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A198685
Mixed palindromic van der Waerden numbers pdw(n,3;2)_2 ("unsatisfiable" part).
1
3, 6, 9, 16, 21, 31, 44, 57, 77, 94, 113, 135, 155, 183, 205, 237, 279, 312, 347, 389, 405, 463, 507, 593, 607, 643, 699
OFFSET
1,1
COMMENTS
The smallest number M such that for all natural numbers m >= M there exists no partitioning of {1,...,m} into 2 parts such that the first part contains no arithmetic progression of length 3, and the second part contains no arithmetic progression of size n, and such that the partitioning is palindromic, that is, written as 0-1 string is a palindrome (reading the same from both sides). So pdw(1,3;2)_2=3 and pdw(2,3;2)_2=6.
pdw(n,3;2) is a pair of natural numbers, where the first part (the "satisfiable part") is given by A198684.
pdw(n,3;2) is the palindromic version of w(n,3;2) which is A007783.
LINKS
Tanbir Ahmed, Oliver Kullmann, and Hunter Snevily, On the van der Waerden numbers w(2;3,t), arXiv:1102.5433 [math.CO], 2011-2014; Discrete Applied Math., 174 (2014), 27-51.
EXAMPLE
pdw(3,3;2)_2=9, since ({2,4,5,7},{1,3,6,8}) is a palindromic partitioning of {1,...,8} such that no part contains an arithmetic progression of length 3, while there is no such a partitioning of {1,...,9} because of w(3,3;2)=9.
CROSSREFS
Cf. A007783.
Sequence in context: A287554 A308777 A057855 * A070120 A070126 A351231
KEYWORD
hard,nonn
AUTHOR
Oliver Kullmann, Oct 28 2011
STATUS
approved