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Lucky numbers properties

by Ulam
Tags: lucky, numbers, properties
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Ulam
#1
Nov4-11, 05:19 PM
P: 5
Let be [tex]l_n[/tex] the n-th lucky number (Ulam sieve) and
[tex]J_n=\{k \in \mathbb{N} :k \le n \}[/tex]. So, is it possible to have a proof that exists a

[tex]u_n(k): J_n \longrightarrow \{-1,+1\}[/tex] such that

[tex]n=\sum_{k=1}^{n}u_n(k)l_k[/tex]

for all [tex]n[/tex] ?
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