Lothar

Lothar Collatz was born 6 July 1910 in Amsberg, Westphalia.
During his

post-doctoral studies at at the age of 27, Collatz developed what is

now known as the Collatz Conjecture.

Simply stated, the Collatz Conjecture is as follows:

Given the function f, defined as:

| n2 if n 0 (mod 2)

f(n) = | 3n + 1 if n 1 (mod 2)

|

for any positive starting integer n, repeated iterations of this

function will always lead to the cycle { 4, 2, 1 }.
In other words,

repeated iterations of some starting number will always be eventually

decreasing and that there are no other cycles in the sequence besides

{ 4, 2, 1 }.

The Reverse function, f, is defined as the sequence moving backward

from an ending integer through to some initial starting integer that

would eventually arrive at the number entered through a series of

iterations.
It is defined as follows:

| n2 if n 0, 1, 2, 3, 5 (mod 6)

`f(n) = | (n - 1)3 if n 4 (mod 6) & Previous pressed` +

| n2 if n 4 (mod 6) & Multiply pressed

This application was written by Jeffrey C.
Jacobs and is Copyright 2010

TimeHorse, LLC; source code is available upon request.,

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