*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

An Infinite Sequence of Positive Integers satisfying

(1) |

(2) |

(3) |

(4) |

**References**

Abbott, H. L. ``On Sum-Free Sequences.'' *Acta Arith.* **48**, 93-96, 1987.

Erdös, P. ``Remarks on Number Theory III. Some Problems in Additive Number Theory.'' *Mat. Lapok* **13**,
28-38, 1962.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/erdos/erdos.html

Guy, R. K. ``-Sequences.'' §E28 in *Unsolved Problems in Number Theory, 2nd ed.*
New York: Springer-Verlag, pp. 228-229, 1994.

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

Zhang, Z. X. ``A Sum-Free Sequence with Larger Reciprocal Sum.'' Unpublished manuscript, 1992.

© 1996-9

1999-05-25