# Collatz tree

## Primary tabs

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A {\em Collatz tree} or {\em Collatz graph} is a tree representation of several Collatz sequences joined together at their common terms the closer they are to the root term, which is 1. Typically the powers of 2 are placed in the central column, though placing to the left or the right are also viable options. In the following illustration, given to a height of 12, the powers of 2 are placed in the rightmost column:

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$\xymatrix{ 96\ar[d] & 17\ar[dr] & 104\ar[d] & 106\ar[d] & 640\ar[d] & 672\ar[d] & 113\ar[dr] & 680\ar[d] & 682\ar[d] & 4096\ar[d] \\ 48\ar[d] & & 52\ar[d] & 53\ar[dr] & 320\ar[d] & 336\ar[d] & & 340\ar[d] & 341\ar[dr] & 2048\ar[d] \\ 24\ar[d] & & 26\ar[d] & & 160\ar[d] & 168\ar[d] & & 170\ar[d] & & 1024\ar[d] \\ 12\ar[d] & & 13\ar[drr] & & 80\ar[d] & 84\ar[d] & & 85\ar[drr] & & 512\ar[d] \\ 6\ar[d] & & & & 40\ar[d] & 42\ar[d] & & & & 256\ar[d] \\ 3\ar[drrrr] & & & & 20\ar[d] & 21\ar[drrrr] & & & & 128\ar[d] \\ & & & & 10\ar[d] & & & & & 64\ar[d] \\ & & & & 5\ar[drrrrr] & & & & & 32\ar[d] \\ & & & & & & & & & 16\ar[d] \\ & & & & & & & & & 8\ar[d] \\ & & & & & & & & & 4\ar[d] \\ & & & & & & & & & 2\ar[d] \\ & & & & & & & & & 1 }$

\begin{thebibliography}{1}
\bibitem{jl} J. C. Lagarias, The $3x + 1$ problem and its generalizations'', {\it Amer. Math. Monthly}, {\bf 92} (1985): 3 - 23
\end{thebibliography}

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