Collatz conjecture states that take any natural number $n$ , if $n$ is even divide it by $2$ to get $n/2$ , if $n$ is odd multiply it by $3$ and add $1$ to get $3n+1$ . Repeat the process indefinitely, no matter what number you start with, you will always eventually reach $1$

Proving or disproving this conjecture is still a open problem in mathematics, but anyways here's the problem :

From first $100$ natural numbers, find the number which takes most number of iterations to reach $1$(Remember we have to stop as soon as we reach to $1$ otherwise we will end in an indefinte cycle of $4-2-1$)

As an example for number $6$ we have :

$6\rightarrow 3\rightarrow 10\rightarrow 5\rightarrow 16\rightarrow 8\rightarrow 4\rightarrow 2\rightarrow 1$

Here it is clear that $8$ iterations are involved

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