September 1st, 2010, 01:30 PM  #1 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Prime and Fibonacci
Let P(n) be prime (P(1) = 2, P(2) = 3, P(3) = 5, P(4) = 7, P(5) = 11, . . .) and F(n) be Fibonacci (F(1) = 1, F(2) = 1, F(3) = 2, F(4) = 3, F(5) = 5, . . .). True or false: 
September 1st, 2010, 01:59 PM  #2 
Member Joined: Dec 2009 From: Spain Posts: 51 Thanks: 0  Re: Prime and Fibonacci
P(n)<n and F(n) approx a^n/sqrt(5) (Binetīs form) with a=(1+sqrt(5))/2 
September 1st, 2010, 02:04 PM  #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  Re: Prime and Fibonacci
Well, P(n) < n log n + n log log n (for n >= 6), but it works out the same.

September 1st, 2010, 02:11 PM  #4 
Member Joined: Dec 2009 From: Spain Posts: 51 Thanks: 0  Re: Prime and Fibonacci
Thatīs right: Pi(n)<n but obviously P(n) not 
September 1st, 2010, 02:19 PM  #5 
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  Re: Prime and Fibonacci
The basic idea is the same, though: P(n) has essentially linear growth, while F(n) has exponential growth.

September 1st, 2010, 05:11 PM  #6  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Quote:
 

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