For an AI wanting to obtain memory states and live on forever a incentivized blockchain would surely be the way to go, say if we reached a point where we could store our memory states on the blockchain such as altered carbon, would you really want to store that in a regular distributed system? No you would want to obtain the security that blockchain provides in a trustless manner, as our memory states would need to live on forever.
If only AI or blockchains would work that way.
While I have no idea how consciousness can be stored -- no one has, humanity hasn't yet the slightest clue what consciousness even is -- I'm fairly certain it won't be on a blockchain.
Maybe one day humanity will be able to externally store memories (beyond mere audiovisual reproductions) and minds (be they human or artificial) but that technology is probably still a few generations out and won't be technology we'll be able to fathom.