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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-Sequence.
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/erdos/erdos.html
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 Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html.