Numbers n such that Lucas(n-1) and Lucas(n+1) are both prime.
1, 3, 6, 12, 18
1
No additional terms known. Probably complete.
T. D. Noe, Plot of 5 terms
(Mma) Select[Range[1000], PrimeQ[LucasL[# - 1]] && PrimeQ[LucasL[# + 1]] &]
Cf. A001606 (indices of Lucas primes).
nonn
T. D. Noe, Jun 26 2014