I wrote something for my Mathematical Intelligencer column along these lines, except that for multiple-word number names I mapped to the *product* of the lengths of each individual word, not their sum. This means that 24 -> "twenty four" -> 6*4 = 24 is also a fixed point, as is 84,672. Huh, but I can't find it online everywhere. I think I only put my Intelligencer columns on the arxiv if they had some "real" math to them, and this was too flighty to qualify. Bizarrely, Futility Closet mentioned this last year: https://www.futilitycloset.com/2019/01/12/fortuitous-numbers/. Jim, I'll dig up a paper version for you, if you care. --Michael On Wed, Jun 3, 2020 at 11:53 AM Allan Wechsler <acwacw@gmail.com> wrote:
A052363, Jim. You neglected "zero", so your candidate started differently from the version OEIS has chosen as canonical.
In general, if you fail to find a sequence on OEIS, chopping off the first entry or two is always a good idea, because minor differences in definitions often lead to varying startup transients. Searching for 3,11,13,17,23 gives the sequence you were looking for as the first hit. Adding 73 makes it unique.
Apparently this sequence was added 20 years ago by ... me!
On Wed, Jun 3, 2020 at 11:13 AM Gareth McCaughan < gareth.mccaughan@pobox.com> wrote:
I actually don’t find such sequences very interesting, but I know others do. In particular, my daughter has asked me to write a blog essay about the fact that
repeatedly applying the map k->A005589 <http://oeis.org/A005589>(k) to any starting value n always leads to 4 (cf. A016037 < http://oeis.org/A016037 , A133418 <http://oeis.org/A133418>).
Has anyone (perhaps Diane Karloff, who is credited with this observation) written about this? Then maybe I could give the article to my daughter instead of having to write it myself. :-)
Dunno about "written", though I'm sure it's mentioned in passing in lots of recreational maths books. One of those pop-maths YouTube channels did something about it a little while ago. ... Ah, found it: it's Matt Parker (standupmaths). https://youtube.com/watch?v=LYKn0UTIU4
-- g
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