Find the correct pattern and continue the following sequence
4, 3, 4, 7, 6, 5, 2, 6, 8, 7, 3, ...
You should be able to find at least one hint in the title
EDIT
Just realized I made a little mistake. It is still a valid sequence, but I need to give a hint, because it would be too arbitrary without this one.
The sequence will never contain a number greater than 8
Hint 1
Further explanation of the initial hint, you will need
mod 9
Hint 2
switch (i mod x) {...}
Hint 3
In 1748 you were able to continue this sequence to the
23th24th number
Hint 4
The title might be a hint on (not only) a important number used in this puzzle, even it's not there in its true form
Hint 5
The sequence is based on a number
Hint 6
A hint on how you could create the sequence with some kind of pseudocode (addition to hint 2)
for (i = 0; i < basenumber.length; i++) switch (i mod x) {...}
Hint 7
$2 * 2 = 4, 7 * 3 = 21, 1 * 4 = 4$