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

%I A227590 #40 Sep 03 2025 21:33:36
%S A227590 1,2,4,7,12,18,26,35,45,56,73,86,107,128,152,178,200,217,247,284,334,
%T A227590 357,373,426,481,493,554,586
%N A227590 a(n) = A003022(n)+1 with a(1)=1.
%C A227590 Since A003022 is the most important sequence dealing with Golomb rulers, it seems best to define this sequence in terms of that one.
%C A227590 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.
%C A227590 Bounded above by A005282. - _James Wilcox_, Jul 27 2013
%C A227590 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
%H A227590 Thomas Bloom, <a href="https://www.erdosproblems.com/30">Problem 30</a>, <a href="https://www.erdosproblems.com/43">Problem 43</a>, <a href="https://www.erdosproblems.com/155">Problem 155</a>, and <a href="https://www.erdosproblems.com/861">Problem 861</a>, Erdős Problems.
%H A227590 Isaac Mammel, William Smith, and Carl Yerger, <a href="https://arxiv.org/abs/2502.05162">Ramsey Theory on the Integer Grid: The "L" Problem</a>, arXiv:2502.05162 [math.CO], 2025. See p. 12.
%H A227590 Terence Tao, <a href="https://github.com/teorth/erdosproblems/blob/main/README.md#table">Erdős problem database</a>, see nos. 30, 43, 155, 861.
%Y A227590 Cf. A003022.
%Y A227590 Column k=2 of array A227588.
%K A227590 nonn,hard,more,changed
%O A227590 1,2
%A A227590 _Jens Voß_, Jul 17 2013
%E A227590 More terms from _James Wilcox_, Jul 27 2013
%E A227590 Entry revised by _N. J. A. Sloane_, Apr 08 2016
%E A227590 a(28) from A003022 added by _Michel Marcus_, Feb 10 2025