1,2

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

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

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

Index entries for sequences related to perfect rulers.

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)

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: A138968 A108052 A046868 this_sequence A033035 A047390 A020959

Adjacent sequences: A104306 A104307 A104308 this_sequence A104310 A104311 A104312

hard,more,nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 01 2005