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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao zbMATH Openarrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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License: CC BY
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Shifting Lucas Sequences Away from Primes

Shifting Lucas sequences away from primes
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2025Publisher:Zenodo
Authors: Ismailescu, Dan; Jeon, Daniel Hyunwoo; Kim, Aaron; Kwon, Joonbeom; Lee, Austin;

doi: 10.5281/zenodo.15283739 , 10.5281/zenodo.15283738

Shifting Lucas Sequences Away from Primes

Abstract

Summary: We strengthen a result of Jones by showing that for any positive integer \(P\), the Lucas sequence \((U_n)_n\) defined by \(U_0 = 0\), \(U_1 = 1\), \(U_n=P \cdot U_{n -1} + U_{n - 2}\) can be translated by a positive integer \(K(P)\) such that the shifted sequence with general term \(U_n + K(P)\) contains no primes, nor terms one unit away from a prime.

Keywords

Fibonacci and Lucas numbers and polynomials and generalizations, Primes

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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