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A104309 Minimum length of a perfect ruler that contains a segment not shorter than n. 2
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 (list; graph; refs; listen; history; text; internal format)
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.
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.
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
KEYWORD
hard,nonn
AUTHOR
Hugo Pfoertner, Mar 01 2005
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)