What other sequences solve this equation?

[Kimberling, Clark]

In this query, a(n) and b(n) denote increasing complementary sequences,
such as (1,3,5,7,...) and (2,4,6,8...), as well as pairs of Beatty
sequences.
 
The question is, how can we account for all solutions of the equation 
 
a(b(n)) - b(a(n)) = 1 ?
 
Among the solutions are a = (1,3,5,7,....) and the lower Wythoff
sequence, a(n) = Floor[tau*n)], where tau is the golden mean.
 
Anyone want to look into this?
 
Thanks.
 
Clark Kimberling
 
 
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20060510/b6734e8d/attachment.htm>