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