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Can someone explain what these questions are asking?

  1. Jan 14, 2008 #1
    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.
     
  2. jcsd
  3. Jan 14, 2008 #2
    So, a_0 is given, but arbitrary, and you're trying to find an l for which l > 0 and a_l = 1

    For instance if a_0 = 1
    Then a_1 = 2, a_2 = 1, so l = 2

    If a_0 = 17, then a_1 = 18, a_2 = 9, a_3 = 10, a_4 = 5, a_5 = 6, a_6 = 3, a_7 = 4, a_8 = 2, a_9 = 1
    So l = 9

    You just want to solve for l in terms of a_0
     
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