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**Mcbattle****Member**- Registered: 2014-01-29
- Posts: 5

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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,321

hi Mcbattle

Welcome to the forum.

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

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Mcbattle****Member**- Registered: 2014-01-29
- Posts: 5

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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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.

**226** books currently added on Goodreads

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Ive been given this link (PDF):

**226** books currently added on Goodreads

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 766

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)*

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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