|
%I #19 Jun 26 2019 00:40:41
%S 7,11,29,199,521,3571,6643838879
%N Lucas-Fibonacci prime twins: Prime Lucas numbers Lucas(k) such that Fibonacci numbers Fibonacci(k) are also prime.
%C 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.
%e a(1) = 7 because Lucas(4) = 7 is prime and Fibonacci(4) = 3 is prime too.
%t Do[f=Fibonacci[n]; l=Fibonacci[n-1]+Fibonacci[n+1]; If[PrimeQ[f]&&PrimeQ[l], Print[{f,l}]], {n,10000}]
%t nn=1000;Transpose[Select[Thread[{Fibonacci[Range[nn]], LucasL[ Range[nn]]}],And@@PrimeQ[#]&]][[2]] (* _Harvey P. Dale_, Jul 08 2011 *)
%Y Cf. A121533, A000045, A005478, A001605, A001606, A000032, A000204, A005479, A080327.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Aug 05 2006
%E a(1) and example corrected by _Harvey P. Dale_, Jul 08 2011
| 