Beefy Boxes and Bandwidth Generously Provided by pair Networks
Your skill will accomplish
what the force of many cannot
 
PerlMonks  

Re^4: Fibonacci numbers (again)

by ambrus (Abbot)
on Sep 09, 2005 at 11:28 UTC ( #490517=note: print w/replies, xml ) Need Help??


in reply to Re^3: Fibonacci numbers (again)
in thread Fibonacci numbers (again)

It's all just convention, but I opt for 0,1,1,2,3,5,..., and I have a reason.

If you define F_0 = 0, F_1 = 1, than the nice equation gcd(F_n, F_k) = F_{gcd(n,k)} is true, and as a special case F_k divides F_n iff k divides n. This nice equation would be much more ugly if F_0 != 0.

Update: in case anyone's interested, any integer sequence defined by a second order homogenous linear recursion and starting element 0 has this property. That is, if s_0 = 0, s_1 is and integer, and s_{k+2} = A s_{k+1} + B s_k for given A, B integers; then gcd(s_n, s_k) = s_{gcd(n,k)}.

Update 2006 nov 4: the above paragraph is false. Sorry.

Log In?
Username:
Password:

What's my password?
Create A New User
Domain Nodelet?
Node Status?
node history
Node Type: note [id://490517]
help
Chatterbox?
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others taking refuge in the Monastery: (4)
As of 2022-05-20 16:38 GMT
Sections?
Information?
Find Nodes?
Leftovers?
    Voting Booth?
    Do you prefer to work remotely?



    Results (75 votes). Check out past polls.

    Notices?