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
Welcome to the forum.
Sorry, I'm not following you. Would you fill in more details for an old brain.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Yes that is it. Or to make it easier it is the sum of the last two numbers in the sequence.
I posted your query on another forum: http://www.artofproblemsolving.com/Foru … 8&t=573625.
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Ive been given this link (PDF):
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
which is nothing but powers of 2.So,it is actually
Last edited by iamaditya (2016-11-30 23:05:06)
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