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Almost all orbits of the Collatz map attain almost bounded values (arXiv:1909.03562)
Tao, TerencearXiv.orgPublished Sep 8, 2019Original︎ ↗Archived copy
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As quoted
Theorem 1.3 (Almost all Collatz orbits attain almost bounded values). Let f : N+1 → R be any function with lim_{N→∞} f(N) = +∞. Then one has Col_min(N) < f(N) for almost all N ∈ N+1 (in the sense of logarithmic density).
For any function f tending to infinity, almost all N in logarithmic density have Collatz orbit minimum below f(N).
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Record
- Kind
- unknown
- Authors
- Tao, Terence
- Publisher
- arXiv.org
- Published
- Sep 8, 2019
- DOI
- None
- Link
- https://arxiv.org/abs/1909.03562
- Archived copy
- https://web.archive.org/web/20261029230949/https://arxiv.org/abs/1909.03562
- Stored text
- 5,415 characters, retrieved Nov 11, 2026 · 46 sections, 65 passages
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- This version
- Later · Almost all orbits of the Collatz map attain almost bounded values
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- None recorded
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- None recorded
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- Nov 11, 2026
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