COLLATZ
The Collatz Sequence

COLLATZ is a library of PERL routines for computing the Collatz sequence.

The rules for generation of the Collatz sequence are recursive. If T is the current entry of the sequence, (T is assumed to be a positive integer), then the next entry, U is determined as follows:

1. if T is 1, terminate the sequence;
2. else if T is even, U = T/2.
3. else (if T is odd and not 1), U = 3*T+1;

Although the Collatz sequence seems to be finite for every starting point, this has not been proved. Over the range of starting values that have been examined, a great irregularity has been observed in the number of entries in the corresponding sequence.

The Collatz sequence is also known as the "hailstone" sequence or the "3n+1" sequence.

Related Data and Programs:

COLLATZ is also available in a JAVA version and a MATHEMATICA version and a MATLAB version.

POLPAK includes the routine collatz_count for counting the length of a Collatz sequence.

SEQUENCE_STREAK is a MATLAB program that can be used to make a "streak plot" of a Collatz sequence for a particular starting value, or for the length of the Collatz sequence for a number of starting values.

Reference:

1. Eric Weisstein,
   "The Collatz Problem",
   CRC Concise Encyclopedia of Mathematics,
   CRC 1998.

Source Code:

• collatz.pl, computes the Collatz sequence for a given starting point;
• collatz_count.pl, returns the number of entries in the Collatz sequence for a given starting point;

You can go up one level to the PERL source codes.