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

cc: Category Theory • Cybernetics • Ontolog Forum • Peirce List (1) (2) (3) • SeqFan
cc: FB | Riffs and Rotes • Laws of Form • Structural Modeling • Systems Science

This entry was posted in Arithmetic, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes and tagged , , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

Gravatar
WordPress.com Logo

You are commenting using your WordPress.com account. ( Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. ( Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. ( Log Out /  Change )

Cancel

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.