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Lucas-Sierpiński and Lucas-Riesel Numbers
The Fibonacci Quarterly, 2011Daniel Baczkowski +2 more
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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].
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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].
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Mersenne Numbers in Generalized Lucas Sequences
Proceedings of the Bulgarian Academy of SciencesLet $$k \geq 2$$ 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
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Pseudoprimality related to the generalized Lucas sequences
Mathematics and Computers in Simulation, 2022Dorin Andrica, Ovidiu Bagdasar
exaly
On Some New Arithmetic Properties of the Generalized Lucas Sequences
Mediterranean Journal of Mathematics, 2021Dorin Andrica +2 more
exaly
Lucas Numbers Which Are Concatenations of Two Repdigits
Mathematics, 2020Yunyun Qu, Jiwen Zeng
exaly
On the <i>k</i> -Lucas Numbers and Lucas Polynomials
Turkish Journal of Analysis and Number Theory, 2017Ali Boussayoud, Mohamed Kerada
exaly