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I'm trying to make a table in org-mode, the first column of which should be the Monday of each week starting with a date I specify. So, for example, if I specify Dec 14th, I would get a column with Dec 14, Dec 21, Dec 28, Jan 4, etc. Is this possible? If so, how?

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4

Dates can be used in formulas.

The following example should be similar to what you are asking for:

|   |    | Date               | Other |
|---+----+--------------------+-------|
| $ |    | start=<2015-12-07> |       |
| # | 1  | <2015-12-14 Mon>   |       |
| # | 2  | <2015-12-21 Mon>   |       |
| # | 3  | <2015-12-28 Mon>   |       |
| # | 4  | <2016-01-04 Mon>   |       |
| # | 5  | <2016-01-11 Mon>   |       |
#+TBLFM: $3=$start + $2 * 7
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