A193802 Length of optimal Wichmann rulers.

3, 6, 9, 29, 36, 43, 50, 68, 79, 90, 101, 112, 123, 138, 153, 168, 183, 198, 213

Offset

1,1

Comments

R is an optimal Wichmann ruler iff R is an optimal 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].

a(n) is a subsequence of A193803.

Links

Table of n, a(n) for n=1..19.

L. Egidi and G. Manzini, Spaced seeds design using perfect rulers, Tech. Rep. CS Department Universita del Piemonte Orientale, June 2011.

Peter Luschny, Perfect rulers

B. Wichmann, A note on restricted difference bases, J. Lond. Math. Soc. 38 (1963), 465-466.

Example

[0, 1, 2, 5, 10, 15, 26, 37, 48, 54, 60, 66, 67, 68] is an optimal 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 an optimal ruler with length 68 which is not a Wichmann ruler.

Crossrefs

Cf. A004137, A193803.

Sequence in context: A062927 A349597 A178467 * A254616 A195205 A045638

Adjacent sequences: A193799 A193800 A193801 * A193803 A193804 A193805

Keyword

nonn,hard,more

Author

Peter Luschny, Oct 22 2011

Extensions

a(16)-a(19) from Hugo Pfoertner, Jul 12 2017

Status

approved