Lucas chain

Lucas chain

In mathematics, a Lucas chain is a restricted type of addition chain, named for the French mathematician Edouard Lucas. It is a sequence

:"a"0, "a"1, "a"2, "a"3, ...

that satisfies

:"a"0=1,

and :for each "k" > 0: "a""k" = "a""i" + "a""j", and either "a""i" = "a""j" or |"a""i" − "a""j"| = "a""m", 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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