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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: $\lim_{n\to\infty}\frac{P(n)}{F(n)}\,=\,0?$
 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 Thatīs 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.

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