In mathematics, a Lucas chain is a restricted type of addition chain, named for the French mathematician Édouard Lucas.
It is a sequence that satisfies and 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.
[3] 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.
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