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Fibonacci and Lucas Numbers

1997
Consider the following number trick–try it out on your friends. You ask them to write down the numbers from 0 to 9. Against 0 and 1 they write any two numbers (we suggest two fairly small positive integers just to avoid tedious arithmetic, but all participants should write the same pair of numbers).
Peter Hilton   +2 more
openaire   +1 more source

On Triangular Lucas Numbers

1991
In the paper [3], we have proved that the only triangular numbers (i.e., the positive integers of the form \( \frac{1}{2}m \)(m+1)) in the Fibonacci sequence $$ {u_n} + 2 = {u_{n + 1}} + {u_{{n^,}}}{u_0} = 0, {u_1} = 1 $$ are u ±1=u2=1, u4=3, u8=21 and u10=55. This verifies a conjecture of Vern Hoggatt [2].
openaire   +1 more source

Lucas-Sierpiński and Lucas-Riesel Numbers

The Fibonacci Quarterly, 2011
Daniel Baczkowski   +2 more
openaire   +1 more source

Mersenne Numbers in Generalized Lucas Sequences

Proceedings of the Bulgarian Academy of Sciences
Let $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer.
ALAN, Murat, Altassan, Alaa
openaire   +2 more sources

The Lucas Sequences

CMS/CAIMS Books in Mathematics, 2023
Hugh C Williams, Christian J -C Ballot
exaly  

Pseudoprimality Related to the Generalized Lucas Sequences

Mathematics and Computers in Simulation, 2022
Ovidiu Bagdasar, Dorin Andrica
exaly  

Spatial and Semantic Effects of LUCAS Samples on Fully Automated Land Use/Land Cover Classification in High-Resolution Sentinel-2 Data

International Journal of Applied Earth Observation and Geoinformation, 2020
Michael Wurm   +2 more
exaly  

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