A235054 The greedy sequence of real numbers at least 1 that do not contain any 3-term geometric progressions with integer ratio.

1, 4, 8, 9, 12, 24, 27, 32, 36, 40, 45, 48, 2208, 2209, 2256, 8832, 8836, 9024, 17664, 17672, 18048, 19872, 19881, 20304, 26496, 26508, 27072, 52992, 53016, 54144, 59616, 59643, 60912, 70656, 70688, 72192, 79488, 79524, 81216, 88320, 88360, 90240, 99360, 99405, 101520, 103776, 103823, 105984, 106032, 108192, 108241, 108288

Offset

1,2

Comments

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} with r an integer.

Links

Table of n, a(n) for n=1..52.

M. B. Nathanson, K. O'Bryant, A problem of Rankin on sets without geometric progressions, arXiv preprint arXiv:1408.2880, 2014

Crossrefs

A235054 through A235060 give the greedy sets avoiding k-term geometric progressions for 3 <= k <= 9.

Sequence in context: A082293 A048944 A211658 * A292364 A071835 A308416

Adjacent sequences: A235051 A235052 A235053 * A235055 A235056 A235057

Keyword

nonn

Author

Kevin O'Bryant, Jan 03 2014

Status

approved