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.
- if every number gets doubled,
- 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
- 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