Something like this can be used for "proof of work" in the blockchain world.
That's an interesting point. You could use this to hash values with infinitely scaling difficulty by providing an offset to n where n = difficulty + n. The only issues is collision since the output is always 0-9 but if your POW check is against multiple digits then it might work? Again you could still have potentially infinite repetitions of sequences of digits with different inputs.
Basically the work will be give me starting index from which, next N digits are = "45334138023580". Finding the first digit can take ages while verification is O(1)ish.
Imagine that to provide storage systems similar to IPFS, but the blockchain network only stores the metadata and no data!