Thread: sequence of f_n

Let a and b be odd positive integers.
Define the sequence f_n by putting f_1=a, f_2=b, and by letting f_n for n>2 be the greatest odd divisor of f_(n-1) + f_(n-2).
Show that f_n is constant for n sufficiently large and determine the eventual value as a function of a and b.

Thank you very much.

Originally Posted by Jenny20

Let a and b be odd positive integers.
Define the sequence f_n by putting f_1=a, f_2=b, and by letting f_n for n>2 be the greatest odd divisor of f_(n-1) + f_(n-2).
Show that f_n is constant for n sufficiently large and determine the eventual value as a function of a and b.

Thank you very much.

If a,b>0.
I have already posted my version here.
But it is not able to load yet.

It will be,
f(n)=a*u_n+b*u_{n-1}
Where,
u_n is the Fibonacci numbers

Hi perfecthacker,

Do I have to wait for long to see your version?
Anyway, I will go to check it often.
Thank you very much.

Originally Posted by Jenny20

Hi perfecthacker,

Do I have to wait for long to see your version?

I do not know there is some problem with the equation software.

I see.