We define the function (where excludes zero) such that
Then let the sequence be defined as , with an arbitrary natural seed value.
It is conjectured that the sequence will always end in , repeating infinitely. This has been verified by computer up to very large values of , but is unproven in general. It is also not known whether this problem is decideable. This is generally called the Collatz problem.
The sequence is sometimes called the “hailstone sequence”. This is because it behaves analogously to a hailstone in a cloud which falls by gravity and is tossed up again repeatedly. The sequence similarly ends in an eternal oscillation.
|Date of creation||2013-03-22 11:42:43|
|Last modified on||2013-03-22 11:42:43|
|Last modified by||akrowne (2)|