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 A193803 Length of perfect Wichmann rulers. 3

%I

%S 3,6,9,12,15,18,22,29,36,43,46,50,57,64,68,71,79,90,101,108,112,123,

%T 134,138,145,153,156,168,175,183

%N Length of perfect Wichmann rulers.

%C R is a perfect Wichmann ruler iff R is a perfect ruler (for definition see A103294) and there exist two integers r>=0 and s>=0 such that the type of the difference representation of the ruler is [1*r, r+1, (2r+1)*r, (4r+3)*s, (2r+2)*(r+1), 1*r].

%H L. Egidi and G. Manzini, <a href="http://www.di.unipmn.it/TechnicalReports/TR-INF-2011-06-01-UNIPMN.pdf">Spaced seeds design using perfect rulers</a>, Tech. Rep. CS Department Universita del Piemonte Orientale, June 2011.

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/PerfectRulers">Perfect rulers</a>

%H B. Wichmann, <a href="http://jlms.oxfordjournals.org/content/s1-38/1/465.extract">A note on restricted difference bases</a>, J. Lond. Math. Soc. 38 (1963), 465-466.

%e [0, 1, 2, 5, 10, 15, 26, 37, 48, 54, 60, 66, 67, 68] is a perfect Wichmann ruler with length 68 of Wichmann type (2,3). By contrast [0, 1, 2, 8, 15, 16, 26, 36, 46, 56, 59, 63, 65, 68] is a perfect ruler with length 68 which is not a Wichmann ruler.

%Y Cf. A004137, A193802.

%K nonn,hard,more

%O 1,1

%A _Peter Luschny_, Oct 22 2011

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Last modified May 26 00:32 EDT 2020. Contains 334613 sequences. (Running on oeis4.)