Results 231 to 240 of about 30,143 (265)
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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.
Altassan, Alaa, ALAN, Murat
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Incomplete Fibonacci and Lucas numbers
Rendiconti del Circolo Matematico di Palermo, 1996It is well known that the Fibonacci numbers \(F_n\) and the Lucas numbers \(L_n\) can be written as \[ \begin{aligned} F_n &= \sum^k_{i=0} {{n-1-i} \choose i}, \qquad \lfloor (n- 1)/2 \rfloor\leq k\leq n-1, \tag{1}\\ L_n &= \sum^k_{i=0} {n\over {n-i}} {{n-i} \choose i}, \qquad \lfloor n/2 \rfloor \leq k\leq n-1.
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Journal of Philosophical Logic, 1982
Discussion de l'argumentation de J. R. Lucas suivant laquelle les etres humains ne peuvent etre des machines ("Minds, Machines and Godel", Philosophy, 36, 1961, p. 120-124). L'A. montre que l'argument de Lucas suivant lequel il n'est pas une machine repose sur une premisse erronee: suivant l'A., Lucas est donc lui-meme une machine.
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Discussion de l'argumentation de J. R. Lucas suivant laquelle les etres humains ne peuvent etre des machines ("Minds, Machines and Godel", Philosophy, 36, 1961, p. 120-124). L'A. montre que l'argument de Lucas suivant lequel il n'est pas une machine repose sur une premisse erronee: suivant l'A., Lucas est donc lui-meme une machine.
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Lucas-Sierpiński and Lucas-Riesel Numbers
The Fibonacci Quarterly, 2011Daniel Baczkowski +2 more
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Lucas's Tests for Mersenne Numbers
The American Mathematical Monthly, 1945(1945). Lucas's Tests for Mersenne Numbers. The American Mathematical Monthly: Vol. 52, No. 4, pp. 188-190.
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Lucas–Washburn Equation-Based Modeling of Capillary-Driven Flow in Porous Systems
Langmuir, 2021Jianchao Cai, Jisheng Kou, Shuangmei Zou
exaly
Primitive Divisors of Lucas Numbers
1988Let \( R = \{ {R_n}\} _{n = 1}^\infty \) be a Lucas sequence defined by fixed rational integers A and B and by the recursion relation $$ {R_n} = A \cdot {R_{n - 1}} + B \cdot {R_{n - 2}} $$ for n > 2, where the initial values are R1 = 1 and R2 = A. The terms of R are called Lucas numbers.
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