This project can create a hailstone sequence with any given seed, create a special type of sequence that I came up with myself with any given seed, and create special sequences by the bulk with any given lower and upper bounds. ---------------------------------------------------------------------------------------------------- ~Hailstone Sequences~ To create a hailstone sequence, press the (A) key and type in any positive integer. If it is even, it will be divided by 2. If it is odd, it will be multiplied by 3 and increased by 1. The result will then be put into the system and this will go on until it reaches 1 (See: Collatz conjecture), at which point it will end. ---------------------------------------------------------------------------------------------------- ~Special Sequences~ To create a special sequence, press the (B) key and type in any positive integer. The number will be stored in the "lengths" list used as the seed for the first sequence. The length of the sequence will be stored in the "lengths" and used as the seed for the next sequence. This will go on until it starts to repeat, at which point it will stop and tell you where it repeats. (Most often it ends on a repeating "8 4 3 8 4 3 8 4 3...") ---------------------------------------------------------------------------------------------------- ~Bulk Sequences~ To create special sequences in bulk, press the (C) key and type in two numbers: The lower bound for the starting seeds, and the upper bound for the starting seeds. It will create one special sequence for each seed, one by one, until it finishes. This option is perfect for finding and observing patterns.
I haven't made a project in a while, but I was recently watching the Numberphiles YouTube channel and was inspired to do something related to the Collatz conjecture. My dad @WajihSyed is also working on a MATLAB program that can calculate these special sequences and make them easier to find patterns in and stuff. As far as I know, no one has thought of the special sequences. IF you discover anything interesting about them, tell me!
