A215812 Odd numbers n such that the Lucas number L(n) can be written in the form a^2 + 2*b^2.

1, 3, 5, 9, 13, 17, 27, 29, 37, 41, 53, 61, 65, 89, 97, 113, 123, 137, 157, 169, 185, 197, 267, 281, 289, 305, 313, 349, 353, 369, 397, 411, 433, 457, 461, 481, 493, 509, 541, 557, 593, 613, 617, 661, 673, 697, 809, 829, 841, 857, 877, 901, 1061, 1097

Offset

1,2

Comments

These Lucas numbers L(n) have no prime factor congruent to 5 or 7 (mod 8) to an odd power.

Links

Table of n, a(n) for n=1..54.

Blair Kelly, Fibonacci and Lucas factorizations

Mathematica

Select[Range[1, 200, 2], Length[FindInstance[x^2 + 2*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]%8>4&&a[2, j]%2==1, has=1; break)); if(has==0&&i%2==1, print(i", ")))

Crossrefs

Cf. A000032, A215813.

Sequence in context: A049690 A080075 A007664 * A114395 A075314 A152737

Adjacent sequences: A215809 A215810 A215811 * A215813 A215814 A215815

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

1 added by T. D. Noe, Aug 27 2012

Added 27 more terms - V. Raman, Aug 28 2012

Status

approved