A304884 Size of the largest subset of the cyclic group of order n which does not contain a nontrivial 3-term arithmetic progression.

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, 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, 12, 13, 12, 13, 13, 14, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15

Offset: 1

Author

Daniel Scheinerman, May 20 2018

Keywords

• nonn

Comments

Each term is at most the corresponding term of A003002.

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

Examples

			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
		

Links

• L. Halbeisen and S. Halbeisen, Avoiding arithmetic progressions in cyclic groups, Swiss Mathematical Society, 2005.

Crossrefs

Cf. A003002.

Extensions

a(51)-a(79) from Giovanni Resta, May 22 2018