The On-Line Encyclopedia of Integer Sequences (OEIS)

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A320577

Number of isosceles triangles whose vertices are the vertices of a regular n-gon.
(history; published version)

#45 by Susanna Cuyler at Mon Oct 22 14:29:11 EDT 2018

STATUS

proposed

approved

#44 by Colin Barker at Mon Oct 22 14:16:00 EDT 2018

STATUS

editing

proposed

#43 by Colin Barker at Mon Oct 22 14:15:48 EDT 2018

LINKS

Colin Barker, <a href="/A320577/b320577.txt">Table of n, a(n) for n = 3..1000</a>

STATUS

approved

editing

#42 by Peter Luschny at Sun Oct 21 06:03:21 EDT 2018

STATUS

proposed

approved

#41 by Peter Luschny at Sun Oct 21 06:03:00 EDT 2018

STATUS

editing

proposed

#40 by Peter Luschny at Sun Oct 21 05:58:01 EDT 2018

COMMENTS

Inspired by question 12 of the Turkish National Mathematics Olympics 2015. See (see the link).

LINKS

Turkish Math Olympiad 2015 <a href="/A320577/a320577.jpg">Question 12</a>

Turkish Math Olympiad 2015 <a href="/A320577/a320577.jpg"> </a>Question 12.

Discussion

Sun Oct 21

05:58

Peter Luschny: It's absurd to upload a zip-File containing three pdf files 
filled with unrelated stuff, just to document a 2 and 1/2 line 
question which is only vaguely linked to the definition. 
I'm going to change that.

06:00

Peter Luschny: Jon, you can postpone your translation attempts when you' re happy with them.

#39 by Peter Luschny at Sun Oct 21 05:56:33 EDT 2018

COMMENTS

23rd National Mathematics Olympics 1st Stage Exam Question 12: "The number of isosceles triangles whose vertices are the vertices of a regular polygon, s(n), s(n) > s(n+1). How many n <= 2015 do positive integers provide?"

Inspired by question 12 of the Turkish National Mathematics Olympics 2015. See the link.

LINKS

The Scientific and Technological Research Council of Turkey, <a href="http://www.tubitak.gov.tr/sites/default/files/lise_matematik_2015.zip">2015 Lise Matematik-A.pdf question 12</a>

The Scientific and Technological Research Council of Turkey, <a href="/A320577/a320577.pdf">Turkish Math Olympiad 2015</a>

Turkish Math Olympiad 2015 <a href="/A320577/a320577.jpg"> </a>Question 12.

STATUS

proposed

editing

#38 by Jon E. Schoenfield at Sat Oct 20 19:10:26 EDT 2018

STATUS

editing

proposed

Discussion

Sat Oct 20

22:09

Jon E. Schoenfield: I still don't think the (translated) quote in the Comments section makes sense.  E.g., I don't think it makes sense for

     The number of isosceles triangles whose vertices are the vertices of a regular polygon, s(n), s(n) > s(n+1).

to be a single sentence.  If I were to try to reword the quote to make it convey what I think the intended meaning is, I would try something like

     Let s(n) be the number of isosceles triangles whose vertices are the vertices of a regular n-gon.  For how many positive integers n <= 2015 does s(n) > s(n+1)?

But since it's in quotation marks, it needs to be a direct translation of the text in the actual source.  (And since I can't read Turkish, I can't translate it.)  :-(

#37 by Jon E. Schoenfield at Sat Oct 20 19:10:19 EDT 2018

FORMULA

Alternatively, with the least absolute modulo 'mods' and m = abs(mods(n, 6)), a(n) = n*(n - k)/2 where k = m if m in {1, 2} and otherwise k = (10 - m)/3. # _- _Peter Luschny_, Oct 20 2018

STATUS

reviewed

editing

Discussion

Sat Oct 20

19:10

Jon E. Schoenfield: Thanks, Peter!

#36 by Peter Luschny at Sat Oct 20 18:45:52 EDT 2018

STATUS

proposed

reviewed