Riffs and Rotes • 59281

Posted on September 5, 2021 by Jon Awbrey

Re: Persiflage • 59281

Numberfile • What’s Special About 59,281?

If p is prime then the decimal expansion of 1/p repeats, so it makes sense to talk about the “average” of the digits of 1/p.  The average can be bigger than 4.5, equal to 4.5, or less than 4.5.  Which is most likely?  Which is least likely?  Click to find out.

\textsc{Challenge Problem.}  Is there any prime for which the digit average is bigger than it is for p = 59281?

I can’t imagine this will help with the problem, it’s just a thing I do with interesting numbers I encounter …

See Riffs and Rotes for the basic idea.

Doubly Recursive Factorization 59281

Here is the Riff for 59281

Riff 59281

Here is the Rote for 59281

Rote 59281

One peculiar property of this number I notice is its being “square-free all the way down”.  Once again, I have no clue whether that has anything to do with the problem at hand.

Resources

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