Topic: Way to use computation power for mining coins (Read 188 times)

What are the biggest problems of almost all blockchains which use proof-of-work? There are two:
1. Practically wasted power on generating needed hash to approve block.
2. Enlargement of blockchain.
What if to use 1. to solve 2. ?
What about to use computation power instead of solving arbitrary tasks to solve pragmatic and usefull task: allow new block's size to become smaller?
We have all time growing chain in which at every moment is appearing new unique sequences let's say of 16 bit's: f5d840e715a... etc
And at the same way some there are more and more repeative sequences.
It is not necessary to keep every repeative sequence of 16 bits in the blockchain.
We just need to find the place where the first sequence is on the blockchain, namely number of block and place in block where this seq. starts go and its length.
Then instead of placing raw data in new block we can place archived data, where instead of raw 16 bit sequences there will be links to the same sequences which exists somewhere in the blockchain.
So proof-of-work can be in form of searching matching bit sequnces in the blockchain. When some is found, we save its location as link to it to replace the same sequence in new block with this "archiving data".
So the task for the miner can be to find location of bits sequence in the blockchain which size would be lesser then the sequence itself.
Location or the link to the same sequence in the blockchain are the numbers and they also have size. Even if we find some repeative sequence somewhere in blockchain it is not guarantee that the size of the sequence will be bigger then size to the link to its location in the blockchain.
So the real miner's work should be locating those sequences in the past, which long enogh for their [location-size id] by which we can easy find them should be smaller in size then a pure sequence.
I see many other tasks to be solved even if this theory is working.
But if we can prove that this works, we can build blockchain where miner's work will be much more effective then in most modern blockchains.
The dynamics of increasing in size of the blockchain based on this technology will have lowering factor but not constant as in modern blockchains.

What do you think about it?