re collatz this surprising new finding jumped out at me recently. seems promising, still analyzing it. :idea: :!: :?:

again consider the collatz function as two possible operations, and one can determine a kind of “collatz hash ID” associated with each integer, where the operations are binary digits ‘0’ and ‘1’ in a string. one can define a set of numbers/strings where is the total number of operations and is the number of a specific operation, in this case the “op”. this functions somewhat similar to the combinatorial “Choose(x, y)” operation.