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说明
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.
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新版变化
- 版本: 2.20
- 已更新:
- 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.
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