How many numbers satisfy the \(3x+1\) conjecture? (Q1825890)
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scientific article; zbMATH DE number 4122053
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | How many numbers satisfy the \(3x+1\) conjecture? |
scientific article; zbMATH DE number 4122053 |
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How many numbers satisfy the \(3x+1\) conjecture? (English)
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1989
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Summary: Let \(\theta(x)\) be the number of numbers not exceeding \(x\) satisfy the \(3x+1\)-conjecture. We obtain a system of difference inequalities on functions closely related to \(\theta\). Solving this system in the simplest case, we establish \(\theta(x)>cx^{3/7}\). This improves a result of \textit{R. E. Crandall} [Math. Comput. 32, 1281--1292 (1978; Zbl 0395.10013)].
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Collatz problem
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\(3x+1\) conjecture
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system of difference inequalities
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