I have one for you. 172.16.16.172. I will sell it to you for $172.16.
Okay, seriously now... DON'T DO IT.
Like the famous saying of buying the Brooklyn Bridge, or when Universal Studios tried to sue Nintendo over the use of King Kong, no private entity should be selling you an IP address.
An IPv4 address is basically a fancy way of writing a number between zero and 4,294,967,295. Didn't know that? Try using a Microsoft Windows computer and running:
C:\> ping 134744072
Pinging 8.8.8.8 with 32 bytes of data:
Reply from 8.8.8.8: bytes=32 time=10ms TTL=116
Reply from 8.8.8.8: bytes=32 time=10ms TTL=116
Reply from 8.8.8.8: bytes=32 time=10ms TTL=116
Reply from 8.8.8.8: bytes=32 time=10ms TTL=116
Ping statistics for 8.8.8.8:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 10ms, Maximum = 10ms, Average = 10ms
C:\>
See, 1,348,744,072 (which is 8x256x256x256+8x256x256+8x256+8x1) is really rather equivalent to 8.8.8.8 and Microsoft Windows's ping command even recognizes that.
Just like the government gives free ownership of numbers like seven (written English), 7 (Arabic numeral), you can't copyright the number seven, the number 7, siete (written Spanish), or VII (roman numeral), you likewise cannot own 0.0.0.7 or 8.8.8.8
What you can do is have some control over the number, based on the assignments from the Internet Assigned Numbers Authority who provided some decision making to the regional Internet registries (RIR's) such as ARIN (American Registration of Internet Numbers), who has allocated groups of numbers to certain organizations such as Internet Service Providers. There are some general rules in place, which are followed by the sort of consensus that makes the Internet work as well as it does.
And part of that consensus is that the address 172.16.16.172 is actually free for you to use, as specified by the Internet Engineering Task Force (IETF)'s Best Current Practice 5, which is basically the Request for Comments 1918 (a very minor update to RFC 1597). The public Internet won't accept it, but you may use it privately on your own Internal network, according to that standard.
So, my offer to sell it was clearly a joke. It's not mine to sell. Enjoy using it how you like. (Of course, getting other people to route the traffic to you might be an entirely different challenge. That does get covered by another Superuser question, How to redirect/route IP address to another IP address?.)
Basically, I will acknowledge there is something of a market for IP address blocks. Although, people are usually talking about "blocks", meaning larger groups of addresses, and not just a single address. IP addresses are often most sensibly/efficiently handled in groups of neighboring addresses, because of how Internet routing is designed. Basically, if someone sold you a single address, the rest of the Internet would still route such traffic to the group that the address is a part of. So the seller would still be involved. (That is, at least with traditional standard Unicast routing that we are most used to.) Since that seller would often still be handling bandwidth in order to route traffic to your address, they aren't really free of involvement with the address, so the address isn't really "sold" very fully. The closest thing would probably be when an Internet Service Provider provides access to a single "Static IP" address, often in exchange for a cost that is charged to a customer. But since the customer would lose access to that address once they stop subscribing to that cost, the customer never really had full ownership of the address.
Similar reading: who owns a domain name. (If anybody, the Internet Corporation for Assigned Names and Numbers (ICANN), although the referenced article basically indicates nobody owns them either.)