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So i just found this thing,
Ok so lets just say yoy 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 changes)
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)→a(5)→5→b(3)→b(2)→2→a(1)→1→a(1)→…
What is this type of iterative function thing called doelbeit , has there been ANY paper on things like these (Collatz doesn't count)?
Ok so lets just say yoy 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 changes)
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)→a(5)→5→b(3)→b(2)→2→a(1)→1→a(1)→…
What is this type of iterative function thing called doelbeit , has there been ANY paper on things like these (Collatz doesn't count)?
