I've got an idea for numbers. A new system that you wish you've never seen.
Symbols needed:
0 -> nothing
[] -> declares numbers
() -> represents prime constituants
Examples:
0 obviously stays 0. It's nothing
[0] is a 1. There is something. One nothing, but it is.
Note for the following: the primes will come from right to left
[(0)] is a 2 (obvious). There is one nothing inside of the spot where two is represented. So it is one two and therefore a two.
[(0)0] is 3. There is one nothing inside of the spot where threes are represented and then there is literally nothing where any two could be.
Note for the following: fuck y'all, recursion
[((0))] is a 4. At the spot where the two is represented, there is a number. This number has one nothing where the two is represented. So we have one two inside of the spot where the two is. We have two 2s. 2×2 is 4.
[(0)00] -> 5. One nothing at the spot for the fives.
[(0)(0)] -> 6. One nothing at the 3, one nothing at the 2. So 2×3=6
[(0)000] -> 7.
[((0)0)] -> 8. At the spot where the two is, is a number. This number has one nothing where the three is and nothing at all at the twos. Three twos means 2×2×2=8.
[((0))0] -> looks the same but is a 9. At the spot for the threes there is a number. The number has one nothing where the twos are. So we have a total of two threes and then nothing at the twos. 3×3=9.
[(0)0(0)] -> 10. One nothing at the five, then nothing at the three and then one nothing at the two. 5×2=10.
Now lets try something harder:
[(0)00((0))((0)(0))] clearly a 6336. *inhales* We have one nothing where the 11 is. Then nothing at 7 and nothing at 5. But we have a number where the 3 is. This number is one nothing at the spot of 2. So now we have one 11 and two 3s. After that we also have a number where the 2 is. This number has one nothing at the spot of the 3 and one nothing at the spot of the 2. So we have 2×3=6 2s. We have one 11, two 3s and six 2s. Therefore 11×3×3×2×2×2×2×2×2=6336
Can you tell me what 59,049 is? :D
I played with this number system and have a question for whoever feels worthy enough to answer.
I got interested in numbers that can be mirrored and still are the same number like for example:
8100 which is [((0))(((0)))((0))] or
2 which would be [(0)].
Then I recognized that there are often "twins". Two mirror-numbers that are 2 apart like:
2 [(0)] and 4 [((0))] or
14 [(0)00(0)] and 16 [(((0)))].
Pretty much like twin primes that are 2 apart but in this case not with prime numbers but with numbers in my system that can be mirrored and are the same.
Can someone prove or disprove me if there are infinite pairs of my lovely twin-mirrors?
(The biggest pair I found was 98594 with 98596 because after that I had a StackOverflow sigh...)
