Geodesic
Sequences containing no 3-term arithmetic progressions
Janusz Dybizbański1
1Institute of Informatics University of Gdansk Poland
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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A subsequence of the sequence $(1,2,...,n)$ is called a 3-$AP$-free sequence if it does not contain any three term arithmetic progression. By $r(n)$ we denote the length of the longest such 3-$AP$-free sequence. The exact values of the function $r(n)$ were known, for $n\leq 27$ and $41\leq n \leq 43$. In the present paper we determine, with a use of computer, the exact values, for all $n\leq 123$. The value $r(122)=32$ shows that the Szekeres' conjecture holds for $k=5$.
DOI : 10.37236/2061
Classification : 11B25, 11Y55
Mots-clés : arithmetic progressions

Janusz Dybizbański  1

1 Institute of Informatics University of Gdansk Poland 
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Janusz Dybizbański. Sequences containing no 3-term arithmetic progressions. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2061

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