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

1,1

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

Links

Table of n, a(n) for n=1..16.

Mathematica

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

Prog

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

Crossrefs

Cf. A227576, A088545, A000045, A001605.

Sequence in context: A076994 A327591 A124147 * A335116 A135372 A037021

Adjacent sequences: A227624 A227625 A227626 * A227628 A227629 A227630

Keyword

nonn,more,hard

Author

Vaclav Kotesovec, Jul 18 2013

Status

approved