

A215825


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


3




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



