Sorry, a numeric comparison won’t work correctly here:

#! perl
use strict;
use warnings;

my    $sequence_number = "01";
print $sequence_number,  "\n";

for (1 .. 105)
{
    if (++$sequence_number > 99)
    {
        $sequence_number = "01";
    }

    print $sequence_number, "\n";
}
[download]

Output:

14:20 >perl 1479_SoPW.pl
01
02
3
4
5
6
7
8
9
10
11
12
...
97
98
99
01
02
3
4
5
6
7

14:20 >
[download]

The reason is given in the documentation I quoted above:

If you increment a variable that is numeric, or that has ever been used in a numeric context, you get a normal increment. (emphasis added)

:-(