Get yourself a public/private key pair. Generate sequence numbers (10000, 20000, 30000, 40000, ....) that have some identifying characteristic (e.g divisible by 10000). Encrypt that number using your private key. Encode that value using some human readable system (base 32 or 64) and separate the values into groups to make it easier for people to parse. Distribute the encoded serial number with each sale of you app.
Somewhere in the app, you have the public key hidden away. When a user enters an encoded serial number, first decode it back to binary. Use the public key to decrypt it. Check that it is divisible by 10000.
The hard part is in the implementation - hiding the public key in the app so that it can't be replaced easily. Choosing some sequence that you can identify easily, but not run out of values. Obfuscating the app so that someone can't easily skip past the whole check. etc...
