Journal of Integer Sequences, Vol. 23 (2020), Article 20.9.5

Lucas Representations of Positive Integers

Clark Kimberling
Department of Mathematics
University of Evansville
Evansville, Indiana 47722


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.

Full version:  pdf,    dvi,    ps,    latex    

(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.

Return to Journal of Integer Sequences home page