How to zero pad a sequence of integers in bash so that all have the same width?

In your specific case though it’s probably easiest to use the -f flag to seq to get it to format the numbers as it outputs the list. For example:

for i in $(seq -f "%05g" 10 15)
do
  echo $i
done

will produce the following output:

More generally, bash has printf as a built-in so you can pad output with zeroes as follows:

$ i=99
$ printf "%05d\n" $i
00099

You can use the -v flag to store the output in another variable:

$ i=99
$ printf -v j "%05d" $i
$ echo $j
00099

Notice that printf supports a slightly different format to seq so you need to use %05d instead of %05g.