Edit made on March 10, 2009 by GuestEditor at 11:25:05
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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.
* 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/
* 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.