence the next term is found by adding the previous 2 terms. But if we add all the previous terms before it to get the next no. we will get

1,1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192..........
which is nothing but powers of 2.So,it is actually
2^0,2^0,2^1,2^2,2^3,2^4,2^5,2^6.........

Last edited by iamaditya (2016-11-30 23:05:06)


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