Another 6-branched generalized-Collatz mapping
Consider the function T:
\[
T(x)=\left\{\begin{array}{ccc}
\frac{x}{6} &\mbox{if $x ≡ 0 \pmod{6}$}\\
\frac{7x-1}{2} &\mbox{if $x ≡ 1 \pmod{6}$}\\
\frac{x}{2} &\mbox{if $x ≡ 2 \pmod{6}$}\\
\frac{2x}{3} &\mbox{if $x ≡ 3 \pmod{6}$}\\
2x &\mbox{if $x ≡ 4 \pmod{6}$}\\
\frac{9x-1}{2} &\mbox{if $x ≡ 5 \pmod{6}$}.
\end{array}
\right.
\]
It is seems likely (see link) that trajectories seem certain to enter one of the cycles
\[
\begin{array}{c}
0\to0\\
1\to3\to2\to1\\
11\to49\to171\to114\to19\to66\to11\\
6k+4\to12k+8\to6k+4, k\in\mathbb{Z}.
\end{array}
\]
Last modified 13th April 2023
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