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

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

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

Examples

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

References

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

Links

• 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

Crossrefs

Cf. A065825.

Formula

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

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