A235056 The greedy sequence of real numbers at least 1 that do not contain any 5-term geometric progressions with integer ratio.

1, 16, 32, 96, 144, 576, 4032, 4096, 4608, 32256, 32768, 36288, 36864, 40320, 40960, 41472, 129600, 131072, 147456, 157216, 166464

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} with r an integer.

Links

Table of n, a(n) for n=1..21.

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: A031463 A045071 A007824 * A115686 A088112 A272697

Adjacent sequences: A235053 A235054 A235055 * A235057 A235058 A235059

Keyword

nonn,more

Author

Kevin O'Bryant, Jan 03 2014

Status

approved