User blog:GamesFan2000/Levelled Array Notation (Two Entries and Three Entries)

This notation is an array that creates massive numbers. Sounds like me, does it not?

So, if an entry is 1, it and everything after is cropped off. If 1 is the first entry, the array defaults to 1. If the array contains only one entry, then you do nothing.

Two-entry arrays are very powerful in my notation. Let’s take {3, 3} for instance. First, look at the first entry, or n. Create an n-length chained arrow expression of n’s. Between each n is an n-high tower of arrow levels. So, there are n n’s on each section of each level, and between each n is a section of the next level. On the highest level, each section has n n’s, with n arrows between each n. These are solved from right-to-left, and when there are single arrows on the right-most end, solve the single-arrows as if they were individual and then use the answer as the end number for the later expansions. It works like so: 3>>3>>3 = 3>>3>3>3 = 3>>(3^^^3). The solution for each level section is how many arrows are between the n’s on the level section directly below it. After you’ve solved the full expression, replace n with the answer of the previous expression. The second entry, a, will decrease by 1. Now, take the new n and do exactly what you did the first time, except that the new n is the number that affects the expression. Solve it, decrease a by 1 again, and repeat until a = 1.

So, for {3, 3}, the first expression has 3 3’s in it, and between each of them is an arrow tower with three levels. The first level has two sections with 3 3’s each, the second level has 4 sections with 3 3’s each, and the final level has 8 sections, each with a 3-length chained arrow expression of threes with three arrows between each three. 3→→→3→→→3 becomes 3→→→3→→3→→3, then 3→→→3→→3→3→3. This becomes 3→→→3→→(3^^^3). That’s only for the highest level. Each answer is how many arrows are on the section in the level below it. Once you solve the entire expression, the answer becomes n, a is decreased by 1, and you do it all over again. For {3, 3}, the answer of the second expression is the final answer. {10, 10} has you repeat the process 9 times, with the first expression having 10 levels.

For three entries, i.e. {3, 3, 3}, the third entry, b, tells you to nest the array. Now, how much you nest it is dependent on what the first two entries would give on their own. So, you find out what {n, a} is, and that is how many times you will nest the array. To nest means to do this: {{n, a}, {n, a}, b}. After you’ve solved the nest, you decrease b by 1, and repeat until b = 1, at which point you start the process for two entries.