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%I #17 Apr 23 2015 13:36:33
%S 1,32,64,243,288,576,729,1152,2048,3645,4000,10240,20736,21952,92160,
%T 100000,102400,207360,219520,518400,548800,921600
%N The greedy sequence of real numbers at least 1 that do not contain any 6-term geometric progressions with integer ratio.
%C The union of the half-open intervals [a(2i-1),a(2i)) is the greedy set of real numbers at least 1 that does not contain any subset of the form {a, ar, ar^2, ar^3, ar^4, ar^5} with r an integer.
%H M. B. Nathanson, K. O'Bryant, <a href="http://arxiv.org/abs/1408.2880">A problem of Rankin on sets without geometric progressions</a>, arXiv preprint arXiv:1408.2880, 2014
%Y A235054 through A235060 give the greedy sets avoiding k-term geometric progressions for 3 <= k <= 9.
%K nonn,more
%O 1,2
%A _Kevin O'Bryant_, Jan 03 2014