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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
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