Sierpiński numbers in second-order linear recurrences
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00635657" target="_blank" >RIV/67985840:_____/25:00635657 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1080/00150517.2024.2412960" target="_blank" >https://doi.org/10.1080/00150517.2024.2412960</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00150517.2024.2412960" target="_blank" >10.1080/00150517.2024.2412960</a>
Alternative languages
Result language
angličtina
Original language name
Sierpiński numbers in second-order linear recurrences
Original language description
Let u(a,b), called the Lucas sequence of the first kind (LSFK), denote the second-order linear recurrence satisfying the recursion relation un+2=aun+1+bun with initial terms u0=0, u1=1, where a and b are integers. Given an integer b, let A(b) be the set of positive integers a such that um(a,b) is a Sierpiński number for some natural number m. For particular integers b, we show that the lower asymptotic density of A(b) in the set of positive integers is greater than or equal to 0.992.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fibonacci Quarterly
ISSN
0015-0517
e-ISSN
0015-0517
Volume of the periodical
63
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
57-68
UT code for WoS article
001493758000009
EID of the result in the Scopus database
2-s2.0-105016248757