Collatz problem

We define the function f: (where excludes zero) such that

f(a)={3a+1 if a is odd a/2 if a is even.

Then let the sequence cn be defined as ci=f(ci-1), with c0 an arbitrary natural seed value.

It is conjectured that the sequence c0,c1,c2, will always end in 1,4,2, repeating infinitely. This has been verified by computer up to very large values of c0, but is unproven in general. It is also not known whether this problem is decideable. This is generally called the Collatz problemMathworldPlanetmath.

The sequence cn 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.

Title Collatz problem
Canonical name CollatzProblem
Date of creation 2013-03-22 11:42:43
Last modified on 2013-03-22 11:42:43
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 32
Author akrowne (2)
Entry type Conjecture
Classification msc 11B37
Synonym Ulam’s Problem
Synonym 1-4-2 Problem
Synonym Syracuse problem
Synonym Thwaites conjecture
Synonym Kakutani’s problem
Synonym 3n+1 problem