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This is still not true. The smallest counterexample is given by $n=30$ with $\nu_2(w_{30}) = 10$ and $2s(31)-3=7$. This can be easily verified by computing $w_n$ modulo $2^{11}$.
This is still not true. The smallest counterexample is given by $n=30$ with $\nu_2(w_{30}) = 10$ and $2s(31)-3=7$.
This is still not true. The smallest counterexample is given by $n=30$ with $\nu_2(w_{30}) = 10$ and $2s(31)-3=7$. This can be easily verified by computing $w_n$ modulo $2^{11}$.
