# Lucky numbers properties

1. ### Ulam

5
Let be $$l_n$$ the n-th lucky number (Ulam sieve) and
$$J_n=\{k \in \mathbb{N} :k \le n \}$$. So, is it possible to have a proof that exists a

$$u_n(k): J_n \longrightarrow \{-1,+1\}$$ such that

$$n=\sum_{k=1}^{n}u_n(k)l_k$$

for all $$n$$ ?