What do you mean with no gateway? As default via 172.16.16.16 dev ...
indicates, 172.16.16.1
is your (default) gateway.
nslookup google.com 172.16.16.1
basically asks the DNS server at 172.16.16.1
for the IP of the google.com
domain, you forgot the domain, meaning you asked your default DNS server for the IP of 172.16.16.1
, which can't work.
Since you can't reach 1.1.1.1
you don't seem to have access to the internet. Do you have different devices on 172.16.16.0/24
and do they have internet access? Could you post you network config and ip a
?