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Lothar

Lothar
  • #: 154551
  • Price: free ($0.00) In Apple Store
  • Category: Education
  • Updated: 2016-10-16
  • Current Version: 2.00.1
  • 2.00.1
  • Size: 0.10 MB
  • Language: English
  • Seller: Jeffrey Jacobs
  • Requirements: Compatible with iPhone, iPod touch, and iPad. Requires iOS 4.1 or later.
  • © 2010 TimeHorse, LLC
  •  Add to Favorite apps

 

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.

What's New in Version 2.00.1

* 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!

View iPhone screenshots | View iPad screenshots

iPhone Screenshots

Lothar iPhone Screenshot 1
Lothar iPhone Screenshot 2
Lothar iPhone Screenshot 3

iPad Screenshots

Lothar iPad Screenshot 1
Lothar iPad Screenshot 2
Lothar iPad Screenshot 3

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The information may be outdated (2017-03-08 04:14:35). For actual information go to iTunes


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