

A080327


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


6




OFFSET

1,1


COMMENTS

The intersection of A001605 and A001606. Fibonacci(148091) and Lucas(148091) are probable primes.
Corresponding FibonacciLucas prime twins are listed in A121533. Corresponding LucasFibonacci prime twins are listed in A121534. Fibonacci(148091) and Lucas(148091) are probable FibonacciLucas and LucasFibonacci 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 (61899digits)
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(n1)+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



