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

Author

Peter Luschny, Oct 22 2011

Keywords

• nonn
• hard
• more

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.

Examples

			[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.
		

Links

• 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.

Crossrefs

Cf. A004137, A193803.

Extensions

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