Simple Digit Manipulation — Not So Simple Results
The Steinhaus Cycle — A set of eight
Pick any number. Did you pick 10003? what a coincidence, so did I.
Now let’s perform a simple operation on this number — take the sum of the squares of all digits.
1²+0²+0²+0²+3² = 10
Now let’s perform the same operation on the result 10
1²+0²=1
One more time with the number 1 this time
1²=1
I believe you can see that we will yield the number 1 every time we will repeat this operation now.
In this article, we are going to investigate together the nature of the operation I have described above.
We will answer questions like ‘Do all numbers result in ones eventually? (after performing the operation over and over again)’, ‘If they don’t, is there another number that they result in?’.
After answering the questions above, we will prove that whatever connection we find, will hold for every number.
Does this operation converge to 1 for every number?
Short answer: No.
There Is an infinite amount of numbers that do, but definitely not all of them.
