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A !* !_ Number Chain !_ !* is created by having a rule that takes any number

to some other (not necessarily different) number. Then we start somewhere

and see where we end up.

For example:

* if every number gets doubled,

** every number chain just goes off to infinity.

* if every number gets halved (rounding up),

** every number chain ends with 1.

* if every number gets halved (rounding down),

** every number chain ends with 0.

Now suppose we use the following rule:

* If /n/ is even, halve it.

* If /n/ is odd, send it to /3n+1/

Questions:

* Where does 7 go?

* Where does 17 go?

* Where does 27 go?

* What are the possibilites?

* Where does -5 go?

It is an unproven conjecture that every positive number eventually ends at 1.

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See also: Happy Number.