A227627 Numbers k such that F(5*k)/(5*F(k)) is prime, where F(m) is the m-th Fibonacci number.

2, 3, 5, 7, 13, 25, 29, 37, 47, 67, 457, 2309, 2383, 4133, 5023, 8059

Offset: 1

Author

Vaclav Kotesovec, Jul 18 2013

Keywords

• nonn
• more
• hard

Comments

Except for k = 25, all other terms k are primes. Conjecture: this sequence is infinite. - Thomas Ordowski, Jul 18 2013

a(17) > 50000. - Michael S. Branicky, Nov 06 2024

Crossrefs

Cf. A227576, A088545, A000045, A001605.

Programs

Mathematica

Select[Range[1000],PrimeQ[Fibonacci[5*#]/Fibonacci[#]/5]&]

PARI

is(n)=ispseudoprime(fibonacci(5*n)/fibonacci(n)/5) \\ Charles R Greathouse IV, Nov 25 2014