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A227576 Numbers n such that F(3*n)/(2*F(n)) is prime, where F(k) is the k-th Fibonacci number. 1
5, 7, 11, 13, 17, 31, 37, 41, 67, 107, 151, 257, 349, 457, 787, 911, 1289, 1627, 3271, 8233, 13163, 14551, 31517, 55579 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..24.

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: A109416 A132170 A106309 * 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

STATUS

approved

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Last modified August 18 01:19 EDT 2019. Contains 326059 sequences. (Running on oeis4.)