Blockchain is well known as a decentralized and distributed public digital ledger, and is currently used by most cryptocurrencies to record transactions. One of the fundamental differences between blockchain and traditional distributed systems is that blockchain's decentralization relies on consensus protocols, such as proof of work (PoW). However, computation systems, such as application specific integrated circuit (ASIC) machines, have recently emerged that are specifically designed for PoW computation and may compromise a decentralized system within a short amount of time. These computationally resourceful miners challenge the very nature of blockchain, with potentially serious consequences. Therefore, in this paper, we propose a general and flexible PoW method that enforces memory usage. Specifically, the proposed method blocks computationally resourceful miners and retains the previous design logic without requiring one to replace the original hash function. We also propose the notion of a memory intensive function (MIF) with a memory usage parameter k (kMIF). Our scheme comprises three algorithms that construct a kMIF Hash by invoking any available hash function which is not kMIF to protect against ASICs, and then thwarts the pre-computation of hash results over a nonce. We then design experiments to evaluate memory changes in these three algorithms, and the findings demonstrate that enforcing memory usage in a blockchain can be an effective defense against computationally resourceful miners.