User blog:PlantStarAlpineer0/Cobra Notation

I made a quickly expanding notation derived from Beklemishev's worms.

Define:

s = sequence order number

ƨ = same-number row amount

k = any string of numbers

Here are the rules:

1: In C[n], when n = 0, the next step will be C[].

2: In C[n], if n = any positive number, the next step will be C[n-1,n-1].

3: In C[k,n], if n = 0, the next step will exclude it.

4: If a row of the same number n exceeds the amount of 12, then it will show up as n^ƨ.

5: In C[n,n], if n = any positive number, the next step will be, C[n,n-1^ƨ,n,n-1^ƨ-1,n,n-1^ƨ-2...]

6: Rule 5 also applies to n-1^ƨ if n is a positive number.

Now let's go through the first four cobras.

Cobra(0)

1.	C[0]

2.	C[]

Cobra(0) = 2

Simple. Right?

Cobra(1)

1.	C[1]

2.	C[0,0]

3.	C[0]

4.	C[]

Cobra(1) = 4

So far, so good. However, Cobra(2) gets a little tricky.

Cobra(2)

1.	C[2]

2.	C[1,1]

3.	C[1,0,0,1,0,1]

4.	C[1,0,0,1,0,0,0,0,0]

5.	C[1,0,0,1,0,0,0,0]

6.	C[1,0,0,1,0,0,0]

7.	C[1,0,0,1,0,0]

8.	C[1,0,0,1,0]

9.	C[1,0,0,1]

10.	C[1,0,0,0,0,0,0,0,0,0,0,0,0]

11.	C[1,0,0,0,0,0,0,0,0,0,0,0]

12.	C[1,0,0,0,0,0,0,0,0,0,0]

13.	C[1,0,0,0,0,0,0,0,0,0]

14.	C[1,0,0,0,0,0,0,0,0]

15.	C[1,0,0,0,0,0,0,0]

16.	C[1,0,0,0,0,0,0]

17.	C[1,0,0,0,0,0]

18.	C[1,0,0,0,0]

19.	C[1,0,0,0]

20.	C[1,0,0]

21.	C[1,0]

22.	C[1]

23.	C[0^23]

24.	C[0^22]

25.	C[0^21]

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43.	C[0,0,0]

44.	C[0,0]

45.	C[0]

46.	C[]

Cobra(2) = 46

As you can see, it got rather complicated, rather quickly. But this is almost nothing compared to...

Cobra(3)

1.	C[3]

2.	C[2,2]

3.	C[2,1,1,2,1,2]

4.	C[2,1,0,0,1,0,1,2,1,2]

5.	C[2,1,0,0,1,0,1,2,1,1,1,1,1,1]

6.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,1]

7.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0]

8.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0]

9.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0]

10.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0]

11.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0]

12.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0]

13.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0]

14.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0]

15.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1]

16.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0^18]

17.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0^17]

18.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0^16]

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31.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0]

32.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0]

33.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0]

34.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1]

35.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0^38]

36.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0^37]

37.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0^36]

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70.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0]

71.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0]

72.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0]

73.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1]

74.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0^78]

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152.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0,0,0,0,0,1]

153.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1,0^158]

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311.	C[2,1,0,0,1,0,1,2,1,0,0,0,0,0,0,1]

312.	C[2,1,0,0,1,0,1,2,1,0^318]

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630.	C[2,1,0,0,1,0,1,2,1]

631.	C[2,1,0,0,1,0,1,2,0^631]

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1262.	C[2,1,0,0,1,0,1,2]

1263.	C[2,1,0,0,1,0,1,1^1263]

1264.	C[2,1,0,0,1,0,1,1,0^1264,1,0^1263,1,0^1262,1,0^1261,1,0^1260,…]

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Oh, dear... I'm having trouble here. I'll need some help.