Hailstone number is one of the unsolved mathematical problem. It was introduced by a German Mathematician Lothar Collatz. So it is called as Collatz conjecture or 3n + 1 problem. It is also referred as Syracuse problem. As it involves series of numbers it's called as Hailstone sequence.
The number in the sequence from a rise and fall pattern like a hailstone in the weather cloud before it drops to ground. So it is called as Hailstone numbers.
Collatz framed a simple rule that it's possible to make sequence of numbers that would eventually end with number one. The rule behind is, for any positive integers, if the number is even divide it by two (n/2). If it is a odd number multiply it with three and add one from the obtained value. (3n + 1) The process should be repeated till the sequence end in 4, 2, 1.
Let us try with an example, n = 5
It is an odd number, so apply it with 3n + 1, The obtained value is 16. It's an even number, divide with 2. The value is 8. Repeat the process. The sequence of 5 would be 5, 16, 8, 4, 2, 1.
Here we can see the sequence of numbers rise and fall.
But this Collatz conjecture (Could there be a hailstone sequence that never settles?) was unproven still. It ends up with a question that could there be a sequence that never settles down to a repeating cycle at all?
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Daily Maths Topic Today - collatz conjecture.