A227576 Numbers k such that F(3*k)/(2*F(k)) is prime, where F(m) is the m-th Fibonacci number.
5, 7, 11, 13, 17, 31, 37, 41, 67, 107, 151, 257, 349, 457, 787, 911, 1289, 1627, 3271, 8233, 13163, 14551, 31517, 55579, 103289
Offset: 1
Examples
For n = 5 we have F(3*5)/(2*F(5)) = F(15)/(2*5) = 610/10 = 61 is prime.
Programs
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Mathematica
Select[Range[1000], PrimeQ[Fibonacci[3*#]/Fibonacci[#]/2] &] (* Vaclav Kotesovec, Jul 18 2013 *)
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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
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PFGW
ABC2 F(3*$a)/2/F($a) a: primes from 5 to 25000 // Charles R Greathouse IV, Jul 16 2013
Extensions
a(6)-a(22) from Charles R Greathouse IV, Jul 16 2013
a(23) from Vaclav Kotesovec, Jul 18 2013
a(24) from Charles R Greathouse IV, Jul 18 2013
a(25) from Michael S. Branicky, Nov 06 2024
Comments