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In 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, ... that satisfies a0=1, and for each k > 0: ak = ai + aj, and either ai = aj or |ai − aj| = am, for some i, j, m < k. The sequence of powers of 2 (1, 2, 4, 8, 16, ...) and the Fibonacci sequence (with a slight adjustment of the starting point 1, 2, 3, 5, 8, ...) are simple examples of Lucas chains.

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  • Lucas chain
  • Encadenamiento de Lucas
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  • En matemáticas una Cadena de Lucas es una suma encadenada restringida, cuyo nombre se debe al matemático francés Edouard Lucas. Es una secuencia, tal que: a0, a1, a2, a3, ... que satisface: a0=1, y para cada k > 0: ak = ai + aj, y cualquiera ai = aj o |ai − aj| = am, para algún i, j, m < k. La secuencia de potencias de 2 (1, 2, 4, 8, 16, ...) y la secuencia de Fibonacci (con un ajuste en el primer término de la serie 1, 2, 3, 5, 8, ...) son ejemplos simples de encadenamientos de Lucas.
  • In 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, ... that satisfies a0=1, and for each k > 0: ak = ai + aj, and either ai = aj or |ai − aj| = am, for some i, j, m < k. The sequence of powers of 2 (1, 2, 4, 8, 16, ...) and the Fibonacci sequence (with a slight adjustment of the starting point 1, 2, 3, 5, 8, ...) are simple examples of Lucas chains.
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  • In 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, ... that satisfies a0=1, and for each k > 0: ak = ai + aj, and either ai = aj or |ai − aj| = am, for some i, j, m < k. The sequence of powers of 2 (1, 2, 4, 8, 16, ...) and the Fibonacci sequence (with a slight adjustment of the starting point 1, 2, 3, 5, 8, ...) are simple examples of Lucas chains. Lucas chains were introduced by Peter Montgomery in 1983. If L(n) is the length of the shortest Lucas chain for n, then Kutz has shown that most n do not have L < (1-ε) logφ n, where φ is the Golden ratio.
  • En matemáticas una Cadena de Lucas es una suma encadenada restringida, cuyo nombre se debe al matemático francés Edouard Lucas. Es una secuencia, tal que: a0, a1, a2, a3, ... que satisface: a0=1, y para cada k > 0: ak = ai + aj, y cualquiera ai = aj o |ai − aj| = am, para algún i, j, m < k. La secuencia de potencias de 2 (1, 2, 4, 8, 16, ...) y la secuencia de Fibonacci (con un ajuste en el primer término de la serie 1, 2, 3, 5, 8, ...) son ejemplos simples de encadenamientos de Lucas.
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