A104305 -id:A104305 - cp's OEIS frontend

A104306 Number of perfect rulers of length n having the largest possible difference between consecutive marks that can occur amongst all possible perfect rulers of this length.

1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 5, 2, 1, 5, 6, 2, 1, 7, 8, 2, 2, 2, 1, 2, 6, 2, 2, 3, 1, 12, 6, 2, 2, 1, 1, 1, 8, 4, 2, 3, 1, 1, 1, 8, 2, 2, 5, 1, 1, 1, 2, 8, 2, 2, 4, 1, 1, 1, 10, 8, 2, 2, 6, 1, 1, 1, 1, 1, 4, 2, 6, 2, 2, 1, 2, 2, 3, 1, 1, 2, 2, 2, 2, 1, 2, 1, 3, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Hugo Pfoertner, Feb 28 2005

nonn

			There are 14 perfect rulers of length 12:
[0,1,2,3,8,12], [0,1,2,6,9,12], [0,1,3,5,11,12], [0,1,3,7,11,12],
[0,1,4,5,10,12], [0,1,4,7,10,12], [0,1,7,8,10,12] and their mirror images. The maximum difference between adjacent marks occurs for the 3rd ruler between marks "5" and "11" and for the 7th ruler between marks "1" and "7". Because there are 2 rulers containing the maximum gap between adjacent marks A104305(12)=6 and a(12)=2.

F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, Table of n, a(n) for n = 1..208 [a(212), a(213) commented out by _Georg Fischer_, Mar 25 2022]
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.

Cf. A104305, largest possible difference between consecutive marks for a perfect ruler of length n.

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

Original entry on oeis.org

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

Hugo Pfoertner, Mar 01 2005

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

			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)

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.

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.

cp's OEIS Frontend

A104306 Number of perfect rulers of length n having the largest possible difference between consecutive marks that can occur amongst all possible perfect rulers of this length.

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