Maximum excursion and stopping time record-holders for the problem: Computational results
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- by Tomás Oliveira e Silva PDF
- Math. Comp. 68 (1999), 371-384 Request permission
Abstract:
This paper presents some results concerning the search for initial values to the so-called $3x+1$ problem which give rise either to function iterates that attain a maximum value higher than all function iterates for all smaller initial values, or which have a stopping time higher than those of all smaller initial values. Our computational results suggest that for an initial value of $n$, the maximum value of the function iterates is bounded from above by $n^2 f(n)$, with $f(n)$ either a constant or a very slowly increasing function of $n$. As a by-product of this (exhaustive) search, which was performed up to $n=3 \cdot 2^{53}\approx 2.702 \cdot 10^{16}$, the $3x+1$ conjecture was verified up to that same number.References
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Additional Information
- Tomás Oliveira e Silva
- Affiliation: Departamento de Electrónica e Telecomunicações / INESC Aveiro, Universidade de Aveiro, 3810 Aveiro, Portugal
- ORCID: 0000-0002-8878-3219
- Email: tos@inesca.pt
- Received by editor(s): January 3, 1997
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 371-384
- MSC (1991): Primary 26A18; Secondary 11Y99
- DOI: https://doi.org/10.1090/S0025-5718-99-01031-5
- MathSciNet review: 1613719