I'm trying to create a forumula to get the exact collatz number for a given step, given that it follows a pattern of up/down up/down up/down repeating. In other words, it will grow by approximately 50% plus 1 per every other step count (I think), but I want to get the exact number at a given step (I know the step count, but I don't know the number yet). If you're not familiar with Collatz the equation goes Odd: 3n + 1 Even: n/2 Since we know the repeating pattern that forms for a certain set of numbers (up/down, up/down, up/down), how could we program something to get the growth for a specific step, given the starting number and step count that we want to find the number for. Will need high precision methods that can work with extremely large integers. I'm fairly familiar with Python, so that may be best. If you know a way to do this in another language I'm willing to learn (C++ maybe). To be clear, with the set of numbers I am working with, the up/down up/down up/down pattern will always be there (I can predict the exact moment the pattern will stop, but I want the actual number where that occurs rather than calculating billions of steps using the standard collatz equations). I am aware that most numbers go into chaos quickly, but some follow a predictable pattern and I'm trying to study them at a larger scale. Figuring out how to calculate the number based on the exponential growth pattern that can form will allow me to test more numbers per day. Small Example: StartingNumber = 33554431 There will be 50 stages of up/down before chaos and randomness occurs. So 50 cycles of growth before it starts reducing in this case. What formula will give me 847288609442 or 423644304721 using the starting number and step count of 50? The two numbers I included are just the previous number and current number of the point where I detect two cycles of decreasing value in a row for 33554431. Is this possible? Thanks Continue reading...
