A104308 - OEIS

%I #15 Mar 25 2022 09:27:11

%S 1,1,1,2,1,1,1,2,1,7,3,1,1,3,1,3,1,1,12,3,1,1,1,4,1,6,1,1,1,22,7,1,3,

%T 1,1,1,1,15,3,1,1,1,1,14,3,1,1,1,1,1,3,1,1,3,1,1,1,2,1,13,3,1,1,1,3,1,

%U 2,1,1,1,1,7,3,10,4,2,3,1,1,7,3,26,10,10,2,1,3,1,1,1,26,10,26,2,4,8,3,1,1,1

%N Number of perfect rulers of length n having the least possible largest difference between any adjacent marks that can occur amongst all perfect rulers of this length.

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

%H F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, <a href="/A104308/b104308.txt">Table of n, a(n) for n = 1..208</a> [a(212), a(213) commented out by _Georg Fischer_, Mar 25 2022]

%H Peter Luschny, <a href="http://www.luschny.de/math/rulers/introe.html">Perfect and Optimal Rulers.</a> A short introduction.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/scimath/diffset/consdifs.txt">Largest and smallest maximum differences of consecutive marks of perfect rulers.</a>

%H F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, <a href="https://dx.doi.org/10.21227/cd4b-nb07">MRLA search results and source code</a>, Nov 6 2020.

%H F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, <a href="https://doi.org/10.1109/OJAP.2020.3043541">Large Minimum Redundancy Linear Arrays: Systematic Search of Perfect and Optimal Rulers Exploiting Parallel Processing</a>, IEEE Open Journal of Antennas and Propagation, 2 (2021), 79-85.

%H <a href="/index/Per#perul">Index entries for sequences related to perfect rulers.</a>

%e a(11)=3 because 3 of the A103300(11)/2=15 perfect rulers of length 11 can be constructed using the shortest possible maximum segment length A104307(11)=3: [0,1,2,5,8,11], [0,1,4,6,9,11], [0,1,4,7,9,11], not counting their mirror images.

%Y Cf. A104307 size of minimally required longest segment, A103294 definitions related to complete rulers.

%K nonn

%O 1,4

%A _Hugo Pfoertner_, Mar 01 2005