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A215822
Numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 3*b^2.
3
1, 2, 4, 7, 8, 12, 17, 23, 25, 34, 47, 49, 71, 73, 79, 89, 119, 137, 146, 151, 167, 191, 193, 199, 257, 271, 353, 359, 391, 409, 431, 433, 449, 569, 601, 706, 719, 751, 799, 809, 823, 833, 857, 881, 887, 929, 953, 1138
OFFSET
1,2
COMMENTS
These Fibonacci numbers F(n) have no prime factor congruent to 2 mod 3 to an odd power.
MATHEMATICA
Select[Range[200], 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, print(i", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
V. Raman, Aug 23 2012
EXTENSIONS
1, 12, and 25 added by T. D. Noe, Aug 27 2012
Added 20 more terms - V. Raman, Aug 28 2012
STATUS
approved