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A080327 Numbers n for which Lucas(n) and Fibonacci(n) are both prime. 6
4, 5, 7, 11, 13, 17, 47, 148091 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)