Lothar Lothar $0.99


TimeHorse, LLC

2.00.1 for iPhone, iPad

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6.2 MB

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Lothar Description
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.
Lothar 2.00.1 Update
2016-10-16 Version History
* Numbers can now be of arbitrary length. Enter a million digits if you dare and see how long it takes to get to one.
* Actually, it takes no time at all, because now if you hold down the "Next" button, next is repeated until one is reached.
* So how do you know it got there? Well, now there's a ticker tape below the buttons to show you just how you got there. Scroll through the entire sequence.
* Can't see the end of the numbers in your list? Rotate your screen, Lothar now supports landscape mode.
* Sick of seeing all those old numbers and want to generate a new list? Click the trash can or clear button on larger displays.
* And now you can see the final, spiffy, new feature: the crisp, clear, new background issue of the man who came up with this awesome, unproven algorithm to bring any integer to one, Lothar Collatz, we thank you!
More Information
6.2 MB
Release Date:
TimeHorse, LLC
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