Unlike other proposals of calendar schemes for people living on Mars, ours attempts to keep the Martian date closely in tune with the weekly cycle and Gregorian calendar as employed on Earth. It combines elements of the Gregorian solar and Hindu lunar calendars. (See our book Calendrical Calculations, Cambridge University Press, 1997.) Its peculiarity is in the not infrequent occurrence of skipped days, needed to re-correlate the Martian and Gregorian calendars, and in this respect resembles the Hindu lunar calendar.
The underlying idea is that each sol is named according to the weekday and Gregorian month/day current on Earth. To maximize the overlap between the date on Earth and on Mars, we can choose to name the Martian sol to match the date at the terrestrial international dateline when it is noon at the Martian prime meridian. In effect, Mars is treated like a time-zone on Earth, but with the date and time coinciding with changing locales on Earth.
On account of the longer sol, this scheme would have the unique feature of expunged days (like the Hindu calendar wherein a solar day is longer than a lunar day). One can go from, say, Tuesday, January 5 to Thursday, January 7, with no sol named ``Wednesday, January 6''. This would transpire 9 or 10 times a year, and can be compared with what befalls someone traveling across the dateline.
Such a calendar would have all its units in close agreement with those on Earth. Days would be named as on Earth. Though the sol is longer than a day, the month and year would have the same mean length (in days, not sols) as on Earth. Thus it has the advantage of being familiar to earthlings and facilitates coordination with Earth. Its year, however, bears no correlation with Martian seasons.