format

 function formatDays(days, format)
   function isLeapYear(year)
        return year % 4 == 0 and (year % 100 > 0 or year % 400 == 0)
  end
   function daysInYear(year)
        if isLeapYear(year) then
          return 366
        end
        return 365
  end

   year = 0 -- change this to start in a different year
   mon = 1

  while days >= daysInYear(year) do
        days = days - daysInYear(year);
        year = year + 1;
  end

   _temp = { 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }
  if isLeapYear(year) then
        _temp[2] = 29
  end

  while days >= _temp[mon] do
        days = days - _temp[mon];
        mon = mon + 1;
  end

  return string.format(format, days+1, mon, year) -- here you can change the order of the values if you want something like DD/MM/YYYY or MM/DD/YYY
end