![]() ![]() A table with all terms of the sequence.ĭid you try a negative number to see if you could break the tool? We covered that too, but mathematicians are even more worried about it: there are three loops (starting at − 1 -1 − 1, − 5 -5 − 5, and − 17 -17 − 17) for negative integers, and no-one knows why they exist!.The stopping time (the number of steps before reaching 1 for the first time) and.XKCD's Cueball was caught by the Collatz conjecture, and his social life suffered because of it.Īll you have to do, is choose a number! Our Collatz conjecture calculator will show you: That number is 30,000 digits long, and guess what? After almost a million and a half steps, it ended up at 1. And things don't look promising: researchers have tried numbers up to (are you ready?) 295, 147, 905, 179, 352, 825, 856 295,147,905,179,352,825,856 295, 147, 905, 179, 352, 825, 856 - more seconds than have passed since the Big Bang! And not a single number didn't end up at 1.Īnd in an attempt to show the Collatz conjecture who's boss, researchers tried the number 2 100, 000 − 1 2^- 1 2 100, 000 − 1 (the minus one was used to give the final flex, apparently). ![]() This is why the 3x+1 problem is such a problem for mathematicians: at the moment, the only thing we can do is to brute force our way through numbers, trying to find one of them that would escape the 4, 2, 1 4, 2, 1 4, 2, 1 loop. In layman's terms, there's no computer program that can take a number and say if it will or will not reach one. The sequences follow a random pattern, and by just looking at the initial term, it's impossible to say how its sequence will behave without computing the next steps: mathematicians say that it is an undecidable problem. This wildly unpredictably oscillating behavior earned these sequences the name "hailstone sequences", because the path of the sequence resembles that of a hailstone in a cloud before reaching the ground: swinging up and down before falling (preferably not on our heads). The oscillations may be big, as for x 1 = 31 x_1 = 31 x 1 = 31 which reaches a peak of more than 9,000 before falling down to 1. ![]() Choose any other number, and eventually, the sequence will end up in the 4, 2, 1 4, 2, 1 4, 2, 1 loop. ![]()
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