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Size of the largest subset of the cyclic group of order n which does not contain a nontrivial 3-term arithmetic progression.
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%I #13 Jul 05 2018 00:55:08

%S 1,2,2,2,2,2,3,3,4,4,4,4,4,4,4,4,5,5,6,5,6,6,6,6,7,7,8,8,8,8,8,8,8,8,

%T 9,8,10,8,10,9,9,9,9,9,10,10,10,10,10,10,11,12,11,11,11,11,12,11,12,

%U 12,13,12,13,13,14,13,13,13,14,14,14,14,14,14,14,14,14,14,15

%N Size of the largest subset of the cyclic group of order n which does not contain a nontrivial 3-term arithmetic progression.

%C Each term is at most the corresponding term of A003002.

%C Arithmetic progressions are trivial if they are of the form x,x,x.

%H L. Halbeisen and S. Halbeisen, <a href="http://user.math.uzh.ch/halbeisen/publications/pdf/colmar39.pdf">Avoiding arithmetic progressions in cyclic groups</a>, Swiss Mathematical Society, 2005.

%e For n=10, the integers (mod 10) have sets with four elements like {1,2,4,5} which contain no arithmetic progressions with 3 elements, but no such sets with five elements. For example, {1,2,4,5,8} has the progression 2,8,4, and {1,2,4,5,9} has the progression 4,9,4. Since four is the most elements possible, a(10) = 4. - _Michael B. Porter_, May 26 2018

%Y Cf. A003002.

%K nonn

%O 1,2

%A _Daniel Scheinerman_, May 20 2018

%E a(51)-a(79) from _Giovanni Resta_, May 22 2018