# Collatz problem

The Collatz problem is a problem first posed by the German mathematician Lothar Collatz (1910–1990)
in 1937, that is also known variously as the 3*n* + 1 problem, Kakutani's
problem, the Syracuse problem, Thwaites' conjecture, and Ulam's conjecture.
It runs as follows. Let *n* be any integer. (1) If *n* is odd,
put *n* equal to 3*n* + 1; otherwise, put *n* equal to *n*/2.
(2) If *n* = 1, stop; otherwise go back to step 1. Does this process
always terminate (i.e. end in 1) for any value of *n*? To date, this
question remains unanswered, though the process has been found to stop for
all n up to 5.6 × 10^{13}. British mathematician Bryan Thwaites
(1996) has offered a £1,000 reward for a resolution of the problem. However,
John Conway has shown that Collatz-type problems
can be formally undecidable, so it not known if a solution is even possible.
The sequences of numbers produced by the Collatz problem are sometimes known
as hailstone sequences.

## Reference

1. Guy, Richard K. *Unsolved Problems in Number Theory*, 2nd
ed. New York: Springer-Verlag, 1994.