Collatz conjecture news

The Collatz conjecture asserts that a sequence defined by repeatedly applying the function $$ T(n) = \begin{cases} (3n+1)/2 &\text{ if $n$ is odd, or}\\ n/2 &\text{ if $n$ is even} \end{cases} $$ will always converge to the cycle passing through the number 1 for arbitrary initial positive integer $n$. On May 7, 2020, I managed to verify this conjecture for all numbers below $2^{68}$. The results confirm that the highest number occurring in the Collatz sequence starting at $n$ grows to approximately $n^2$. All source codes are available on this GitHub repository.

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