A193803 Length of perfect Wichmann rulers.

3, 6, 9, 12, 15, 18, 22, 29, 36, 43, 46, 50, 57, 64, 68, 71, 79, 90, 101, 108, 112, 123, 134, 138, 145, 153, 156, 168, 175, 183

Offset: 1

Author

Peter Luschny, Oct 22 2011

Keywords

• nonn
• hard
• more

Comments

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].

Examples

			[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.
		

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, A193802.