A215825 Even numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 3*b^2.

2, 4, 8, 12, 34, 146, 706, 1138, 1714, 1762

Offset

1,1

Comments

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

Note that F(12) = 144 = 2^4 * 3^2. - T. D. Noe, Aug 27 2012

Links

Table of n, a(n) for n=1..10.

Blair Kelly, Fibonacci and Lucas factorizations

Mathematica

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

Prog

(PARI) for(i=2, 500, a=factorint(fibonacci(i))~; 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. A000045, A215822, A215823, A215824.

Sequence in context: A007374 A105207 A202148 * A177268 A289085 A242924

Adjacent sequences: A215822 A215823 A215824 * A215826 A215827 A215828

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

Edited by N. J. A. Sloane, Aug 23 2012

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

Added 4 more terms - V. Raman, Aug 28 2012

Status

approved