Set a network range in the no_proxy environment variable

You're looking at it the wrong way. The no_proxy environment variable lists the domain suffixes, not the prefixes. From the documentation:

no_proxy: This variable should contain a comma-separated list of domain extensions proxy should not be used for.

So for IPs, you have two options:

1) Add each IP in full:

printf -v no_proxy '%s,' 10.1.{1..255}.{1..255};
export no_proxy="${no_proxy%,}";

2) Rename wget to wget-original and write a wrapper script (called wget) that looks up the IP for the given URL's host, and determines if it should use the proxy or not:

#!/bin/bash
ip='';
for arg; do
   # parse arg; if it's a URL, determine the IP address
done;
if [[ "$ip" =~ ^10\.1\. ]]; then
   wget-original --no-proxy "$@";
else
   wget-original "$@";
fi;

info wget says:

 `no_proxy'
     This variable should contain a comma-separated list of domain
     extensions proxy should _not_ be used for.  For instance, if the
     value of `no_proxy' is `.mit.edu', proxy will not be used to
     retrieve documents from MIT.

So the variable should contain a list of domains, not IP ranges. You'll need to set up proper local aliases for your local machines in /etc/hosts file(s).

Apart from this, bear in mind that setting an environment variable does not guarantee that a proxy will or will not be used. It is just an information that may be used by programs that support it.

Not exactly a correct solution but it might solve the problem for you. If you assume that accessing anything from the outside of the proxy will be using DNS-names and not directly using IP-addresses, you can set it like:

export no_proxy=0,1,2,3,4,5,6,7,8,9

As far as I know, no top domain ends with a number so if it does, it must be an IP-address.