A216554 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 3*b^2.

2, 4, 11, 17, 19, 41, 113, 313, 353, 617, 1097, 1361, 4787, 4793, 5851, 8467, 10691, 12251, 13963, 14449, 35449, 36779, 44507, 51169, 56003, 89849, 140057, 148091, 159521, 183089, 193201, 202667, 387433, 443609, 574219, 616787, 692147

Offset: 1

Author

V. Raman, Sep 08 2012

Keywords

• nonn

Links

• Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Crossrefs

Cf. A000032, A001606.

Programs

Mathematica

Select[Range[693000],PrimeQ[LucasL[#]]&&Length[Solve[{a^2+3b^2==LucasL[#],a>=0,b>=0},{a,b},Integers]]>0&] (* Harvey P. Dale, Apr 19 2020 *)