So i just found this thing,

Ok so lets just say you can only use the functions a(x) = 2x and b(x) = 2x-1 with x being any natural number,
And lets just say that you have to get the result of one of these 2 functions being applied to a number y, like
y>a(y_1)>y_1>b(y_2)>y_2>…a(y_n)>y_n>….
(The greater than are supposed to be arrows if the symbol change becuase obsessed formatting)
so, The minimum iterations for a number y to get to 1 is floor(log_4(y)) (things such as a/b(n) are ignored)
Example:
77>b(39)>39>b(20)>20>a(10)>10>a(5)>5>b(3)>3>b(2)>2>a(1)>1>a(1)>…
77>39>20>10>5>3>2>1>1….
What is this type of iterative function thing called doelbeit , has there been ANY paper on things like these (Collatz doesn't count)?
>OP why didn't you extend it to the rationals and integers?
For rationals It either Leads to either y diverging to infinity or converging to 0 for the example i gave,
And for integers the amount of steps is the same for negatives or something,
>OP what happens if i have a lot of possible functions to use
Either turns into a chaotic mess (like dynamical systems) or something similiar to what i posted (that is trivial btw)
>Have you tried doing things with complex numbers,irrationals,primes etc… Yet?
Not yet
Thoughts?