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

An infinite sequence of Positive Integers

is a nonaveraging sequence if it contains no three terms which are in an Arithmetic Progression, so that

for all distinct , , . Wróblewski (1984) showed that

**References**

Behrend, F. ``On Sets of Integers which Contain no Three Terms in an Arithmetic Progression.''
*Proc. Nat. Acad. Sci. USA* **32**, 331-332, 1946.

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

Gerver, J. L. ``The Sum of the Reciprocals of a Set of Integers with No Arithmetic Progression of Terms.''
*Proc. Amer. Math. Soc.* **62**, 211-214, 1977.

Gerver, J. L. and Ramsey, L. ``Sets of Integers with no Long Arithmetic Progressions Generated by the Greedy
Algorithm.'' *Math. Comput.* **33**, 1353-1360, 1979.

Guy, R. K. ``Nonaveraging Sets. Nondividing Sets.'' §C16 in
*Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, pp. 131-132, 1994.

Wróblewski, J. ``A Nonaveraging Set of Integers with a Large Sum of Reciprocals.'' *Math. Comput.* **43**, 261-262, 1984.

© 1996-9

1999-05-25