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September 15th, 2007, 09:13 PM  #1 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Fibonacci & Prime Numbers
Let F(n) be an function for Fibonacci numbers, and let P(n) be an function for prime numbers. Then, evaluate limx>inf (F(n)/P(n)). Is this possible, or is this impossible to evaluate? 
September 16th, 2007, 03:25 AM  #2 
Senior Member Joined: May 2007 Posts: 402 Thanks: 0 
I supose that "the function for prime numbers" is a function that would for any n E Integers return the nth prime? If so, then asymptoticly it can be approximated with P(n)=C*n*ln(n) where C is a constant (not sure what it equals, but it's Real and >0) Now, F(n)= 1/sqr(5)*(((1+sqr(5))/2)^n((1sqr(5))/2)^n) you can see that the Fibonacci sequence grows with an exponential rate, and the prime numbers function at a lower rate, so the limF(n)/P(n),n>00 =+00 
September 16th, 2007, 07:44 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Heck, the Prime Number Theorem is overkill  even knowing that p_n is O(n^k) for some k suffices.


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