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A comment on Decomposing a Factorial into Large Factors.

Re:Decomposing a Factorial into Large Factors by zahlman on Friday March 28, 2025 @12:39PM (#43507412)
From comments:

>No; in fact, in Guy’s article on this problem, he notes that there is a jump of 2 from t(124)=35 to t(125)=37

Huh. Can we actually prove t(N) is monotonic? Jumps like that seem like they could be one-offs in some cases.

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Re:Decomposing a Factorial into Large Factors by intuitionist on Friday March 28, 2025 @01:02PM (#43507685)
Yeah, since t(N) < N, you can use the decomposition for N! and one extra factor (N+1) to get a decomposition for (N+1)! with a smallest part equal to t(N).
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Re:Decomposing a Factorial into Large Factors by zahlman on Friday March 28, 2025 @09:15PM (#43511800)
Oh, that's much easier than I thought it would be. Nice job being rigorous, too.
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