A305414 Numbers k such that F(k)*F(k+1) + F(k+2) is a prime, where F = A000045 (Fibonacci numbers).

1, 2, 3, 4, 5, 7, 8, 10, 11, 15, 16, 18, 29, 40, 55, 134, 159, 261, 276, 519, 1792, 2045, 2111, 2830, 2878, 3575, 6301, 7394, 9432, 13558, 19714, 21396, 25731, 26790, 28792, 32070, 33951, 46997, 63134, 66272, 67619, 70448, 75525, 77994, 90437

Offset: 1

Author

Vincenzo Librandi, Jun 09 2018

Keywords

• nonn

Comments

Primes in A305412.

a(46) > 10^5. - Robert Price, Jun 18 2018

Crossrefs

Cf. A000045, A305412.

Programs

Magma

[n: n in [1..1500] | IsPrime(Fibonacci(n) * Fibonacci(n+1) + Fibonacci(n+2))];

Mathematica

Select[Range[1000], PrimeQ[(Fibonacci[#] Fibonacci[# + 1] + Fibonacci[# + 2])]&]

Extensions

More terms from Vaclav Kotesovec, Jun 11 2018

a(39) from Giovanni Resta, Jun 11 2018

a(40)-a(45) from Robert Price, Jun 18 2018