A235057 The greedy sequence of real numbers at least 1 that do not contain any 6-term geometric progressions with integer ratio.

1, 32, 64, 243, 288, 576, 729, 1152, 2048, 3645, 4000, 10240, 20736, 21952, 92160, 100000, 102400, 207360, 219520, 518400, 548800, 921600

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, ar^3, ar^4, ar^5} with r an integer.

Links

Table of n, a(n) for n=1..22.

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: A076469 A256819 A358250 * A339358 A249116 A110562

Adjacent sequences: A235054 A235055 A235056 * A235058 A235059 A235060

Keyword

nonn,more

Author

Kevin O'Bryant, Jan 03 2014

Status

approved