OFFSET
1,1
COMMENTS
These are the only proven unique non-Wichmann sparse rulers:{0,1,2,8,15,16,26,36,46,56,66,76,79,83,85,88},
{0,1,2,8,15,16,26,36,46,56,66,76,86,89,93,95,98},
{0,1,2,5,10,15,20,25,36,52,58,69,85,91,97,98,99},
{0,1,2,5,10,15,20,25,36,52,63,69,80,96,102,108,109,110},
{0,1,3,10,19,28,32,37,47,62,77,92,107,122,137,143,149,155,157,160,161,163},
{0,1,3,6,7,13,19,25,40,55,70,85,100,115,130,141,145,150,159,168,173,176,177},
{0,1,3,10,19,28,32,37,47,62,77,92,107,122,137,152,158,164,170,172,175,176,178}.
Values with a single known sparse ruler include 334, 335, 385, 408, 426, 427, 449, 450, 473, 475, 560, 583, 608, 610. Cf. A326499 for representations.
LINKS
J. Leech, On the representation of 1, 2, ..., n by differences, J. Lond. Math. Soc. 31 (1956), 160-169.
Peter Luschny, Perfect and Optimal Rulers
Peter Luschny, Are optimal rulers of Wichmann type?
Peter Luschny, Perfect Rulers.
Peter Luschny, Wichmann Rulers.
Ed Pegg Jr., Sparse Rulers (Wolfram Demonstrations Project)
Ed Pegg Jr., Wichmann-like Rulers (Wolfram Demonstrations Project)
Ed Pegg Jr, Table of n, a(n) for n=1..10501 in batches of A289761. Transpose for Dark Mills pattern.
Ed Pegg Jr, Picture of a(n) for n = 1..10501 in batches of A289761. This is the Dark Mills pattern.
L. Rédei, A. Rényi, On the representation of the numbers 1, 2, ..., N by means of differences, Matematicheskii Sbornik, Vol. 24(66) Num. 3 (1949), 385-389 (in Russian).
B. Wichmann, A note on restricted difference bases, J. Lond. Math. Soc. 38 (1963), 465-466.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Ed Pegg Jr, Oct 16 2022
STATUS
approved