

A198684


Mixed palindromic van der Waerden numbers pdw(n,3;2)_1 ("satisfiable" part).


1



2, 3, 6, 15, 16, 30, 41, 52, 62, 93, 110, 126, 142, 174, 200, 232, 256, 299, 338, 380, 400, 444, 506, 568, 586, 634, 664
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OFFSET

1,1


COMMENTS

The largest number M such that for all natural numbers 1 <= m <= M there exists a 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 01 string is a palindrome (reading the same from both sides). So trivially pdw(1,3;2)=2 and pdw(2,3;2)=3.
pdw(n,3;2) is a pair of natural numbers, where the second part (the "unsatisfiable part") is given by A198685.


LINKS



EXAMPLE

For n=3 we have pdw(3,3;2)_1=6, because ({1,2,5,6},{3,4}) is a palindromic partitioning of {1,...,6} into two parts such that no part contains an arithmetic progression of size 3, while {1,...,7} has no such *palindromic* partitioning (though it has a nonpalindromic partitioning by w(3,3;2)=9), since one of the parts needs to contain the midpoint 4 and thus cannot contain any other number (by palindromicity we would get an arithmetic progression of size 3).


CROSSREFS



KEYWORD

hard,nonn


AUTHOR



STATUS

approved



