A235060 The greedy sequence of real numbers at least 1 that do not contain any 9-term geometric progressions with integer ratio.

1, 256, 512, 6561, 6912, 13824, 19683, 131072, 221184, 492075, 655360

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, ar^6, ar^7, ar^8} with r an integer.

Links

Table of n, a(n) for n=1..11.

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: A031465 A045081 A294153 * A260243 A206137 A206130

Adjacent sequences: A235057 A235058 A235059 * A235061 A235062 A235063

Keyword

nonn

Author

Kevin O'Bryant, Jan 03 2014

Status

approved