Collatz help!

let us take a natural number n then we perform 2 operations (1) add 2 and divide by 7 if n+2 is divisible by 7. (2) if 1st is not possible then multiply by 2. Repeat the same operations. I observed for quite a few numbers that it tends to infinity and i strongly believe that every number should tend to infinity. Does there exist a number for which it does not tend to infinity or makes a loop. !!!( ^-^ )

#NumberTheory

Easy Math Editor

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`2^{34}`	$2^{34}$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$