Lots of hubcaps<https://www.google.com/search?site=imghp&tbm=isch&source=hp&biw=1280&bih=847&q=Hubcaps&oq=Hubcaps&gs_l=img.3..0l10.2591.5550.0.6038.7.6.0.1.1.0.97.481.6.6.0....0...1ac.1.32.img..0.7.493.Xp3soaiR-SE> I see one that has n-fold symmetry for all n. So there is no smallest n not made. I guess you mean has symmetry group C_n or D_n. On Tue, Jan 7, 2014 at 9:21 AM, Veit Elser <ve10@cornell.edu> wrote:
On the topic of small interesting numbers:
What's the smallest n>2 such that no auto manufacturer has made a hubcap with n-fold symmetry?
Or equivalently, if you were to write an illustrated children's book on the natural numbers with each number rendered as an actual hubcap, how many pages would such a book have?
Now that I've forever changed your life, when walking along a line of parked cars, here are some tips for speed-hubcapping:
Deciding that n is even is easy, and the eye is also good at noticing perpendicular mirror lines to determine divisibility by 4. Then deciding between 12, 16, 20 or 10, 14, 18 is easy because the gaps are large.
The case of odd n is harder. While I can quickly recognize 5, 7, and even 9 (as three 3's), starting will 11 I usually end up just counting (and then having to run to catch up with the people I'm walking with).
-Veit
On Jan 5, 2014, at 5:46 PM, James Propp <jamespropp@gmail.com> wrote:
What is the smallest value of n such that n+1 appears in more of the increasing sequences in the OEIS than n does?
The reason I want to restrict attention to increasing sequences in the OEIS is that these correspond to interesting subsets of the positive integers. I suppose if anyone wants to answer my question with the word "increasing" omitted, I'd be interested in that too. Conjecture: The n that you get is the same for both versions of my question. Refined conjecture: in both cases, n is 11.
Jim Propp
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