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A121534
Lucas-Fibonacci prime twins: Prime Lucas numbers Lucas(k) such that Fibonacci numbers Fibonacci(k) are also prime.
6
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.
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 *)
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Aug 05 2006
EXTENSIONS
a(1) and example corrected by Harvey P. Dale, Jul 08 2011
STATUS
approved