Depends on the year. For 2009, Jan 1 is a Thursday, so:

my $day_of_year  = 1; # or whatever
@days_of_week = ('Sunday', 
                 'Monday', 
                 'Tuesday', 
                 'Wednesday', 
                 'Thursday', 
                 'Friday', 
                 'Saturday');
print $days_of_week[($day_of_year+3)%7];
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Update: fixed typo s/$dayofyear/$day_ of_year/ -- thanks ww