Journal of Integer Sequences, Vol. 24 (2021), Article 21.5.4

Complete Sequences of Weighted r-Generalized Fibonacci Powers

Passawan Noppakaew and Thanakorn Prinyasart
Department of Mathematics
Faculty of Science
Silpakorn University
Nakhon Pathom 73000


In this paper, we study the least number LN 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 mN.

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(Concerned with sequences A000032 A000045 A007598.)

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.

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