Lothar

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更新日期：2016-10-16

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支援語言：英語

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

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