To write out all the integers in the range [220210,220221] to a file using the bash shell (or any shell that has brace expansions):
printf '%s\n' {220210..220221} >file
What's happening here is that the shell will expand the brace expansion {220210..220221} to the list of all the integers in the range. These will then be used as arguments to the printf command.
The printf command outputs its arguments in accordance with its format string (the 1st argument). The format string %s\n tells printf to output each argument as a string with a trailing newline. Since you're outputting integers, you could also have used %d\n, but it would have made no difference.
The redirection >file tells the shell to put all output of the printf command into the file called file. The file will be created or, if it already exists, it will first be truncated (emptied).
If you're using a shell that does not understand brace expansions, then the above would just print {220210..220221} on a line.
In such a shell, you may want to do an explicit loop:
n=220210
while [ "$n" -le 220221 ]; do
printf '%s\n' "$n"
n=$(( n + 1 ))
done
This creates a variable n that we print and increment in each iteration. The initial value of the variable is set to 220210 before the loop and the loop terminates whenever $n reaches 220222 (that value won't be printed).