A104310 Maximum length of perfect rulers that can be made from segments not exceeding n.

2, 7, 18, 25, 32, 59, 71, 81, 103, 135

Offset: 1

Author

Hugo Pfoertner, Mar 01 2005

Keywords

• hard
• more
• nonn

Comments

We conjecture the extension a(8)=81. For nomenclature related to perfect and optimal rulers see Peter Luschny's "Perfect Rulers" web pages.

Examples

			The complete list of these rulers starts:
n.a(n)..rulers
1..2....[0,1,2]
2..7....[0,1,3,5,7]
3.18....[0,1,4,7,10,13,16]
4.25....[0,1,2,6,10,13,17,21,25]
........[0,1,2,6,10,14,17,21,25]
........[0,1,2,6,10,14,18,21,25]
........[0,1,3,7,11,15,19,23,25]
5.37....[0,1,2,3,8,13,18,23,28,33,37]
6.59....[0,1,4,10,16,22,28,34,40,46,52,54,57,59]
		

Links

• 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.

Crossrefs

Cf. A104307 Least maximum of differences between consecutive marks, A104309 minimum length of perfect rulers containing a segment of length n, A103294 definitions related to complete rulers.

Extensions

Conjectured a(8) proven via exhaustive search and a(9) ... a(10) added by Fabian Schwartau, Yannic Schröder, Lars Wolf, Joerg Schoebel, Feb 23 2021