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By definition of Collatz Conjecture or $3n+1$, regardless of the sequence (ie.$ m1,m2,m3....mn$), at the end, it eventually produces 1 at the end. For example, if you let $m=10$ (ie. $10, 5, 16, 8, 4, 2, 1, 4, 2, 1...$), you must repeat 6 times and eventually reach to 1.

How can Module

Collatz[m_]:= Module[{...}]

be used that takes positive integer $m$ and outputs the "number of times" that the procedure must be repeated until obtaining 1?

Side Note: Although the link does incorporate the Module function, It's not about longest [Collatz] chain.

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    $\begingroup$ It can be done as a straightforward loop. Not necessarily the best way, but reasonably effective. Collatz[m_] := Module[{j = 0, m1 = m}, While[m1 =!= 1, j++; m1 = If[OddQ[m1], 3*m1 + 1, m1/2]]; j] $\endgroup$ Commented Apr 2, 2018 at 22:11

1 Answer 1

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Recursion comes in handy here:

Collatz[m_] := Collatz[m] = 1 + If[EvenQ[m], Collatz[m/2], Collatz[3 m + 1]]; Collatz[1] := 0; Collatz[10] (* 6 *)
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    $\begingroup$ +1 Recommend that definition start off as Collatz[m_Integer?Positive] :=... $\endgroup$ Commented Apr 3, 2018 at 1:44

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