Infinite integer series where the next number is the sum of the two preceding it
Not to be confused with Lucas sequences, the general class of sequences to which the Lucas numbers belong.
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The Lucas spiral, made with quarter-arcs, is a good approximation of the golden spiral when its terms are large. However, when its terms become very small, the arc's radius decreases rapidly from 3 to 1 then increases from 1 to 2.
The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences.
The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values.[1] This produces a sequence where the ratios of successive terms approach the golden ratio, and in fact the terms themselves are roundings of integer powers of the golden ratio.[2] The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between.[3]
in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences. The Lucas sequence...
the numbers derived from it to John Pell. The Pell–Lucas numbers are also named after Édouard Lucas, who studied sequences defined by recurrences of this...
Lucas in Wiktionary, the free dictionary. Lucas or LUCAS may refer to: Lucas (surname) Lucas (given name) Luca Family Singers, also known as "lucas ligner...
2^{n}(J_{-n}+J_{n})=3J_{n}^{2}} (see OEIS: A139818) Jacobsthal–Lucas numbers represent the complementary Lucas sequence V n ( 1 , − 2 ) {\displaystyle V_{n}(1,-2)}...
closely related to Lucas numbers, which obey the same recurrence relation and with the Fibonacci numbers form a complementary pair of Lucas sequences. The...
{\displaystyle \ldots } (OEIS: A000045). The sequence of Lucas numbers (not to be confused with the generalized Lucas sequences, of which this is part) is like the...
Lucas has founded and supported multiple philanthropic organizations and campaigns dedicated to education and the arts, including the George Lucas Educational...
Henry Lee Lucas (August 23, 1936 – March 12, 2001), also known as The Confession Killer, was an American convicted murderer. Lucas was convicted of murdering...
destinations, Cabo San Lucas is known for its beaches, scuba diving locations, Balnearios, the sea arch El Arco de Cabo San Lucas, and marine life. The...
related to Lucas Hernández. Profile at the Paris Saint-Germain F.C. website Lucas Hernandez at BDFutbol Lucas Hernandez at Futbolme (in Spanish) Lucas Hernandez...
given Mersenne number is prime makes the search for Mersenne primes a difficult task, since Mersenne numbers grow very rapidly. The Lucas–Lehmer primality...
is the only prime pronic number. It is also the only pronic number in the Fibonacci sequence and the only pronic Lucasnumber. The arithmetic mean of two...
if the modulo base is a Lucasnumber (≥ 3) with an even index, the period is four times the index. If the base is a Lucasnumber (≥ 4) with an odd index...
Gary Maurice "Joyner" Lucas Jr. (born 1988) is an American rapper, actor and entrepreneur. Lucas first received widespread exposure and critical acclaim...
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