[seqfan] Re: Fibonacci sequences sharing no terms

[franktaw at netscape.net]

Are you familiar with the Zeckendorf (or base Fibonacci) representation?

The numbers in Fib(4,6), expressed in that representation, are 
(101,)1001, 10010, 100100, .... Obviously this pattern continues, and 
obviously there can be no Fibonacci numbers in it.

Take a look at https://oeis.org/A035513 .

Franklin T. Adams-Watters

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Tue, Sep 24, 2013 10:16 am
Subject: [seqfan] Fibonacci sequences sharing no terms


Hello Seqfans,
please forgive me if this question is naïve.
Consider Fib(1,2) = 
1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,...
Now will Fib(4,6) = 4,6,10,16,26,42,68,110,178,288,466,... share at 
some point
one term (or more) with Fib(1,2)?
If yes or no, do we know why? Are there constraints on 'a' and 'b' 
leading to
a Fib(a,b) which will never share any term with Fib(1,2)?
Many thanks,
É.
[I've never subscribed to Fibonacci Quarterly...]



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