====== Collatz conjecture ======

Using the formula :

$$ {\displaystyle f(n)={\begin{cases}{\frac {n}{2}}\quad\quad\quad{\text{if }}n\equiv 0{\pmod {2}}\\[4px]3n+1\quad{\text{if }}n\equiv 1{\pmod {2}}.\end{cases}}} $$

The Collatz conjecture states that this process will eventually reach the number 1, regardless of which positive integer is chosen initially.

For example, using //n// = 12 generates the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1.

The conjecture remains open : i.e. neither proven or disproven.

Further reading : [[https://en.wikipedia.org/wiki/Collatz_conjecture|Wikipedia]]

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Also see : 
[[content:mathematics:juggler_sequences|]]