Try the following:
INSERT INTO your_table (your_column)
SELECT (MAX(auto_increment_column) / 3) + 2 FROM your_table;
EDIT
If you want to calculate the column depending on the number of values use this:
INSERT INTO your_table (your_column)
SELECT (COUNT(*) / 3) + 2 FROM your_table;
EDIT 2
You can accomplish the same using:
INSERT INTO your_table (your_column) VALUES (
(SELECT (MAX(aa.auto_increment_column) / 3) + 2 FROM your_table AS aa)
);
EDIT 3
For more columns you can use something like this:
INSERT INTO your_table (your_column, some_other_column) VALUES (
(SELECT (MAX(aa.auto_increment_column) / 3) + 2 FROM your_table AS aa), some_other_column
);
You can find more info here:
Select from same table as an Insert or Update
In fact you have to add +2 because it's 1 from you rule and +1 to increment the MAX(id).