Lucas Representations of Positive Integers
Clark Kimberling
Department of Mathematics
University of Evansville
Evansville, Indiana 47722
USA
Abstract:
Various kinds of representations of positive integers using nonconsecutive Lucas numbers are used to define arrays related to the Wythoff array. The columns of these arrays, or their order arrays, partition the positive integers. Limiting densities are found for numbers whose Lucas representations all have the same least term.
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(Concerned with sequences
A000027
A000032
A000045
A000201
A001622
A001950
A003622
A035513
A080164
A188378
A214979
A214981
A333029
A335499
A335500.)
Received June 14 2020; revised version received September 29 2020; October 13 2020.
Published in Journal of Integer Sequences,
October 15 2020.
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