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A227576 Numbers k such that F(3*k)/(2*F(k)) is prime, where F(m) is the m-th Fibonacci number.

%I A227576 #31 Nov 06 2024 18:07:29
%S A227576 5,7,11,13,17,31,37,41,67,107,151,257,349,457,787,911,1289,1627,3271,
%T A227576 8233,13163,14551,31517,55579,103289
%N A227576 Numbers k such that F(3*k)/(2*F(k)) is prime, where F(m) is the m-th Fibonacci number.
%C A227576 All terms are primes. Conjecture: this sequence is infinite.
%e A227576 For n = 5 we have F(3*5)/(2*F(5)) = F(15)/(2*5) = 610/10 = 61 is prime.
%t A227576 Select[Range[1000], PrimeQ[Fibonacci[3*#]/Fibonacci[#]/2] &] (* _Vaclav Kotesovec_, Jul 18 2013 *)
%o A227576 (PARI) forprime(p=5,1e4,if(ispseudoprime(t=fibonacci(3*p)/fibonacci(p) /2), print1(p", "))) \\ _Charles R Greathouse IV_, Jul 16 2013
%o A227576 (PFGW) ABC2 F(3*$a)/2/F($a)
%o A227576 a: primes from 5 to 25000
%o A227576 // _Charles R Greathouse IV_, Jul 16 2013
%Y A227576 Cf. A001605, A000045, A227627.
%K A227576 nonn,more
%O A227576 1,1
%A A227576 _Thomas Ordowski_, Jul 16 2013
%E A227576 a(6)-a(22) from _Charles R Greathouse IV_, Jul 16 2013
%E A227576 a(23) from _Vaclav Kotesovec_, Jul 18 2013
%E A227576 a(24) from _Charles R Greathouse IV_, Jul 18 2013
%E A227576 a(25) from _Michael S. Branicky_, Nov 06 2024