A305415 Numbers k such that F(k)*F(k+1) - F(k+2) is prime, where F = A000045.

4, 6, 7, 8, 10, 11, 14, 25, 34, 40, 44, 54, 62, 63, 66, 108, 190, 266, 299, 306, 310, 343, 350, 638, 726, 984, 1626, 2223, 2591, 2843, 3291, 3694, 4198, 4473, 4494, 5128, 7934, 10595, 12515, 17433, 17883, 19979, 23887, 28847, 30071, 64168, 79073, 81971

Offset

1,1

Comments

Primes in A059769: 7, 83, 239, 659, 4751, 12583, 228983, 9107313407, 52623175261103, 16944503546101559, 796030992711071707, 12041560801669230246323, etc.

Links

Table of n, a(n) for n=1..48.

Maple

with(combinat, fibonacci): select(n->isprime(fibonacci(n)*fibonacci(n+1)-fibonacci(n+2)), [$1..8000]); # Muniru A Asiru, Jun 12 2018

Mathematica

Select[Range[3000], PrimeQ[(Fibonacci[#] Fibonacci[# + 1] - Fibonacci[# + 2])]&]

Prog

(Magma) [n: n in [1..800] | IsPrime(Fibonacci(n)*Fibonacci(n+1)-Fibonacci(n+2))];
(PARI) isok(k) = isprime(fibonacci(k)*fibonacci(k+1) - fibonacci(k+2)); \\ Michel Marcus, Jun 13 2018

Crossrefs

Cf. A000045, A059769.

Sequence in context: A171413 A225551 A247359 * A105432 A324704 A203168

Adjacent sequences: A305412 A305413 A305414 * A305416 A305417 A305418

Keyword

nonn

Author

Vincenzo Librandi, Jun 09 2018

Extensions

a(38)-a(46) from Giovanni Resta, Jun 15 2018

a(47)-a(48) from Robert Price, Jun 18 2018

Status

approved