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## Main Question or Discussion Point

Let [tex]a_{0}[/tex] be any positive integer and let [tex]a_{k+1}=a_{k}+1[/tex] if [tex]a_{k}[/tex] is odd, and let [tex]a_{k+1}=a_{k}/2[/tex] if [tex]a_{k}[/tex] is even.

Let [tex]\ell[/tex] be the smallest positive integer where [tex]a_{\ell}[/tex] = 1. Find an expression for [tex]\ell[/tex] in terms of [tex]a_{0}[/tex] that is non-recursive.

Let [tex]\ell[/tex] be the smallest positive integer where [tex]a_{\ell}[/tex] = 1. Find an expression for [tex]\ell[/tex] in terms of [tex]a_{0}[/tex] that is non-recursive.