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I have thought of a notation that generates large numbers. It is called bracket notation. It starts with the default parentheses. The rules for parentheses are as follows. (x(y,z)x) represents [y,z] where [ and ] represent x parentheses.

  • (a(b,c)a)=(a-1((a-1(b,c,)a-1),(a-1(c,b)a-1))a-1)
  • (a,b)=a^b
  • (a,b,c)=a^(b^c)
  • (a,b,c,d)=a^(b^(c^d))
  • etc.
  • (a(b,c,d)a)=(a-1((a-1(b,c,d)a-1),(a-1(d,c,b)a-1))a-1)
  • etc,
  • [a,b,c]=(a(b,c)a)
  • {a,b,c,d}=[a[b,c,d]a]
  • The first rule applies for any type of bracket.

[2,2,2]=((2,2))=((2,2),(2,2))=(4,4)=256, for example

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