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%I #23 Jul 18 2013 16:38:36
%S 5,7,11,13,17,31,37,41,67,107,151,257,349,457,787,911,1289,1627,3271,
%T 8233,13163,14551,31517,55579
%N Numbers n such that F(3*n)/(2*F(n)) is prime, where F(k) is the k-th Fibonacci number.
%C All terms are primes. Conjecture: this sequence is infinite.
%e For n = 5 we have F(3*5)/(2*F(5)) = F(15)/(2*5) = 610/10 = 61 is prime.
%t Select[Range[1000], PrimeQ[Fibonacci[3*#]/Fibonacci[#]/2] &] (* _Vaclav Kotesovec_, Jul 18 2013 *)
%o (PARI) forprime(p=5,1e4,if(ispseudoprime(t=fibonacci(3*p)/fibonacci(p) /2), print1(p", "))) \\ _Charles R Greathouse IV_, Jul 16 2013
%o (PFGW) ABC2 F(3*$a)/2/F($a)
%o a: primes from 5 to 25000
%o // _Charles R Greathouse IV_, Jul 16 2013
%Y Cf. A001605, A000045, A227627.
%K nonn,more
%O 1,1
%A _Thomas Ordowski_, Jul 16 2013
%E a(6)-a(22) from _Charles R Greathouse IV_, Jul 16 2013
%E a(23) from _Vaclav Kotesovec_, Jul 18 2013
%E a(24) from _Charles R Greathouse IV_, Jul 18 2013
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