I am not sure what you want. I am guessing that you want to create a file which gets appended with the range of numbers that are entered.
You will have to open a file, append the data to it.

#!/usr/bin/perl
print "enter the START number: \n";
$number1 = <STDIN>;
print "enter END number: \n";
$number2 = <STDIN>;
@list=($number1..$number2);
print "@list\n";

# if the file already exists.
open OUTFILE, ">>/path/to/outfile" or die "Cannot open $!\n";
# if you want to create new file each time the program is executed.
# open OUTFILE, ">/path/to/outfile" or die "Cannot open $!\n";

map { print OUTFILE $_, "\n"; } @list;

close (OUTFILE);
[download]

Hope this helps.