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

1,2

Comments

Each term is at most the corresponding term of A003002.

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

Links

Table of n, a(n) for n=1..79.

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

Example

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

Crossrefs

Cf. A003002.

Sequence in context: A238457 A291310 A336014 * A286707 A025788 A071806

Adjacent sequences: A304881 A304882 A304883 * A304885 A304886 A304887

Keyword

nonn

Author

Daniel Scheinerman, May 20 2018

Extensions

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

Status

approved