A308766 Numbers k such that the minimal mark in a length k sparse ruler is round(sqrt(9 + 12*k)/2) + 1.

51, 59, 69, 113, 124, 125, 135, 136, 139, 149, 150, 151, 164, 165, 166, 179, 180, 181, 195, 196, 199, 209, 210, 211

Offset: 1

Author

Ed Pegg Jr, Jun 23 2019

Keywords

• nonn
• hard
• more

Comments

Other sparse rulers in the range length 1 to 213 have round(sqrt(9 + 12*k)/2) minimal marks.

Minimal vertices in k-edge graceful graph = minimal marks in length k sparse ruler.

Minimal marks can be derived from A004137 and using zero-count values in A103300.

Conjecture: Minimal marks k - round(sqrt(9 + 12*k)/2) is always 0 or 1.

Links

• P. Luschny, The Perfect Ruler Pyramid (1-101)
• P. Luschny, Perfect and Optimal Rulers

Crossrefs

Cf. A046693, A004137, A103300, A103294.