Collatz Conjecture

FILE INFORMATION
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collatz.zip

Filename

collatz.zip (Download)

Title

Collatz Conjecture

Description

These are four programs on Collatz Conjecture, also called the 3X+1 problem, a prediction that states that whatever positive integer you start with, you will end up on one, if you divide with two if even, or multiply with three and add one, if odd, and keep repeating that on the numbers you get. Program COLLATZ shows just that, and it also gives the number of iterations until you reach one. COLLATZ2 shows that the inverse of the conjecture can give the continuous integers from 1 and upwards, if the number you start with: A=1, is counted up by one repeatedly. COLLATZ3 is a demonstration of how futile it is, to try and make the inverse of the conjecture give a continuous number of integers from 1 and upwards: if you let it go to 100, 13 numbers will be missing: the pathway down to 1 from any number, is like a tree with an infinite number of branches, and so by trying the inverse of the prediction, you are inevitably going to end up in a branch, and miss numbers. COLLATZ4 is a bit more complicated. It lets you give a number that the inverse conjecture is going to achieve. Then it makes a calculation as to the highest number it has to go, to get there. 31 for example, demands that you go as high as to 9232, and so it takes several thousand iterations before you get there. So it is no wonder that 31 is one of the numbers that are missing, when you let COLLATZ3 count to 100. This conjecture is a problem that aspiring mathematicians are advised to avoid, and for good reasons.

Author

Anders Tiberg (anders.tiberg@telia.com)

Category

TI84 Plus C Silver Edition/CE BASIC Math Programs

File Size

10,590 bytes

File Date and Time

Mon Jan 10 17:53:24 2022

Documentation Included?

Yes


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