# Testing Collatz Conjecture

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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