  Given a set of integers containing no 3-term arithmetic progressions, one
constructs a Stanley sequence by choosing integers greedily without forming
such a progression. Independent Stanley sequences are a "well-structured" class
of Stanley sequences with two main parameters: the character $\lambda(A)$ and
the repeat factor $\rho(A)$. Rolnick conjectured that for every $\lambda \in
\mathbb{N}_0\backslash\{1, 3, 5, 9, 11, 15\}$, there exists an independent
Stanley sequence $S(A)$ such that $\lambda(A) =\lambda$. This paper
demonstrates that $\lambda(A) \not\in \{1, 3, 5, 9, 11, 15\}$ for any
independent Stanley sequence $S(A)$.
