A215810 Numbers n such that the Lucas number L(n) can be written in the form a^2 + 3*b^2.

1, 2, 3, 4, 9, 11, 17, 19, 20, 22, 26, 27, 28, 33, 41, 43, 46, 51, 52, 57, 67, 68, 73, 76, 81, 83, 99, 113, 116, 118, 121, 123, 129, 139, 140, 153, 164, 171, 172, 194, 201, 219, 241, 242, 243, 244, 249, 281, 283, 284, 297, 313, 314, 316, 323, 339, 353, 356, 358, 362, 363, 369, 379, 382, 387, 401, 404, 417, 428

Offset

1,2

Comments

These Lucas numbers L(n) have no prime factor congruent to 2 mod 3 to an odd power.

Links

V. Raman, Table of n, a(n) for n = 1..109

Blair Kelly, Fibonacci and Lucas factorizations

Mathematica

Select[Range[200], Length[FindInstance[x^2 + 3 y^2 == LucasL[#], {x, y}, Integers]] > 0 &] (* T. D. Noe, Aug 27 2012 *)

Prog

(PARI) for(i=2, 500, a=factorint(fibonacci(i-1)+fibonacci(i+1))~; has=0; for(j=1, #a, if(a[1, j]%3==2&&a[2, j]%2==1, has=1; break)); if(has==0, print(i", ")))

Crossrefs

Cf. A000032, A215811, A215815, A215816.

Sequence in context: A212989 A211546 A093514 * A080231 A217493 A368349

Adjacent sequences: A215807 A215808 A215809 * A215811 A215812 A215813

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

Corrected by T. D. Noe, Aug 27 2012

Added 18 more terms - V. Raman, Aug 28 2012

Status

approved