The “\(3x + 1\)” problem and finite automata. (English) Zbl 0757.68084
Summary: Let \(f(x)=3x+1\) if \(x\) odd, and \(x/2\) if \(x\) even. The “\(3x+1\)” conjecture states that for all integers \(n\geq 1\), there exists an \(i\geq 0\) such that \(f^ i(n)=1\). We give a relationship between this famous conjecture and finite automata.
MSC:
68Q45 | Formal languages and automata |
Online Encyclopedia of Integer Sequences:
Numbers with 2 odd integers in their Collatz (or 3x+1) trajectory.Injection of the sequence of positive integers used in recursive calls (including initial call) in the execution of the Collatz (3n+1) function into the positive integers using the standard power-of-primes encoding (‘Goedel-coding’).