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#!/usr/bin/env perl -l

...
for (1 .. 7) { # Time::Piece->wday returns: Sunday = 1, ..., Saturday 
+= 7
    print +($_ - Time::Piece->strptime("$year$month" . '01', '%Y%m%d')
+->wday) % 7 + 1;
}

6
7
...
3
4
5

$ cal 10 2013
    October 2013
...
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31