Generate a sequence of numbers I want to generate an infinite sequence of numbers between $0$ and $9$ such that the percentage of number $i$ appearing in the sequence is $p_i$. Let $p=\lbrace p_0,...,p_9\rbrace$.

Another agent $B$ will observe $k$ consecutive elements from the sequence. Then it will update its belief about the probability of $p_i$ using a belief update rule (let's say a simple frequentist, i.e., the number of occurrences of each digit divided by $k$).

The question is how can I generate the sequence such that $B$'s belief $q$ is close to $p$, i.e., $d(p,q)$ is minimized where $d(p,q)$ is the dsitance function of two distributions, e.g., $d(p,q)=(\sum_i (p_i-q_i)^2)^0.5$.

Note that I don't know how $B$ will choose the $k$ numbers. Let's consider the worst case (i.e., worst $p'$).
For observing consecutive elements: pick up the best sequence of $k$ elements (depending on your proximity measure), and repeat it. Then B will always observe the same sequence (I assume that cyclical permutation doesn't affect B).

For observing random elements: how would you pick them randomly? Do you want a deterministic sequence?