User blog comment:ArtismScrub/New array notation idea?/@comment-32876686-20171205034832

Your array notation idea is not unique, but, it is understandably difficult to create something truly unique and powerful, when the first inclination is to make a simple recursive notation, or an array which expands to another array whose values are in turn other arrays which are altered in some simple way.

Rather than using traditional definitions based on what you might have seen before, try to define an array notation which takes numbers and does something with them that has never been done before. Nayuta Ito's SIR function is a good example of a simple but powerful, (I believe uncomputable), array function. So is the Bashicu pair sequence system, which is also capable of generating large countable ordinals.

From looking at these and other examples, I hope you're able to come up an array notation you feel is unique. :)