superset of Fermat numbers (see below). Lucas sequences are named after the French mathematician Édouard Lucas. Given two integer parameters P {\displaystyle...
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The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and...
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Pell number (redirect from Pell Sequence)
derived from it to John Pell. The Pell–Lucas numbers are also named after Édouard Lucas, who studied sequences defined by recurrences of this type; the...
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numbers pass: in this case, criteria relative to some Lucas sequence. Baillie and Wagstaff define Lucas pseudoprimes as follows: Given integers P and Q, where...
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known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him. Lucas was born in Amiens and educated at...
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related to Lucas numbers, which obey the same recurrence relation and with the Fibonacci numbers form a complementary pair of Lucas sequences. The Fibonacci...
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Generalizations of Fibonacci numbers (redirect from Tribonacci sequence)
the Lucas sequence is the second row. See also Fibonacci integer sequences modulo n. A different generalization of the Fibonacci sequence is the Lucas sequences...
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Jacobsthal number (redirect from Jacobsthal-Lucas number)
integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence U n...
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odd composite number N is a Somer–Lucas d-pseudoprime (with given d ≥ 1) if there exists a nondegenerate Lucas sequence U ( P , Q ) {\displaystyle U(P,Q)}...
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29341, 42799, 49141, and 52633 (sequence A001262 in the OEIS). The first ten strong Lucas pseudoprimes (with Lucas parameters (P, Q) defined by Selfridge's...
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F_{6}=F_{5}+F_{4}=5+3=8} . The sequence 2, 1, 3, 4, 7, 11, ... of Lucas numbers satisfies the same recurrence as the Fibonacci sequence but with initial conditions...
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algorithm is very similar to the Lucas–Lehmer test, but with a variable starting point depending on the value of k. Define a sequence ui for all i > 0 by: u i...
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mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of the first kind Un(P, Q) with relatively prime parameters P, Q and...
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Fibonacci polynomials (redirect from Lucas polynomials)
polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in a similar way from the Lucas numbers...
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algorithm. Choose some integer A greater than 2 which characterizes the Lucas sequence: V 0 = 2 , V 1 = A , V j = A V j − 1 − V j − 2 {\displaystyle V_{0}=2...
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The sequence of Lucas numbers (not to be confused with the generalized Lucas sequences, of which this is part) is like the Fibonacci sequence, in which...
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In mathematics, a Lehmer sequence is a generalization of a Lucas sequence. If a and b are complex numbers with a + b = R {\displaystyle a+b={\sqrt {R}}}...
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Perrin number (redirect from Perrin sequence)
integer sequence with characteristic equation x3 = x + 1. The Perrin numbers bear the same relationship to the Padovan sequence as the Lucas numbers do...
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Lucas has founded and supported multiple philanthropic organizations and campaigns dedicated to education and the arts, including the George Lucas Educational...
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mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers. The test was originally developed by Édouard Lucas in 1878 and subsequently...
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mathematics, a Lucas chain is a restricted type of addition chain, named for the French mathematician Édouard Lucas. It is a sequence a0, a1, a2, a3,...
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the p {\displaystyle p} -th Lucas number.: 42 McIntosh and Roettger establish several equivalent characterizations of Lucas–Wieferich primes. In particular...
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preceding denominator to form the new numerator. This sequence of denominators is a particular Lucas sequence known as the Pell numbers. We can gain further...
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divisibility sequence. More generally, any Lucas sequence of the first kind Un(P,Q) is a divisibility sequence. Moreover, it is a strong divisibility sequence when...
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THX 1138 (redirect from THX 1138: The George Lucas Director's Cut)
Lucas. THX 1138 is the first film of a planned seven-picture slate commissioned by Warner Bros. from the 1969 incarnation of American Zoetrope. Lucas...
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consolidated theories. Integer sequence Fibonacci sequence Golden mean base Fibonacci coding Lucas sequence Padovan sequence Figurate numbers Polygonal number...
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as assistant editors, including George Lucas. The following spring, the newly engaged Marcia moved in with Lucas at his hilltop apartment on Portola Drive...
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if ( a n ) n ≥ 1 {\displaystyle (a_{n})_{n\geq 1}} is a Lucas sequence or a Lehmer sequence, then Z ( a n ) ⊆ { 1 ≤ n ≤ 30 } {\displaystyle {\mathcal...
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polynomials Lagrange polynomials Lucas polynomials Spread polynomials Touchard polynomials Rook polynomials Polynomial sequences of binomial type Orthogonal...
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The Human Centipede 2 (Full Sequence) is a 2011 psychological body horror film written, directed, and co-produced by Tom Six. An international co-production...
44 KB (5,229 words) - 22:49, 7 November 2024