International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 457-462
Partitioning the positive integers with higher order recurrences
University of Evansville, 1800 Lincoln Avenue, Evansville 47722, IN, USA
Received 17 June 1990; Revised 25 January 1991
Copyright © 1991 Clark Kimberling. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Associated with any irrational number and the function is an
array of positive integers defined inductively as follows: ,
for all , the least positive integer not among for for , and
for . This work considers algebraic integers of degree for which
the rows of the array partition the set of positive integers. Such an array is called a Stolarsky
array. A typical result is the following (Corollary 2): if is the positive root of
for , then is a Stolarsky array.