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

Mcbattle
Member
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
Moderator
Registered: 2010-06-20
Posts: 6,466

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


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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From: London
Registered: 2013-03-09
Posts: 615
Website

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
Member
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
Member
From: London
Registered: 2013-03-09
Posts: 615
Website

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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From: London
Registered: 2013-03-09
Posts: 615
Website

Re: Something I found about the Fibonacci sequence


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