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

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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..7.

Example

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

Mathematica

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 *)

Crossrefs

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

Sequence in context: A153867 A153325 A109907 * A083363 A027707 A046861

Adjacent sequences: A121531 A121532 A121533 * A121535 A121536 A121537

Keyword

nonn

Author

Alexander Adamchuk, Aug 05 2006

Extensions

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

Status

approved