James Propp <propp(a)math.wisc.edu> writes:
> Does the group of order 168 shed any light on the curious fact that
> the map
> (x,y) |-> (y,(y+1)/x)
> (from C(x,y) to itself) is of order 7?
> (Another way of stating this fact is that the sequence x,y,(y+1)/x,
> ((y+1)/x)+1)/y,... satisfying a(n+1) = (a(n)+1)/a(n-1) is periodic
> with period 7. This sequence is usually attributed to someone named
> Lyness, but I don't know why Lyness studied it.)
> Jim Propp
Are you sure? I get
x, y, (y+1)/x, (x+y+1)/(xy), (x+1)/y, x, y, ...
with period 5.
Cute, the way it follows the same rule forwards as backwards. But
of course the rule a(n)+1 = a(n+1)a(n-1) is symmetric.
Dan
