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

1,2

Comments

Primes in A305412.

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

Links

Table of n, a(n) for n=1..45.

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A305412.

Sequence in context: A190850 A066077 A219040 * A317296 A103740 A317578

Adjacent sequences: A305411 A305412 A305413 * A305415 A305416 A305417

Keyword

nonn

Author

Vincenzo Librandi, Jun 09 2018

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

Status

approved