The sequence generated by the Levine-O'Sullivan greedy algorithm: 1, 2, 4, 6, 9, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, 50, 55, 60, 65, ... (Sloane's A014011). The reciprocal sum of this sequence is conjectured to bound the reciprocal sum of all A-sequences. However, this sequence is not itself an -sequence.

Finch, S. R. "Erdős' Reciprocal Sum Constants." §2.20 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 163-166, 2003.

Levine, E. and O'Sullivan, J. "An Upper Estimate for the Reciprocal Sum of a Sum-Free Sequence." Acta Arith. 34, 9-24, 1977.

Sloane, N. J. A. Sequence A014011 in "The On-Line Encyclopedia of Integer Sequences."

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Weisstein, Eric W. "Levine-O'Sullivan Sequence." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Levine-OSullivanSequence.html