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 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)
 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 That�s right: Pi(n)
 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
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Quote:
 Originally Posted by CRGreathouse . . . P(n) < n log n + n log log n (for n >= 6) . . .
? As n ? ?, P(n)/F(n) = 0. Tags fibonacci, 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 tahir.iman Number Theory 12 December 28th, 2012 04:53 AM PerAA Number Theory 2 November 11th, 2012 05:34 AM restin84 Number Theory 5 December 14th, 2011 04:52 PM soandos Number Theory 44 November 19th, 2007 12:07 PM johnny Number Theory 2 September 16th, 2007 06:44 AM

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