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

1,1

Comments

All terms are primes. Conjecture: this sequence is infinite.

Links

Table of n, a(n) for n=1..25.

Example

For n = 5 we have F(3*5)/(2*F(5)) = F(15)/(2*5) = 610/10 = 61 is prime.

Mathematica

Select[Range[1000], PrimeQ[Fibonacci[3*#]/Fibonacci[#]/2] &] (* Vaclav Kotesovec, Jul 18 2013 *)

Prog

(PARI) forprime(p=5, 1e4, if(ispseudoprime(t=fibonacci(3*p)/fibonacci(p) /2), print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2013
(PFGW) ABC2 F(3*$a)/2/F($a)
a: primes from 5 to 25000
// Charles R Greathouse IV, Jul 16 2013

Crossrefs

Cf. A001605, A000045, A227627.

Sequence in context: A132170 A106309 A371566 * A114262 A255229 A230217

Adjacent sequences: A227573 A227574 A227575 * A227577 A227578 A227579

Keyword

nonn,more

Author

Thomas Ordowski, 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

Status

approved