The Collatz problem

DOI10.1007/BF03023011zbMath0566.10008OpenAlexW4230641081MaRDI QIDQ1059095

Stan Wagon

Publication date: 1985

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03023011

zbMATH Keywords

stopping timeCollatz functioncurrent numerical evidenceexpected number of iterationsnontrivial cycleprobability assumption

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Radix representation; digital problems (11A63) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (9)

On generalized circuit of the Collatz conjecture ⋮ Lower bounds for the total stopping time of 3𝑥+1 iterates ⋮ Progress of iteration theory since 1981 ⋮ Representing the integers with powers of 2 and 3. ⋮ The Distribution of 3x+1 Trees ⋮ The \(3x+1\) problem: New lower bounds on nontrivial cycle lengths ⋮ On consecutive numbers of the same height in the Collatz problem ⋮ An automated approach to the Collatz conjecture ⋮ An automated approach to the Collatz conjecture

Cites Work

• Disproof of the Mertens conjecture.
• On the Collatz 3n + 1 Algorithm
• A stopping time problem on the positive integers
• Details of the First Region of Integers x with π 3,2 (x) < π 3,1 (x)
• On the "3x + 1" Problem
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• Unnamed Item

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