A215821 Even numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 2*b^2.

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.

Links

Table of n, a(n) for n=1..17.

Blair Kelly, Fibonacci and Lucas factorizations

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

Cf. A000045, A215818, A215819, A215820.

Sequence in context: A225566 A273009 A051683 * A332284 A192096 A181740

Adjacent sequences: A215818 A215819 A215820 * A215822 A215823 A215824

Keyword

nonn,more

Author

V. Raman, Aug 23 2012

Extensions

a(12)-a(17) from V. Raman, Aug 28 2012

Status

approved