z(9)=z(3), so it's not injective.
From 9 onwards, the sequence is periodic, because z(3+k+6n)=z(3+k), so it's not surjective.
My question is:
The function z from to is defined recursively by:
z(1)=1 and
for all .
Show that z is neither an injection or a surjection.
What I've done so far is find the first couple of values of z(n) up to n=7, where I got z(2)=2, z(3)=7, z(4)=5, z(5)=4, z(6)=9, and z(7)=6. At this point, I'm not sure about what to do, so any help would be greatly appreciated!