Not a fan of 3

Probability Level 5

How many positive integers $n \leq 1000$ are there which satisfy the following condition:

We can rearrange the positive integers from 1 to $n$ in a row, where the sum of the first $k$ terms is not a multiple of 3, for every $1 \leq k < n$ .

Note: To avoid ambiguity, the integer 1 satisfies the above condition.