Hofstadter-like sequences

[franktaw at netscape.net]

I don't quite see my way to a proof, but it appears to me that 1 and 2 
are the only cases that converge.  As soon as you have a difference 
other than at the very beginning, it makes a difference again further 
on.

Of course, we need not confine our attention to single numbers starting 
the sequence.  For example, we could start with 1 4:

1 4 6 11 18
 3 2 5  7

Franklin T. Adams-Watters

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

Hello SeqFans,

I was wondering: do sequences which have a different
start than A005228 converge to said A005228?

...

If we start with "2" (instead of "1") the new seq
converges immediately:

...

But what about starting with "3":

...

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