A121533 -id:A121533 - cp's OEIS frontend

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

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

Offset: 1

T. D. Noe, Feb 15 2003

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

Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 246.

David Broadhurst, Prime Curio: 10660...49391 (61899-digits)
Gerry Myerson, Western Number Theory Problems, 17 & 19 Dec 2007.

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

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

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

A121534 Lucas-Fibonacci prime twins: Prime Lucas numbers Lucas(k) such that Fibonacci numbers Fibonacci(k) are also prime.

Original entry on oeis.org

7, 11, 29, 199, 521, 3571, 6643838879

Offset: 1

Alexander Adamchuk, Aug 05 2006

nonn

Indices for Lucas-Fibonacci prime twins are A080327(n). Corresponding Fibonacci-Lucas prime twins are A121533(n). Probable primes Fibonacci(148091) and Lucas(148091) are the next probable Fibonacci-Lucas and Lucas-Fibonacci prime twins. They have 30949 and 30950 digits.

			a(1) = 7 because Lucas(4) = 7 is prime and Fibonacci(4) = 3 is prime too.

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

Do[f=Fibonacci[n]; l=Fibonacci[n-1]+Fibonacci[n+1]; If[PrimeQ[f]&&PrimeQ[l], Print[{f,l}]], {n,10000}]
nn=1000;Transpose[Select[Thread[{Fibonacci[Range[nn]], LucasL[ Range[nn]]}],And@@PrimeQ[#]&]][[2]] (* Harvey P. Dale, Jul 08 2011 *)

a(1) and example corrected by Harvey P. Dale, Jul 08 2011

cp's OEIS Frontend

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

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