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:
| n÷2 if n ≡ 0 (mod 2)
f(n) = | 3×n + 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:
| n×2 if n ≡ 0, 1, 2, 3, 5 (mod 6)
f(n) = | (n - 1)÷3 if n ≡ 4 (mod 6) & "Previous" pressed
| n×2 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.