| Abstrakt: |
Let the sequence of nonnegative integers be generated by the following conditions. Set the first term , and for all , let be the least integer greater than such that no element of is the average of distinct other elements. Szekeres gave a closed-form description of in 1936, and Layman provided a similar description for in 1999. We first find closed forms for some similar greedy sequences that avoid averages in terms not all the same. Then, we extend the closed-form description of from the known cases when and to any integer . With the help of a computer, we also generalize this to sequences that avoid solutions to specific weighted averages in distinct terms. Finally, from the closed forms of these sequences, we find bounds for their growth rates. [ABSTRACT FROM AUTHOR] |
