Complete Sequences of Weighted r-Generalized Fibonacci Powers
Passawan Noppakaew and Thanakorn Prinyasart
Department of Mathematics
Faculty of Science
Nakhon Pathom 73000
In this paper, we study the least number L ∈ N that makes
the L-fold of a weighted r-generalized Fibonacci power
complete. We can establish an upper bound and a lower bound for L,
depending on the first r terms and the limit of the consecutive
ratios. We also give the explicit value of L in some special
cases. In the end, we study a particular minimal complete sequence
called a generalized distinguished sequence and show that there exists
a generalized distinguished sequence of a weighted r-generalized
Fibonacci mth power for all large m ∈ N.
Full version: pdf,
(Concerned with sequences
Received September 13 2020; revised versions received September 14 2020; February 10 2021; February 26 2021.
Published in Journal of Integer Sequences,
April 25 2021.
Journal of Integer Sequences home page