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For example, are there only certain groups of numbers that have a total stopping time of 6 or 30?

Tylersamuels643
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  • There are different definitions of "stopping time" around (depending on which transformation-rule is used). Please uncover what you mean with "stopping time" (surely you don't measure it in microseconds...). – Gottfried Helms Jan 17 '20 at 20:58

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The conjecture is "They are all finite"

There are a lot of know "groups" of all kind, but it depends on what you look for. Do you talk about Total stopping time (reach 1) or just Stopping time (reach a smaller value) ? Are you looking at the "compressed form" (you only look at odd numbers), or the classic "shortcut form" or the "original form"?

e.g., if you want to know which numbers have a stopping time of 6 in the compressed form, here they are: $$1024k+507$$ $$1024k+347$$ $$1024k+923$$ $$1024k+583$$ $$1024k+423$$ $$1024k+999$$ $$1024k+975$$ $$1024k+815$$ $$1024k+367$$ $$1024k+735$$ $$1024k+287$$ $$1024k+575$$

If you want to know which numbers have a total stopping time of 6 in the compressed form, here is a General formula

e.g: $$19=\frac{2^{4+3+2+1+3+1}}{3^6}-\frac{2^{3+2+1+3+1}}{3^6}-\frac{2^{2+1+3+1}}{3^5}-\frac{2^{1+3+1}}{3^4}-\frac{2^{3+1}}{3^3}-\frac{2^{1}}{3^2}-\frac{2^0}{3^1} $$

Collag3n
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  • I mean the total stopping time (reach 1). Is there a chart with total stopping times and the corresponding numbers? – Tylersamuels643 Jan 17 '20 at 21:00
  • I am not sure what you mean by "chart" or "corresponding numbers" (formulas, enumerations, ....). There is an infinite number of them for each stopping time. – Collag3n Jan 17 '20 at 21:19