Collatz conjecture
 

The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture , Kakutani's problem, the Thwaites conjecture, Hasse's algorithm , or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers, or as wondrous numbers.


Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called "Half Or Triple Plus One", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.


In 2007, researchers Kurtz and Simon, proved that a natural generalization of the Collatz problem is algorithmically undecidable.

define the function f as follows:
 f(n) = begin{cases} n/2 &text{if } n equiv 0 pmod{2} 3n+1 & text{if } nequiv 1 pmod{2} end{cases}
Now, form a sequence by performing this operation repeatedly, beginning with any positive integer, and taking the result at each step as the input at the next.

The Collatz conjecture is: This process will eventually reach the number 1, regardless of which positive integer is chosen initially.

You can obtain Collatz conjecture of any number by putting it in following box.

Insert The Natural Number :
 
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