Generalized Nonaveraging Integer Sequences
-
Dennis Tseng
Abstract.
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.
© 2012 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- Odd Catalan Numbers Modulo
- Variations of the Poincaré Map
- Diophantine Equations of Matching Games I
- Norm Euclidean Quaternionic Orders
- A New Proof of Winquist's Identity
- Counting Depth Zero Patterns in Ballot Paths
- Codes Associated with and Power Moments of Kloosterman Sums
- Subprime Factorization and the Numbers of Binomial Coefficients Exactly Divided by Powers of a Prime
- Generalized Nonaveraging Integer Sequences
- The Robin Inequality for 7-Free Integers
- On 3-adic Valuations of Generalized Harmonic Numbers
Articles in the same Issue
- Masthead
- Odd Catalan Numbers Modulo
- Variations of the Poincaré Map
- Diophantine Equations of Matching Games I
- Norm Euclidean Quaternionic Orders
- A New Proof of Winquist's Identity
- Counting Depth Zero Patterns in Ballot Paths
- Codes Associated with and Power Moments of Kloosterman Sums
- Subprime Factorization and the Numbers of Binomial Coefficients Exactly Divided by Powers of a Prime
- Generalized Nonaveraging Integer Sequences
- The Robin Inequality for 7-Free Integers
- On 3-adic Valuations of Generalized Harmonic Numbers
