# Lucky numbers properties

by Ulam
Tags: lucky, numbers, properties
 P: 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 $$n$$ ?

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