(notes by Roberto Bigoni)

A number *c _{0}* ≥ 1 generates a

If *C* contains the number 1, this number can be considered the last of
the sequence, because from this number forward the sequence oscillates in the cycle
1-4-2-1.

A conjecture is made that **from whatever c_{0}
a Collatz sequence starts, it reaches always 1**.

Even though this conjecture has been tested for many numbers by calculation programs like
the in the above form, **it is not generally demonstrated for every
natural number**.

If your browser can run Java applets, you can visit the page CollatzJava, where a java applet calculates the sequences in wider, faster and more reliable way.

Many mathematicians were involved in the search of a demonstration. See:

last reviewed: July 2015