n kinds of "base n" representations

[sweety439]

For all integer n>=1, there are n kinds of "base n" representations, choose n consecutive (positive or negative or 0) integers, including the integer 1, there are n ways to choose

n=1:

{1}: unary numeral system (1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, ...)

n=2:

{0,1}: standard binary number system (1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, ...)

{1,2}: bijective base 2 number system (1, 2, 11, 12, 21, 22, 111, 112, 121, 122, 211, 212, ...)

n=3:

{-1,0,1}: balanced ternary number system (1, 1z, 10, 11, 1zz, 1z0, 1z1, 10z, 100, 101, 11z, 110, ...)

{0,1,2}: standard ternary number system (1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, ...)

{1,2,3}: bijective base 3 number system (1, 2, 3, 11, 12, 13, 21, 22, 23, 31, 32, 33, ...)

n=4:

{-2,-1,0,1}: (1, 1y, 1z, 10, 11, 1yy, 1yz, 1y0, 1y1, 1zy, 1zz, 1z0, ...)

{-1,0,1,2}: (1, 2, 1z, 10, 11, 12, 2z, 20, 21, 22, 1zz, 1z0, ...)

{0,1,2,3}: standard quaternary number system (1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, ...)

{1,2,3,4}: bijective base 4 number system (1, 2, 3, 4, 11, 12, 13, 14, 21, 22, 23, 24, ...)