# Lothar

> Educational app for exploring the Collatz Conjecture and its reverse function. (iPhone/iPad app by TimeHorse, LLC.)

- Source: https://appshunter.io/ios/app/lothar/id388891196 (this page in markdown: same URL + `.md`)
- Developer: [TimeHorse, LLC](https://appshunter.io/developer/388891199)
- Category: Education
- Price: $0.99
- Rating: 5.00/5 from 1 App Store ratings · 1 written reviews indexed
- Age rating: 4+
- Requires: iOS 14.0 · 8 MB
- Languages: American English
- Released: 2010-10-25
- Data updated: 2026-09-08
- Monetization: paid
- User reviews in markdown: https://appshunter.io/ios/app/lothar/id388891196/reviews.md

## What is 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:

         | 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.

## Key features

- Collatz Conjecture exploration
- Forward function simulation
- Reverse function simulation
- Interactive number sequences
- Mathematical concept learning

## Recent user reviews (1 of 1)

All indexed reviews: https://appshunter.io/ios/app/lothar/id388891196/reviews.md

### 5/5 — Simple, But Effective

*2023-01-09*

The Collatz conjecture is one of the greatest enigmas in mathematics: so simple that an eight year-old can understand it but a proof or counterexample has evaded everyone. Simply start with a positive integer. If it’s even, divide it by two: if it’s odd, multiply it by three and add one. Keep applying those rules to the resulting numbers and, no matter what number you start with, the sequence will always collapse to one. Or will it? The great Hungarian number theorists, Pál Erdős, when asked about the Collatz conjecture, replied: “I don’t think that mathematics is ready for this yet.”

This simple program allows you to try it, saving yourself a few calculator keystrokes. The amazing thing about the CC, is that adjacent integers can take wildly differing numbers of steps to reach one (try 26 and 27, for instance).

Lots of videos about the CC on YouTube if you want to know more.

## Frequently asked questions about Lothar

### What is the Collatz Conjecture?

The Collatz Conjecture is a mathematical problem that states that for any positive integer, repeatedly applying the function f(n) = n/2 if n is even, and f(n) = 3n + 1 if n is odd, will eventually lead to the number 1. This app allows you to explore this conjecture.

### Does Lothar have ads?

No, Lothar is ad-free. You can explore the Collatz Conjecture without any interruptions from advertisements.

### What devices does Lothar support?

Lothar is available on iPhone, iPad, and iPod. It is designed to run on Apple's mobile operating systems.

### How often is Lothar updated?

The latest version of Lothar is 2.20, and it was last updated on April 5, 2023. Updates typically focus on performance improvements and bug fixes.

### What is the age rating for Lothar?

Lothar has an age rating of 4+. This indicates it is suitable for young children and does not contain mature content.

### Can I use Lothar offline?

Yes, Lothar is designed to be used offline. You do not need an internet connection to explore the Collatz Conjecture or its reverse function.

### What is the price of Lothar?

Lothar is a paid application, priced at $0.99. This one-time purchase gives you full access to all its features.

### What is the reverse function in Lothar?

The reverse function in Lothar allows you to explore sequences by moving backward from a given number. It helps in understanding how different starting integers can lead to the same sequence.

## Version history (last 4 releases)

### 2.20 — 2023-04-05

Replaced the web viewer in the help window, fixed the placement of the reverse title, added the ability to force reload in the web browser by double-clicking the refresh button—but note, if clicked too fast, why the stop load is presented, it may cancel the page load. If you are having trouble double-clicking the refresh button because the stop load isn't disappearing in time or the time to second click is too short, you can now change the timeout in settings. Updated help.

### 2.11 — 2019-11-25

Ready for iOS 13

### 2.00.1 — 2016-10-16

* 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!

### 1.01 — 2010-10-25

No release notes.

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## Related topics

[lothar](https://appshunter.io/ios/topics/lothar)

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*Data collected daily from the US App Store and indexed by [AppsHunter](https://appshunter.io/). User reviews are verbatim App Store reviews. Ratings, prices and chart positions refresh continuously; this snapshot is from 2026-09-08.*