NumberChain

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.

See also: Happy Number.

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