A104310 -id:A104310 - cp's OEIS frontend

A104307 Least maximum of differences between consecutive marks that can occur amongst all possible perfect rulers of length n.

1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 4, 4, 4, 5, 6, 4, 4, 5, 5, 6, 6, 5, 5, 5, 6, 6, 6, 7, 5, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 7, 7, 7, 7, 9, 6, 7, 7, 7, 7, 7, 8, 11, 9, 10, 7, 7, 7, 8, 8, 9, 10, 9, 10, 10, 11, 8, 8, 9, 9, 10, 9, 11, 10, 10, 11, 11, 9, 9, 10, 9, 10, 11, 10

Offset: 1

Hugo Pfoertner, Mar 01 2005

nonn

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

			There are A103300(13)=6 perfect rulers of length 13: [0,1,2,6,10,13], [0,1,4,5,11,13], [0,1,6,9,11,13] and their mirror images. The first ruler produces the least maximum difference 4=6-2=10-6 between any of its adjacent marks. Therefore a(13)=4.

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. A104308 corresponding occurrence counts, A104310 position of latest occurrence of n as a sequence term, A103294 definitions related to complete rulers.

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

A104307 Least maximum of differences between consecutive marks that can occur amongst all possible perfect rulers of length n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs