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A227576
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Numbers n such that F(3*n)/(2*F(n)) is prime, where F(k) is the k-th Fibonacci number.
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1
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5, 7, 11, 13, 17, 31, 37, 41, 67, 107, 151, 257, 349, 457, 787, 911, 1289, 1627, 3271, 8233, 13163, 14551, 31517, 55579
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OFFSET
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1,1
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COMMENTS
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All terms are primes. Conjecture: this sequence is infinite.
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LINKS
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EXAMPLE
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For n = 5 we have F(3*5)/(2*F(5)) = F(15)/(2*5) = 610/10 = 61 is prime.
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MATHEMATICA
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Select[Range[1000], PrimeQ[Fibonacci[3*#]/Fibonacci[#]/2] &] (* Vaclav Kotesovec, Jul 18 2013 *)
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PROG
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(PARI) forprime(p=5, 1e4, if(ispseudoprime(t=fibonacci(3*p)/fibonacci(p) /2), print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2013
(PFGW) ABC2 F(3*$a)/2/F($a)
a: primes from 5 to 25000
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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