A356368 Sparse ruler lengths with unique non-Wichmann solutions.

88, 98, 99, 110, 163, 177, 178

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

Table of n, a(n) for n=1..7.

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, Sparse rulers and excess values for lengths n=1..10501.

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

Cf. A046693, A289761, A308766, A309407, A326499.

Sequence in context: A361105 A255226 A241491 * A068356 A215830 A216873

Adjacent sequences: A356365 A356366 A356367 * A356369 A356370 A356371

Keyword

nonn,hard,more

Author

Ed Pegg Jr, Oct 16 2022

Status

approved