Lothar|教育線上App不用買

Lothar Collatz was born 6 July 1910 in Amsberg, Westphalia. During hispost-doctoral studies at at the age of 27, Collatz developed what isnow 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 thisfunction will always lead to the cycle { 4, 2, 1 }. In other words,repeated iterations of some starting number will always be eventuallydecreasing and that there are no other cycles in the sequence besides{ 4, 2, 1 }.The Reverse function, f', is defined as the sequence moving backwardfrom an ending integer through to some initial starting integer thatwould eventually arrive at the number entered through a series ofiterations. 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" pressedThis application was written by Jeffrey C. Jacobs and is Copyright ©2010TimeHorse, LLC; source code is available upon request.

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