Maximum excursion and stopping time record-holders for the problem: Computational results

DOI10.1090/S0025-5718-99-01031-5zbMath0919.11020MaRDI QIDQ4221986

Tomás Oliveira e Silva

Publication date: 3 December 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

algorithmcomputational resultsCollatz problem\(3x+1\) problemmaximum excursion of the trajectory

Mathematics Subject Classification ID

Recurrences (11B37) Special sequences and polynomials (11B83) Software, source code, etc. for problems pertaining to number theory (11-04)

Related Items (9)

Lower bounds for the total stopping time of 3𝑥+1 iterates ⋮ Quantifying the degree of average contraction of Collatz orbits ⋮ The \(3x+1\) problem as a string rewriting system ⋮ Unnamed Item ⋮ A reduced Collatz dynamics maps to a residue class, and its count of \((x/2)\) over the count of \(3\ast x+1\) is larger than \(\ln 3/\ln 2\) ⋮ Generalized inverses and the total stopping times of collatz sequences ⋮ The \(3x+1\) semigroup ⋮ On the almost sure convergence of Syracuse sequences ⋮ A new approach on proving Collatz conjecture

Cites Work

• The \(3x+1\) problem: New lower bounds on nontrivial cycle lengths
• The \(3x +1\) problem: Two stochastic models
• The 3x + 1 Problem and Its Generalizations
• \(3x + 1\) search programs

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