A104309 Minimum length of a perfect ruler that contains a segment not shorter than n.

1, 3, 5, 7, 10, 12, 14, 16, 18, 20, 24, 24, 27, 30, 31, 33, 37, 37, 39, 44, 44, 45, 51, 51, 51, 54, 59, 59, 60, 62, 69, 69, 69, 70, 80, 80, 80, 81, 83, 91, 91, 91, 91, 93

Offset

1,2

Comments

For nomenclature related to perfect and optimal rulers see Peter Luschny's "Perfect Rulers" web pages.

Links

F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, Table of n, a(n) for n = 1..92

Peter Luschny, Perfect and Optimal Rulers. A short introduction.

Hugo Pfoertner, Largest and smallest maximum differences of consecutive marks of perfect rulers.

F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, MRLA search results and source code, Nov 6 2020.

F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, Large Minimum Redundancy Linear Arrays: Systematic Search of Perfect and Optimal Rulers Exploiting Parallel Processing, IEEE Open Journal of Antennas and Propagation, 2 (2021), 79-85.

Index entries for sequences related to perfect rulers.

Example

The list of shortest perfect rulers containing a segment>=n starts:
n.a(n)..rulers..(marks enclosing longest segment)
1..1....[0,1]........(0,1)
2..3....[0,1,3]......(1,3)
3..5....[0,1,2,5]....(2,5)
4..7....[0,1,2,3,7]..(3,7)
5.10....[0,1,2,4,9,10]..(4,9)
........[0,1,3,4,9,10]..(4,9)
........[0,1,6,7,8,10]..(1,6)
6.12....[0,1,3,5,11,12]..(5,11)
........[0,1,7,8,10,12]..(1,7)
7.14....[0,1,2,4,6,13,14]...(6,13)
........[0,1,3,4,6,13,14]...(6,13)
........[0,1,3,5,6,13,14]...(6,13)
........[0,1,8,9,10,12,14]..(1,8)
........[0,1,8,9,11,12,14]..(1,8)
8.16....[0,1,3,5,7,15,16]....(7,15)
........[0,1,9,10,12,14,16]..(1,9)

Crossrefs

Cf. A104305 largest possible segment in a perfect ruler of length n, A104310 maximum length of perfect rulers made from segments not exceeding n, A103294 definitions related to complete rulers.

Sequence in context: A359113 A046868 A225240 * A306683 A184586 A190511

Adjacent sequences: A104306 A104307 A104308 * A104310 A104311 A104312

Keyword

hard,nonn

Author

Hugo Pfoertner, Mar 01 2005

Status

approved