A005047 Minimal span of set of n elements with no 3-term arithmetic progression.

0, 1, 3, 4, 8, 10, 12, 13, 19, 23, 25, 29, 31, 35, 39, 40, 50, 53, 57, 62, 70, 73, 81, 83, 91, 94, 99, 103, 110, 113, 120, 121, 136, 144, 149, 156, 162, 164, 168, 173, 193, 203, 208

Offset

1,3

Comments

Length of shortest ruler with n marks, with no mark halfway between two other marks. - Christian Häggström, Nov 19 2018

References

R. K. Guy, Unsolved Problems in Number Theory, E10 (but beware of errors).

Links

Table of n, a(n) for n=1..43.

Noam Benson-Tilsen, Samuel Brock, Brandon Faunce, Monish Kumar, Noah Dokko Stein, and Joshua Zelinsky, Total Difference Labeling of Regular Infinite Graphs, arXiv:2107.11706 [math.CO], 2021.

B. E. Brown and D. M. Gordon, On sequences without geometric progressions, Math. Comp. 65 (1996), no. 216, 1749-1754.

Index entries related to non-averaging sequences

Formula

a(n) = A065825(n) - 1.

Example

Example for a(10) = 23: 0 1 4 6 10 15 17 18 22 23.

Crossrefs

Cf. A065825.

Sequence in context: A327185 A047343 A155730 * A083317 A268514 A024514

Adjacent sequences: A005044 A005045 A005046 * A005048 A005049 A005050

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(18)-a(41) derived from A065825 by Rob Pratt, Jul 09 2015

a(1)-a(2) prepended and a(42)-a(43) derived from A065825 by Alois P. Heinz, Nov 18 2018

Status

approved