This can even be further optimized on memory usage.
1. TAN = Hash(2. TAN)
2. TAN = Hash(3. TAN)
3. TAN = Hash(4. TAN)
...
30. TAN = Hash(whatever)

So i only have to save the hash of the first TAN in the AT.
If for example the 7. TAN is provided, it has to be hashed 7 times and will result in hash of first TAN.