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A215821
Even numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 2*b^2.
3
2, 4, 6, 12, 18, 26, 36, 52, 122, 244, 314, 628, 794, 866, 1588, 1732, 1754
OFFSET
1,1
COMMENTS
These Fibonacci numbers F(n) have no prime factor congruent to 5 or 7 mod 8 to an odd power.
MATHEMATICA
Select[Range[2, 200, 2], Length[FindInstance[x^2 + 2*y^2 == Fibonacci[#], {x, y}, Integers]] > 0 &] (* G. C. Greubel, Apr 14 2017 *)
PROG
(PARI) for(i=2, 500, a=factorint(fibonacci(i))~; 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==0, print(i", ")))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
V. Raman, Aug 23 2012
EXTENSIONS
a(12)-a(17) from V. Raman, Aug 28 2012
STATUS
approved