What's the notation for writing a number as its digits

Question

Hoping this is a simple question, I'm pretty certain this is covered in number theory, but I haven't had much time to pour through my number theory book. I'm wondering what the notation for writing an integer as its digits is.

For example, given $435$ is it something like $4|3|5$?

Thanks

Answer 1

I think you're looking for something like $\overline{ABCD}$ as a shorthand for $1000A+100B+10C+D$. I see this notation used sometimes in problems dealing with a number's digits.

Answer 2

I always used

$$[a,b,c,\dots,z]_B$$

where $a,b,c,\dots,z$ are base-$10$ numbersto represent a number in base $B$. The advantage is that $a,b,c, \dots$ don't have to be single-digit integers.

For example, $[10, 9, 8]_{16} = 10\cdot 16^2 + 9 \cdot 16 + 8$. If it is clear what I'm doing, I don't use the brackets when doing arithmetic in base $B$.

For example, to compute $3 \times [10, 9, 8]_{16}$:

\begin{array}{c} & 10 & 9 & 8 \\ \times & & & 3 \\ -- & -- & -- & -- \\ & 30 & 27 & 24 \\ \end{array}

and $[30, 27, 24]_{16} = [30, 28, 8]_{16} = [31, 12, 8]_{16} = [15, 1, 12, 8]_{16}$.

Answer 3

If you want to do something, just do it.

Say: For purpose of notation am going to indicate a number use expression seperated by $|$ to mean an integer whose digits are the values between bars. What I mean for example $|a|9-a|2$ will mean a three digit number where the first digit is $a$, the second $9-a$, and the third digit is $2$. i.e. $a|9-a|2 = a*10^2 + (9-a)*10 + 2$.

It doesn't matter if there is or isn't any standard notation (there isn't). You have expressed what you intend.