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

%I A104309 #11 Feb 23 2021 12:27:54
%S A104309 1,3,5,7,10,12,14,16,18,20,24,24,27,30,31,33,37,37,39,44,44,45,51,51,
%T A104309 51,54,59,59,60,62,69,69,69,70,80,80,80,81,83,91,91,91,91,93
%N A104309 Minimum length of a perfect ruler that contains a segment not shorter than n.
%C A104309 For nomenclature related to perfect and optimal rulers see Peter Luschny's "Perfect Rulers" web pages.
%H A104309 F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, <a href="/A104309/b104309.txt">Table of n, a(n) for n = 1..92</a>
%H A104309 Peter Luschny, <a href="http://www.luschny.de/math/rulers/introe.html">Perfect and Optimal Rulers.</a> A short introduction.
%H A104309 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 A104309 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 A104309 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 A104309 <a href="/index/Per#perul">Index entries for sequences related to perfect rulers.</a>
%e A104309 The list of shortest perfect rulers containing a segment>=n starts:
%e A104309 n.a(n)..rulers..(marks enclosing longest segment)
%e A104309 1..1....[0,1]........(0,1)
%e A104309 2..3....[0,1,3]......(1,3)
%e A104309 3..5....[0,1,2,5]....(2,5)
%e A104309 4..7....[0,1,2,3,7]..(3,7)
%e A104309 5.10....[0,1,2,4,9,10]..(4,9)
%e A104309 ........[0,1,3,4,9,10]..(4,9)
%e A104309 ........[0,1,6,7,8,10]..(1,6)
%e A104309 6.12....[0,1,3,5,11,12]..(5,11)
%e A104309 ........[0,1,7,8,10,12]..(1,7)
%e A104309 7.14....[0,1,2,4,6,13,14]...(6,13)
%e A104309 ........[0,1,3,4,6,13,14]...(6,13)
%e A104309 ........[0,1,3,5,6,13,14]...(6,13)
%e A104309 ........[0,1,8,9,10,12,14]..(1,8)
%e A104309 ........[0,1,8,9,11,12,14]..(1,8)
%e A104309 8.16....[0,1,3,5,7,15,16]....(7,15)
%e A104309 ........[0,1,9,10,12,14,16]..(1,9)
%Y A104309 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.
%K A104309 hard,nonn
%O A104309 1,2
%A A104309 _Hugo Pfoertner_, Mar 01 2005