A080327 Numbers n for which Lucas(n) and Fibonacci(n) are both prime.

4, 5, 7, 11, 13, 17, 47, 148091

Offset

1,1

Comments

The intersection of A001605 and A001606. Fibonacci(148091) and Lucas(148091) are probable primes.

Corresponding Fibonacci-Lucas prime twins are listed in A121533. Corresponding Lucas-Fibonacci prime twins are listed in A121534. Fibonacci(148091) and Lucas(148091) are probable Fibonacci-Lucas and Lucas-Fibonacci prime twins. They have 30949 and 30950 digits. - Alexander Adamchuk, Aug 05 2006

Heuristically, this sequence is finite. It is quite probable, but presently unprovable, that it is now complete. - David Broadhurst, Jun 25 2008

Western Number Theory problem 007:13 by Gary Walsh asks to prove that a(8) = 148091 is in this sequence. - Charles R Greathouse IV, May 21 2014

Links

Table of n, a(n) for n=1..8.

David Broadhurst, Prime Curio: 10660...49391 (61899-digits)

Gerry Myerson, Western Number Theory Problems, 17 & 19 Dec 2007.

Mathematica

Select[Range[0, 100], PrimeQ[Fibonacci[#]] && PrimeQ[LucasL[#]] & ] (* Robert Price, May 27 2019 *)

Prog

(PARI) is(n)=isprime(n) && ispseudoprime(fibonacci(n)) && ispseudoprime(fibonacci(n-1)+fibonacci(n+1)) \\ Charles R Greathouse IV, May 21 2014

Crossrefs

Cf. A001605, A001606, A121533, A121534, A000045, A005478, A000032, A000204, A005479, A080327.

Sequence in context: A291741 A084087 A175903 * A283485 A184778 A240118

Adjacent sequences: A080324 A080325 A080326 * A080328 A080329 A080330

Keyword

hard,nonn,more

Author

T. D. Noe, Feb 15 2003

Status

approved