A227590 a(n) = A003022(n)+1 with a(1)=1.

1, 2, 4, 7, 12, 18, 26, 35, 45, 56, 73, 86, 107, 128, 152, 178, 200, 217, 247, 284, 334, 357, 373, 426, 481, 493, 554, 586

Offset: 1

Author

Jens Voß, Jul 17 2013

Keywords

• nonn
• hard
• more

Comments

Since A003022 is the most important sequence dealing with Golomb rulers, it seems best to define this sequence in terms of that one.

Original name was: Maximum label within a minimal labeling of 2 identical n-sided dice yielding the most possible sums. For example, two hexahedra labeled (1, 3, 8, 14, 17, 18) yield the 21 possible sums 2, 4, 6, 9, 11, 15, 16, 17, 18, 19, 20, 21, 22, 25, 26, 28, 31, 32, 34, 35, 36. No more sums can be obtained by different labelings, and no labeling with labels < 18 yields 21 possible sums. Therefore a(6) = 18.

Bounded above by A005282. - James Wilcox, Jul 27 2013

Minimum greatest integer in a set of n positive integers with all the differences between any two of its elements being different. - Javier Múgica, Jul 31 2015

Links

• Isaac Mammel, William Smith, and Carl Yerger, Ramsey Theory on the Integer Grid: The "L" Problem, arXiv:2502.05162 [math.CO], 2025. See p. 12.

Crossrefs

Cf. A003022.

Column k=2 of array A227588.

Extensions

More terms from James Wilcox, Jul 27 2013

Entry revised by N. J. A. Sloane, Apr 08 2016

a(28) from A003022 added by Michel Marcus, Feb 10 2025