A215815 Even numbers n such that the Lucas number L(n) can be written in the form a^2 + 3*b^2.

2, 4, 20, 22, 26, 28, 46, 52, 68, 76, 116, 118, 140, 164, 172, 194, 242, 244, 284, 314, 316, 356, 358, 362, 382, 404, 428, 458, 478, 598, 698, 746, 772, 794, 812, 914, 988, 1004, 1082

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..39.

Blair Kelly, Fibonacci and Lucas factorizations

Mathematica

Select[Range[2, 200, 2], Length[FindInstance[x^2 + 3*y^2 == LucasL[#], {x, y}, Integers]] > 0 &] (* G. C. Greubel, Apr 14 2017 *)

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&&i%2==0, print(i", ")))

Crossrefs

Cf. A000032, A215810, A215811, A215816.

Sequence in context: A122158 A178223 A033180 * A295826 A201502 A069535

Adjacent sequences: A215812 A215813 A215814 * A215816 A215817 A215818

Keyword

nonn,more

Author

V. Raman, Aug 23 2012

Extensions

a(22)-a(39) from V. Raman, Aug 28 2012

Status

approved