a[n] is a[n] terms from term = a[n]+1

[Ralf Stephan]

Leroy Quet: 
> You have a sequence where:
> a[1] = 1;
> and either a[n -a[n]] = a[n]+1
> or
> a[n +a[n]] = a[n]+1
> 
> such that a[n -a[n]] is chosen whenever it is not equal
> to any positive integer <= a[n] already.
> 
> The sequnce begins, with 0 representing "empty" a[n]'s:
> 
> 1, 2, 5, 3, 0, 0, 4, 6, 17, 15, 13, 11, 9, 7, 0, 
> 0, 0, 0, 0, 0, 8, 10, 12, 14, 16, 18,...
> 
> Does this sequence continue forever (so that no a[n] = more than one
> different value at once, of course)?

Don't such questions awfully look like the halting problem and/or the
busy beaver problem?

Just a thought,
ralf