Sum of Fibonacci(n)/Lucas(n)

[Max A.]

On 12/7/06, Jonathan Post <jvospost3 at gmail.com> wrote:

>  In January, when I can submit "made up" sequences again to OEIS, I'll be
> sure to give your comment and email address, okay?

Whatever you think appropriate. Personally, I do not consider that
asymptotic as a great discovery. ;)

>  I wonder how often the numerator and denominator of A000045(i)/A000032(i)
> have a factor in common, and reduce?

It can be shown that gcd(A000045(i),A000032(i)) <= 2.
So, A000045(i) and A000032(i) have a non-trivial factor in common iff
they both are even.
And that takes place only when i is a multiple of 3.

Max