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Home » Olympiad Section » Number Theory » Number Theory Open Questions
 
number of primes in sequence
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rex88
P versus NP
P versus NP

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#1
number of primes in sequence
let A_n = 4^{n-1}-n

we have (A_2,A_3,A_5)=(2, 13, 251 ) - primes.
are there any other primes in this sequence?
is the number of primes in (A_n) finite?

PostPosted: Mon Oct 19, 2009 6:01 am  Back to top 
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fuzzypeg
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#2
Yes there are other primes, e.g. for n=17, 945, 33479 (thanks to Mathematica).
It's the sort of sequence where you would "expect" infinitely many primes but there seems at present no hope of proving this.

PostPosted: Wed Oct 21, 2009 7:05 am  Back to top 
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