User Name Remember Me? Password

 Number Theory Number Theory Math Forum

 September 15th, 2007, 08:13 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, 02:25 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 n-th 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-((1-sqr(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, 06:44 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. Tags fibonacci, numbers, prime Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post PerAA Number Theory 2 November 11th, 2012 05:34 AM johnny Number Theory 5 September 1st, 2010 05:11 PM zolden Number Theory 12 January 26th, 2009 02:27 PM Fra Real Analysis 1 March 21st, 2008 10:50 AM soandos Number Theory 44 November 19th, 2007 12:07 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      