A227590 - OEIS

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

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OFFSET

1,2

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

Table of n, a(n) for n=1..28.

Thomas Bloom, Problem 30, Problem 43, Problem 155, and Problem 861, Erdős Problems.

Erdős problems database contributors, Erdős problem database, see nos. 30, 43, 155, 861.

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.

Sequence in context: A345731 A084672 A011910 * A267529 A005521 A135901

Adjacent sequences: A227587 A227588 A227589 * A227591 A227592 A227593

KEYWORD

nonn,hard,more