7月16日 的 Lothar 應用程式分析

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.