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

1,1

Links

Table of n, a(n) for n=1..37.

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

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 *)

Crossrefs

Cf. A000032, A001606.

Sequence in context: A331653 A286293 A167801 * A018625 A360401 A123557

Adjacent sequences: A216551 A216552 A216553 * A216555 A216556 A216557

Keyword

nonn

Author

V. Raman, Sep 08 2012

Status

approved